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Research ArticleClassification System of Pathological Voices Using Correntropy
Aluisio I R Fontes12 Pedro T V Souza3 Adriatildeo D D Neto2
Allan de M Martins3 and Luiz F Q Silveira2
1 Postgraduate Program in Electrical and Computer Engineering (PPgEEC) Federal University of Rio Grande do Norte59078-970 Natal RN Brazil
2 Department of Computer Engineering Federal University of Rio Grande do Norte 59078-970 Natal RN Brazil3 Department of Electrical Engineering Federal University of Rio Grande do Norte 59078-970 Natal RN Brazil
Correspondence should be addressed to Aluisio I R Fontes aluisioigorgmailcom
Received 16 April 2014 Accepted 22 July 2014 Published 19 August 2014
Academic Editor Pak-Kin Wong
Copyright copy 2014 Aluisio I R Fontes et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
This paper proposes the use of a similarity measure based on information theory called correntropy for the automatic classificationof pathological voices By using correntropy it is possible to obtain descriptors that aggregate distinct spectral characteristics forhealthy and pathological voices Experiments using computational simulation demonstrate that such descriptors are very efficientin the characterization of vocal dysfunctions leading to a success rate of 97 in the classification With this new architecture theclassification process of vocal pathologies becomes much more simple and efficient
1 Introduction
In the past few decades medicine has received noteworthycontributions which have allowed for great advancementin medical activity within various contexts for exampleimprovement of surgery techniques description of thehuman genome or even assistance in medical diagnosisIn particular regarding medical diagnosis digital signalprocessing techniques have been employed recently as anefficient noninvasive and low-cost tool to analyze vocalsignals with the aim of detecting and classifying alterationsin the production of sounds that may be associated withlarynx pathologies [1] The human voice is an importantcommunication tool and any inadequate behavior may havedeep implications in an individualrsquos social and professionallife
The acoustic analysis is a complementary technique tomethods based on the direct inspection of vocal folds whichmay reduce the frequency of invasive exams since suchmeasurements are able to reveal important physiologicalcharacteristics of the vocal tract [2] In general most of thetechniques involving the analysis of dysfunctions available inthe literature employ several sorts of preprocessing stages inorder to extract useful characteristics for the classification of
diverted patterns and to obtain performance improvement ofclassifiers [2ndash11]
The existing systems for detection and classification oflaryngeal pathologies are phoneme-dependent where thetrain step used fixed phonemes for example a [2 3]and diagnosis can be done by taking any vowel whichcan be phonated comfortably Various techniques have beenproposed for the extraction of signal features in order toimprove the performance of automatic pathological speechdetection systems A method based on MPEG-7 audio lowlevel is proposed in [3] for the extraction of features thatcan be classified by support vectormachine (SVM) SimilarlySVM classifiers have also been used in the features extractionbased on wavelet transform nonlinear analysis of temporalseries and information theory [4ndash8] Mel-frequency cepstralcoefficients and linear prediction cepstral coefficients areused as acoustic features in [9] associated with a strategybased on combining classifiers with Gaussianmixturemodelhidden Markov model (HMM) and SVM Specifically fea-ture extraction is achieved in [10] by using eight measuresderived from the nonlinear dynamic analysis (correlationdimension four entropy measures Hurst exponent thelargest Lyapunov exponent and the first minimum of mutual
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 924786 7 pageshttpdxdoiorg1011552014924786
2 Mathematical Problems in Engineering
information function) and quadratic discriminant analysis(QDA) by classifier [10] Nonlinear Teager-Kaiser energyoperator has been used for features extraction in [11] witha classifier based on neural system of multilayer perceptron(MLP)
Thus it is possible to state that all aforementionedmethods employ classifiers with complex architectures forexample MLP SVM and HMM and a complex stage forthe features extraction which can restrict their applicationor even make the technique unfeasible in real-time systemsIn addition most research works are based on the discrimi-nation between healthy and pathological voices but not thepathology types
This paper introduces a new low-complexity approachfor the detection and classification of laryngeal pathologiesThis system uses a measure of information theory known ascorrentropy to characterize vocal pathologies by means ofspectral characteristics and statistical moments of high orderinvolving the vocal signalThe system is characterized by highsuccess rates and low computational complexity associatedwith a simple classification stage based on Euclidian distanceThe influence of the kernel size in the classification hit rate isanalyzed since it is the only free parameter of the methodBesides the classification between healthy and pathologicalvoices it is possible to define which pathology is most likelyto exist in the voice under analysis
The paper is organized as follows Section 2 presentsthe main concepts related to correntropy The proposedarchitecture is described in Section 3 In Section 4 the perfor-mance results of the proposed technique are discussed whileSection 5 presents the final considerations
2 Correntropy
The extraction of information from a database is a frequentand relevant problem in various applications involving signalprocessing Within this context statistical measures of sim-ilarity such as correntropy may be successfully used for theextraction of information and data characterization
Correntropy is a generalization of the correlation mea-sure between random signals because such measure is ableto extract both second-order and higher-order statisticalinformation from the analyzed signals [12] In the past fewyears this concept been successfully applied in the solutionof various engineering problems such as the modeling oftemporal series [13] nonlinearity tests [14] objects recog-nition [15] analysis of independent components [16] andautomatic modulation classification [17] Although corren-tropy is similar to correlation by definition recent studieshave demonstrated that its performance is superior whendealing with nonlinear or non-Gaussian systems without anysignificant increase of computational cost [12]
According to [12] correntropy is between random signals119909119905 119905 isin 119879 where 119905 represents time and119879 is the set of interest
indices defined as119881 (1199051 1199052) = 119864 [119896
120590(1199091199051
1199091199052
)]
= ∬119896120590(1199091199051
1199091199052
) 119901 (1199091199051
1199091199052
) 1198891199091199051
1198891199091199052
(1)
where 119864[sdot] is the expectation operator and 119896120590(sdot sdot) corre-
sponds to any symmetric function defined as positive It isobserved that correntropy is defined as the joint expectationof 119896120590(1199091199051
1199091199052
) In this work 119896120590(sdot sdot) is a Gaussian kernel given
as
119896120590(1199091199051
1199091199052
) =1
radic2120587120590119890minus(1199091199051minus1199091199052)221205902
(2)
where 120590 is the variance defined as the kernel size The kernelsize may be interpreted as the resolution for which corren-tropy measures similarity in a space with characteristics ofhigh dimensionality [12]
In fact by applying an extension of the Taylor series to thecorrentropy measure (1) can be rewritten as [12]
119881 (1199051 1199052) =
1
radic2120587120590
infin
sum119899=0
(minus1)119899
21198991205902119899119899119864 [100381710038171003817100381710038171199091199051
minus 1199091199052
10038171003817100381710038171003817
2119899
] (3)
It is possible to notice that (3) defines the sum of infinitemoments of even order which therefore includes its ownconventional covariance Consequently correntropy containsinformation of infinite statistical moments involving its data
It is interesting to observe that the kernel size in (3) isa parameter that ponders the influence of the second-orderand higher-order moments For sufficiently large values thesecond-order moments are dominant and the measure getscloser to the correlation
When only a finite amount of data is available thatis (119909119899 119909119899)119873
119899=1 it is possible to define the estimator to the
autocorrentropy function as [18]
(119898) =1
119873 minus 119898
119873minus1
sum119899=119898
119896120590(119909 (119899) 119909 (119899 minus 119898)) (4)
The autocorrentropy with an estimator defined by (4)does not ensure zero average even when the input data arecentralized due to the nonlinear transforms produced by thekernel However a centralized estimator for correntropy hasbeen defined in [18] which is given as
(119898) =1
119873 minus 119898
119873minus1
sum119899=119898
119896120590(119909 (119899) 119909 (119899 minus 119898))
minus
119873
sum119899=1
119873
sum119898=1
119896120590(119909 (119899) 119909 (119899 minus 119898))
(5)
This work explores the spectral properties of centralizedautocorrentropy in voice signals in order to detect and classifyvocal pathologies Specifically the spectral descriptors ofhealthy pathological voices used in the classification areextracted from the signals analyzed by the correntropyspectral density (CSD) function defined as [19]
119875120590(119908) =
infin
sum119898=minusinfin
(119898) exp (minus119895119908119898) (6)
where 119908 is the digital frequency given in radians The CSDfunction may be considered a generalization of the powerspectral density (PSD) of a signal
Mathematical Problems in Engineering 3
One of the advantages of using correntropy measuresin the classification of vocal signals lies in the robustnessof such measures against impulsive noise due to the use ofthe Gaussian kernel in (5) which is close to zero that is119896120590= (119909(119899) 119909(119899 minus 119898)) when 119909(119899) or 119909(119899 minus 119898) is an outlier
In addition the correntropy function extract informationof higher-order statistical moments present in the datathus potentially increasing the classification efficiency theproposed technique
3 Proposed Architecture
The classification method of vocal pathologies proposed inthis paper is composed of two stages The first stage ischaracterized by the extraction of descriptors for the voicesignals based on the CSD defined in (6) The second stage isresponsible for the classification of voices by simple metricsof the Euclidian distance
Since the analyzed voice signals may vary in amplitudethe normalization of all signals in the database is performedThen the signals are clustered into two sets one set withhealthy voice signals and another one with pathological voicesignals which contain voices with edema and nodules Afterthe calculation of the CSD for all signals in each set theaverage value of CSD is calculated for each set The averageCSDs of the sets are used as descriptors for the healthy andpathological voicesThis procedure is depicted in Figure 1 Anequivalent methodology is applied to obtain the descriptorsfor the voices with edema and nodules This procedure isdetailed in Figure 2
The CSDs of the healthy and pathological voices and therespective descriptors stored for the classification stage areshown in Figures 3 and 4 It is possible to observe in Figure 3that the average CSDs in the healthy voices have correntropyand frequency values that are different from those in theaverage CSDs of pathological voices On the other handit may be observed in Figure 4 that the average CSDs forvoices with edema and nodules have different correntropyvalues even though the frequencies are similar In order todecrease computational cost and improve the success ratethe descriptors of different classes considered in this workare constituted by the first fifty samples because there is aclear distinction involving the respective average CSDs ofeach class within this interval
The classification architecture proposed in this work ispresented in Figure 5 Initially the desired voice signal to becalculated is normalized and its respective CSDs are obtainedfrom (6) Then the Euclidian distance between the voiceCSD and each descriptor for the classes defined as healthyand pathological voices is calculated The closer descriptorobtained according to the Euclidian distance criterion definesthe class of such signal If the analyzed voice is classified aspathological it is necessary to apply a new classification stagein order to distinguish between an edema and a nodule
4 Experiments and Results
The proposed architecture has been validated by com-puter simulation performed in MATLAB The architecture
Normalization
CSD
FFT
Pathological voice
Healthyvoice
features
Average
FFT
Average
Pathologicalvoices
features
Proposedarchitecture
healthyvoices Edema NoduleP0
V(P0)
P1
P0 P1
V(P1)
Figure 1 Extractor for the characteristics of healthy and pathologi-cal voices
performance was evaluated according to Monte Carlorsquosmethod For each experiment a minimum number of 100trials were usedThe set of voices for each class is divided intotwo subsets one to extract the descriptors and another for theclassification test Crossvalidation is used in this case where50 of the voices are for the extraction of descriptors and theremaining 50 are used for test purposes The evaluation ofthe architecture is based on the average success rates and alsomaximum minimum and standard deviation
41 Database Thedatabase used for this workwas developedby Massachusetts Eye and Ear Infirmary (MEEI) Voiceand Speech [20] This database has been widely used ininternational research works in acoustic analysis of disor-dered voices and in the discrimination between healthy andpathological voices It contains the sustained pronunciationof vowel ldquoardquo with 116 files from distinct speakers where 53 arehealthy voices 43 are voices affected by edema and 20 arevoices with nodules All used signals have the duration from1 to 3 seconds sampling frequency of 25 kHz and resolutionof 16 bits
42 Experiments Initially 43 voices affected by edema and 20voices with nodules are joined in one database called patho-logical The first experiment is characterized by extracting
4 Mathematical Problems in Engineering
edema nodule
Edemavoices
features
Nodulevoices
features
ProposedArchitecture
P3
P3
P2
P2
Figure 2 Extractor for the characteristics of voices with edema andnodules
the success rate between healthy and pathological voicesThen the success rate is assessed among 43 voices with edemaand 20 voices with nodules
The only adjustable parameter in the architecture is thevariance of the Gaussian kernel that is the kernel sizeMany systems use a heuristic known as Silvermanrsquos ruleto determine such variance [21] However this work hasemployed a numerical evaluation method to determine theinfluence of the kernel size on the accurate classification ratefor the proposed architecture The performed experimentsare represented in Figures 6 and 7
From the aforementioned experiments it is possible todetermine suboptimal values for the kernel width associatedwith each class of vocal disease The kernel size was tested byusing a logarithmic scale with values ranging from 001 to 10The kernel adjustment has provided an effective mechanismto eliminate outliers The right choice of its size may increasethe success rate considerably The amount of samples is alsoa fundamental factor in the classification rates according tothe results given in Figures 6 and 7
The results shown in Figure 6 demonstrate that theindependently of the kernel size the classifier for healthy andpathological voices represents an unsatisfactory result whenonly a few samples are used However when the kernel isequal to 077 and about 1000 signal samples are used theclassifier has presented a success rate of 93
One of the goals of this work is to reduce the complexityassociated with the architecture while a classifier based onthe Euclidean distance is used However it is sensitive to
6000
5000
4000
3000
2000
1000
0
6000
5000
4000
3000
2000
1000
0
10 20 30 40 50
50 100 150 200 250 300
Frequency (Hz)
HealthyPathological
Cor
rent
ropy
Descriptors
Figure 3 Correntropy spectral density for healthy and pathologicalvoices obtained for a kernel size equal to 0003
Table 1 Performance of classification for healthy and pathologicalclasses with kernel size of 077 and 1000 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9122 9381 9565 130Correlation 6042 7143 8233 912
the sample size as it is necessary optimize such parameterThus it is possible to state that amounts of samples higherthan 1000 affect success rates between healthy and patholog-ical voices
The success rate in the classification between voices withedema and nodules varied from 65 (when the kernel sizeis 031 and the number of samples is 700) to 98 (when thekernel size is 177 and 1300 samples are adopted) accordingto Figure 7
After adjusting the architecture with the adequate valuesfor the kernel size and number of samples the correntropymeasure was investigated regarding its capability of classify-ing and characterizing the statistical independencies of theconsidered voice signals Accordingly correlation is adoptedas a reference measure since it can be seen as a particularcase of correntropy and is very often used in classification
Mathematical Problems in Engineering 5
3500
3000
2500
2000
1500
1000
500
010 20 30 40 50
3500
3000
2500
2000
1500
1000
500
050 100 150 200 250 300
Frequency (Hz)
EdemaNodule
Cor
rent
ropy
Descriptors
Figure 4 Correntropy spectral density for voices with edema andnodules obtained for a kernel size equal to 00129
problemsTheobtained results are presented inTables 1 and 2The average success rate is determined considering 100 trials
Based on Table 1 it is possible to observe that the archi-tecture based on correntropy is able to distinguish betweenhealthy and pathological voices with a success rate between9122 and 9565 and average rate of 9381 while thestandard deviation is 130 On the other hand when anarchitecture based on correlation is used the success rate ofthe classifier is reduced considerably Besides it can be statedthat the standard deviation of the recognition rate for theproposed architecture is much lower if compared to that forthe architecture based on correlation thus indicating higherreliability of the classifier with correntropy
From Table 2 it can be seen that the recognition ratebetween the voices with edema and nodules is considerablyhigher in the architecture based on correntropy Once againthe success rate of the proposed architecture is within anacceptable range of values and with low standard deviation
43 Comparison with Existing Methods Several methods forthe detection of vocal pathologies have been proposed inthe literature With the aim of better assessing the classifierdeveloped in this work the obtained results are comparedwith those regarding the works in [6 8 10] which were alsoobtained using the MEEI database [20]
Feature extractor
Decision 01Euclidean distance
Healthy Pathological
Decision 02
NoduleEdema
Voice signal
Feat
ures
Feat
ures
Step 1
Step 2
Euclidean distance
P0P1
P2P3
Figure 5 Automatic classification process of pathological voices
4 6 8 10 12 14 16
06507
07508
08509
0951
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 6 Influence of the kernel size and amount of samples on thesuccess rates between healthy and pathological voices
Table 2 Performance of classification for edemas and nodules withkernel size of 177 and 1300 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9555 9643 9823 143Correlation 7783 7975 8312 643
The work in [6] considers a transform initially appliedto the voice signal to obtain a space of smaller dimensionby using the decomposition in singular values that ishigher-order singular value decomposition (HOSVD) In theclassification stage measure of mutual information and a
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
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2 Mathematical Problems in Engineering
information function) and quadratic discriminant analysis(QDA) by classifier [10] Nonlinear Teager-Kaiser energyoperator has been used for features extraction in [11] witha classifier based on neural system of multilayer perceptron(MLP)
Thus it is possible to state that all aforementionedmethods employ classifiers with complex architectures forexample MLP SVM and HMM and a complex stage forthe features extraction which can restrict their applicationor even make the technique unfeasible in real-time systemsIn addition most research works are based on the discrimi-nation between healthy and pathological voices but not thepathology types
This paper introduces a new low-complexity approachfor the detection and classification of laryngeal pathologiesThis system uses a measure of information theory known ascorrentropy to characterize vocal pathologies by means ofspectral characteristics and statistical moments of high orderinvolving the vocal signalThe system is characterized by highsuccess rates and low computational complexity associatedwith a simple classification stage based on Euclidian distanceThe influence of the kernel size in the classification hit rate isanalyzed since it is the only free parameter of the methodBesides the classification between healthy and pathologicalvoices it is possible to define which pathology is most likelyto exist in the voice under analysis
The paper is organized as follows Section 2 presentsthe main concepts related to correntropy The proposedarchitecture is described in Section 3 In Section 4 the perfor-mance results of the proposed technique are discussed whileSection 5 presents the final considerations
2 Correntropy
The extraction of information from a database is a frequentand relevant problem in various applications involving signalprocessing Within this context statistical measures of sim-ilarity such as correntropy may be successfully used for theextraction of information and data characterization
Correntropy is a generalization of the correlation mea-sure between random signals because such measure is ableto extract both second-order and higher-order statisticalinformation from the analyzed signals [12] In the past fewyears this concept been successfully applied in the solutionof various engineering problems such as the modeling oftemporal series [13] nonlinearity tests [14] objects recog-nition [15] analysis of independent components [16] andautomatic modulation classification [17] Although corren-tropy is similar to correlation by definition recent studieshave demonstrated that its performance is superior whendealing with nonlinear or non-Gaussian systems without anysignificant increase of computational cost [12]
According to [12] correntropy is between random signals119909119905 119905 isin 119879 where 119905 represents time and119879 is the set of interest
indices defined as119881 (1199051 1199052) = 119864 [119896
120590(1199091199051
1199091199052
)]
= ∬119896120590(1199091199051
1199091199052
) 119901 (1199091199051
1199091199052
) 1198891199091199051
1198891199091199052
(1)
where 119864[sdot] is the expectation operator and 119896120590(sdot sdot) corre-
sponds to any symmetric function defined as positive It isobserved that correntropy is defined as the joint expectationof 119896120590(1199091199051
1199091199052
) In this work 119896120590(sdot sdot) is a Gaussian kernel given
as
119896120590(1199091199051
1199091199052
) =1
radic2120587120590119890minus(1199091199051minus1199091199052)221205902
(2)
where 120590 is the variance defined as the kernel size The kernelsize may be interpreted as the resolution for which corren-tropy measures similarity in a space with characteristics ofhigh dimensionality [12]
In fact by applying an extension of the Taylor series to thecorrentropy measure (1) can be rewritten as [12]
119881 (1199051 1199052) =
1
radic2120587120590
infin
sum119899=0
(minus1)119899
21198991205902119899119899119864 [100381710038171003817100381710038171199091199051
minus 1199091199052
10038171003817100381710038171003817
2119899
] (3)
It is possible to notice that (3) defines the sum of infinitemoments of even order which therefore includes its ownconventional covariance Consequently correntropy containsinformation of infinite statistical moments involving its data
It is interesting to observe that the kernel size in (3) isa parameter that ponders the influence of the second-orderand higher-order moments For sufficiently large values thesecond-order moments are dominant and the measure getscloser to the correlation
When only a finite amount of data is available thatis (119909119899 119909119899)119873
119899=1 it is possible to define the estimator to the
autocorrentropy function as [18]
(119898) =1
119873 minus 119898
119873minus1
sum119899=119898
119896120590(119909 (119899) 119909 (119899 minus 119898)) (4)
The autocorrentropy with an estimator defined by (4)does not ensure zero average even when the input data arecentralized due to the nonlinear transforms produced by thekernel However a centralized estimator for correntropy hasbeen defined in [18] which is given as
(119898) =1
119873 minus 119898
119873minus1
sum119899=119898
119896120590(119909 (119899) 119909 (119899 minus 119898))
minus
119873
sum119899=1
119873
sum119898=1
119896120590(119909 (119899) 119909 (119899 minus 119898))
(5)
This work explores the spectral properties of centralizedautocorrentropy in voice signals in order to detect and classifyvocal pathologies Specifically the spectral descriptors ofhealthy pathological voices used in the classification areextracted from the signals analyzed by the correntropyspectral density (CSD) function defined as [19]
119875120590(119908) =
infin
sum119898=minusinfin
(119898) exp (minus119895119908119898) (6)
where 119908 is the digital frequency given in radians The CSDfunction may be considered a generalization of the powerspectral density (PSD) of a signal
Mathematical Problems in Engineering 3
One of the advantages of using correntropy measuresin the classification of vocal signals lies in the robustnessof such measures against impulsive noise due to the use ofthe Gaussian kernel in (5) which is close to zero that is119896120590= (119909(119899) 119909(119899 minus 119898)) when 119909(119899) or 119909(119899 minus 119898) is an outlier
In addition the correntropy function extract informationof higher-order statistical moments present in the datathus potentially increasing the classification efficiency theproposed technique
3 Proposed Architecture
The classification method of vocal pathologies proposed inthis paper is composed of two stages The first stage ischaracterized by the extraction of descriptors for the voicesignals based on the CSD defined in (6) The second stage isresponsible for the classification of voices by simple metricsof the Euclidian distance
Since the analyzed voice signals may vary in amplitudethe normalization of all signals in the database is performedThen the signals are clustered into two sets one set withhealthy voice signals and another one with pathological voicesignals which contain voices with edema and nodules Afterthe calculation of the CSD for all signals in each set theaverage value of CSD is calculated for each set The averageCSDs of the sets are used as descriptors for the healthy andpathological voicesThis procedure is depicted in Figure 1 Anequivalent methodology is applied to obtain the descriptorsfor the voices with edema and nodules This procedure isdetailed in Figure 2
The CSDs of the healthy and pathological voices and therespective descriptors stored for the classification stage areshown in Figures 3 and 4 It is possible to observe in Figure 3that the average CSDs in the healthy voices have correntropyand frequency values that are different from those in theaverage CSDs of pathological voices On the other handit may be observed in Figure 4 that the average CSDs forvoices with edema and nodules have different correntropyvalues even though the frequencies are similar In order todecrease computational cost and improve the success ratethe descriptors of different classes considered in this workare constituted by the first fifty samples because there is aclear distinction involving the respective average CSDs ofeach class within this interval
The classification architecture proposed in this work ispresented in Figure 5 Initially the desired voice signal to becalculated is normalized and its respective CSDs are obtainedfrom (6) Then the Euclidian distance between the voiceCSD and each descriptor for the classes defined as healthyand pathological voices is calculated The closer descriptorobtained according to the Euclidian distance criterion definesthe class of such signal If the analyzed voice is classified aspathological it is necessary to apply a new classification stagein order to distinguish between an edema and a nodule
4 Experiments and Results
The proposed architecture has been validated by com-puter simulation performed in MATLAB The architecture
Normalization
CSD
FFT
Pathological voice
Healthyvoice
features
Average
FFT
Average
Pathologicalvoices
features
Proposedarchitecture
healthyvoices Edema NoduleP0
V(P0)
P1
P0 P1
V(P1)
Figure 1 Extractor for the characteristics of healthy and pathologi-cal voices
performance was evaluated according to Monte Carlorsquosmethod For each experiment a minimum number of 100trials were usedThe set of voices for each class is divided intotwo subsets one to extract the descriptors and another for theclassification test Crossvalidation is used in this case where50 of the voices are for the extraction of descriptors and theremaining 50 are used for test purposes The evaluation ofthe architecture is based on the average success rates and alsomaximum minimum and standard deviation
41 Database Thedatabase used for this workwas developedby Massachusetts Eye and Ear Infirmary (MEEI) Voiceand Speech [20] This database has been widely used ininternational research works in acoustic analysis of disor-dered voices and in the discrimination between healthy andpathological voices It contains the sustained pronunciationof vowel ldquoardquo with 116 files from distinct speakers where 53 arehealthy voices 43 are voices affected by edema and 20 arevoices with nodules All used signals have the duration from1 to 3 seconds sampling frequency of 25 kHz and resolutionof 16 bits
42 Experiments Initially 43 voices affected by edema and 20voices with nodules are joined in one database called patho-logical The first experiment is characterized by extracting
4 Mathematical Problems in Engineering
edema nodule
Edemavoices
features
Nodulevoices
features
ProposedArchitecture
P3
P3
P2
P2
Figure 2 Extractor for the characteristics of voices with edema andnodules
the success rate between healthy and pathological voicesThen the success rate is assessed among 43 voices with edemaand 20 voices with nodules
The only adjustable parameter in the architecture is thevariance of the Gaussian kernel that is the kernel sizeMany systems use a heuristic known as Silvermanrsquos ruleto determine such variance [21] However this work hasemployed a numerical evaluation method to determine theinfluence of the kernel size on the accurate classification ratefor the proposed architecture The performed experimentsare represented in Figures 6 and 7
From the aforementioned experiments it is possible todetermine suboptimal values for the kernel width associatedwith each class of vocal disease The kernel size was tested byusing a logarithmic scale with values ranging from 001 to 10The kernel adjustment has provided an effective mechanismto eliminate outliers The right choice of its size may increasethe success rate considerably The amount of samples is alsoa fundamental factor in the classification rates according tothe results given in Figures 6 and 7
The results shown in Figure 6 demonstrate that theindependently of the kernel size the classifier for healthy andpathological voices represents an unsatisfactory result whenonly a few samples are used However when the kernel isequal to 077 and about 1000 signal samples are used theclassifier has presented a success rate of 93
One of the goals of this work is to reduce the complexityassociated with the architecture while a classifier based onthe Euclidean distance is used However it is sensitive to
6000
5000
4000
3000
2000
1000
0
6000
5000
4000
3000
2000
1000
0
10 20 30 40 50
50 100 150 200 250 300
Frequency (Hz)
HealthyPathological
Cor
rent
ropy
Descriptors
Figure 3 Correntropy spectral density for healthy and pathologicalvoices obtained for a kernel size equal to 0003
Table 1 Performance of classification for healthy and pathologicalclasses with kernel size of 077 and 1000 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9122 9381 9565 130Correlation 6042 7143 8233 912
the sample size as it is necessary optimize such parameterThus it is possible to state that amounts of samples higherthan 1000 affect success rates between healthy and patholog-ical voices
The success rate in the classification between voices withedema and nodules varied from 65 (when the kernel sizeis 031 and the number of samples is 700) to 98 (when thekernel size is 177 and 1300 samples are adopted) accordingto Figure 7
After adjusting the architecture with the adequate valuesfor the kernel size and number of samples the correntropymeasure was investigated regarding its capability of classify-ing and characterizing the statistical independencies of theconsidered voice signals Accordingly correlation is adoptedas a reference measure since it can be seen as a particularcase of correntropy and is very often used in classification
Mathematical Problems in Engineering 5
3500
3000
2500
2000
1500
1000
500
010 20 30 40 50
3500
3000
2500
2000
1500
1000
500
050 100 150 200 250 300
Frequency (Hz)
EdemaNodule
Cor
rent
ropy
Descriptors
Figure 4 Correntropy spectral density for voices with edema andnodules obtained for a kernel size equal to 00129
problemsTheobtained results are presented inTables 1 and 2The average success rate is determined considering 100 trials
Based on Table 1 it is possible to observe that the archi-tecture based on correntropy is able to distinguish betweenhealthy and pathological voices with a success rate between9122 and 9565 and average rate of 9381 while thestandard deviation is 130 On the other hand when anarchitecture based on correlation is used the success rate ofthe classifier is reduced considerably Besides it can be statedthat the standard deviation of the recognition rate for theproposed architecture is much lower if compared to that forthe architecture based on correlation thus indicating higherreliability of the classifier with correntropy
From Table 2 it can be seen that the recognition ratebetween the voices with edema and nodules is considerablyhigher in the architecture based on correntropy Once againthe success rate of the proposed architecture is within anacceptable range of values and with low standard deviation
43 Comparison with Existing Methods Several methods forthe detection of vocal pathologies have been proposed inthe literature With the aim of better assessing the classifierdeveloped in this work the obtained results are comparedwith those regarding the works in [6 8 10] which were alsoobtained using the MEEI database [20]
Feature extractor
Decision 01Euclidean distance
Healthy Pathological
Decision 02
NoduleEdema
Voice signal
Feat
ures
Feat
ures
Step 1
Step 2
Euclidean distance
P0P1
P2P3
Figure 5 Automatic classification process of pathological voices
4 6 8 10 12 14 16
06507
07508
08509
0951
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 6 Influence of the kernel size and amount of samples on thesuccess rates between healthy and pathological voices
Table 2 Performance of classification for edemas and nodules withkernel size of 177 and 1300 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9555 9643 9823 143Correlation 7783 7975 8312 643
The work in [6] considers a transform initially appliedto the voice signal to obtain a space of smaller dimensionby using the decomposition in singular values that ishigher-order singular value decomposition (HOSVD) In theclassification stage measure of mutual information and a
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
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Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
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Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Mathematical PhysicsAdvances in
Complex AnalysisJournal of
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OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
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Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
One of the advantages of using correntropy measuresin the classification of vocal signals lies in the robustnessof such measures against impulsive noise due to the use ofthe Gaussian kernel in (5) which is close to zero that is119896120590= (119909(119899) 119909(119899 minus 119898)) when 119909(119899) or 119909(119899 minus 119898) is an outlier
In addition the correntropy function extract informationof higher-order statistical moments present in the datathus potentially increasing the classification efficiency theproposed technique
3 Proposed Architecture
The classification method of vocal pathologies proposed inthis paper is composed of two stages The first stage ischaracterized by the extraction of descriptors for the voicesignals based on the CSD defined in (6) The second stage isresponsible for the classification of voices by simple metricsof the Euclidian distance
Since the analyzed voice signals may vary in amplitudethe normalization of all signals in the database is performedThen the signals are clustered into two sets one set withhealthy voice signals and another one with pathological voicesignals which contain voices with edema and nodules Afterthe calculation of the CSD for all signals in each set theaverage value of CSD is calculated for each set The averageCSDs of the sets are used as descriptors for the healthy andpathological voicesThis procedure is depicted in Figure 1 Anequivalent methodology is applied to obtain the descriptorsfor the voices with edema and nodules This procedure isdetailed in Figure 2
The CSDs of the healthy and pathological voices and therespective descriptors stored for the classification stage areshown in Figures 3 and 4 It is possible to observe in Figure 3that the average CSDs in the healthy voices have correntropyand frequency values that are different from those in theaverage CSDs of pathological voices On the other handit may be observed in Figure 4 that the average CSDs forvoices with edema and nodules have different correntropyvalues even though the frequencies are similar In order todecrease computational cost and improve the success ratethe descriptors of different classes considered in this workare constituted by the first fifty samples because there is aclear distinction involving the respective average CSDs ofeach class within this interval
The classification architecture proposed in this work ispresented in Figure 5 Initially the desired voice signal to becalculated is normalized and its respective CSDs are obtainedfrom (6) Then the Euclidian distance between the voiceCSD and each descriptor for the classes defined as healthyand pathological voices is calculated The closer descriptorobtained according to the Euclidian distance criterion definesthe class of such signal If the analyzed voice is classified aspathological it is necessary to apply a new classification stagein order to distinguish between an edema and a nodule
4 Experiments and Results
The proposed architecture has been validated by com-puter simulation performed in MATLAB The architecture
Normalization
CSD
FFT
Pathological voice
Healthyvoice
features
Average
FFT
Average
Pathologicalvoices
features
Proposedarchitecture
healthyvoices Edema NoduleP0
V(P0)
P1
P0 P1
V(P1)
Figure 1 Extractor for the characteristics of healthy and pathologi-cal voices
performance was evaluated according to Monte Carlorsquosmethod For each experiment a minimum number of 100trials were usedThe set of voices for each class is divided intotwo subsets one to extract the descriptors and another for theclassification test Crossvalidation is used in this case where50 of the voices are for the extraction of descriptors and theremaining 50 are used for test purposes The evaluation ofthe architecture is based on the average success rates and alsomaximum minimum and standard deviation
41 Database Thedatabase used for this workwas developedby Massachusetts Eye and Ear Infirmary (MEEI) Voiceand Speech [20] This database has been widely used ininternational research works in acoustic analysis of disor-dered voices and in the discrimination between healthy andpathological voices It contains the sustained pronunciationof vowel ldquoardquo with 116 files from distinct speakers where 53 arehealthy voices 43 are voices affected by edema and 20 arevoices with nodules All used signals have the duration from1 to 3 seconds sampling frequency of 25 kHz and resolutionof 16 bits
42 Experiments Initially 43 voices affected by edema and 20voices with nodules are joined in one database called patho-logical The first experiment is characterized by extracting
4 Mathematical Problems in Engineering
edema nodule
Edemavoices
features
Nodulevoices
features
ProposedArchitecture
P3
P3
P2
P2
Figure 2 Extractor for the characteristics of voices with edema andnodules
the success rate between healthy and pathological voicesThen the success rate is assessed among 43 voices with edemaand 20 voices with nodules
The only adjustable parameter in the architecture is thevariance of the Gaussian kernel that is the kernel sizeMany systems use a heuristic known as Silvermanrsquos ruleto determine such variance [21] However this work hasemployed a numerical evaluation method to determine theinfluence of the kernel size on the accurate classification ratefor the proposed architecture The performed experimentsare represented in Figures 6 and 7
From the aforementioned experiments it is possible todetermine suboptimal values for the kernel width associatedwith each class of vocal disease The kernel size was tested byusing a logarithmic scale with values ranging from 001 to 10The kernel adjustment has provided an effective mechanismto eliminate outliers The right choice of its size may increasethe success rate considerably The amount of samples is alsoa fundamental factor in the classification rates according tothe results given in Figures 6 and 7
The results shown in Figure 6 demonstrate that theindependently of the kernel size the classifier for healthy andpathological voices represents an unsatisfactory result whenonly a few samples are used However when the kernel isequal to 077 and about 1000 signal samples are used theclassifier has presented a success rate of 93
One of the goals of this work is to reduce the complexityassociated with the architecture while a classifier based onthe Euclidean distance is used However it is sensitive to
6000
5000
4000
3000
2000
1000
0
6000
5000
4000
3000
2000
1000
0
10 20 30 40 50
50 100 150 200 250 300
Frequency (Hz)
HealthyPathological
Cor
rent
ropy
Descriptors
Figure 3 Correntropy spectral density for healthy and pathologicalvoices obtained for a kernel size equal to 0003
Table 1 Performance of classification for healthy and pathologicalclasses with kernel size of 077 and 1000 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9122 9381 9565 130Correlation 6042 7143 8233 912
the sample size as it is necessary optimize such parameterThus it is possible to state that amounts of samples higherthan 1000 affect success rates between healthy and patholog-ical voices
The success rate in the classification between voices withedema and nodules varied from 65 (when the kernel sizeis 031 and the number of samples is 700) to 98 (when thekernel size is 177 and 1300 samples are adopted) accordingto Figure 7
After adjusting the architecture with the adequate valuesfor the kernel size and number of samples the correntropymeasure was investigated regarding its capability of classify-ing and characterizing the statistical independencies of theconsidered voice signals Accordingly correlation is adoptedas a reference measure since it can be seen as a particularcase of correntropy and is very often used in classification
Mathematical Problems in Engineering 5
3500
3000
2500
2000
1500
1000
500
010 20 30 40 50
3500
3000
2500
2000
1500
1000
500
050 100 150 200 250 300
Frequency (Hz)
EdemaNodule
Cor
rent
ropy
Descriptors
Figure 4 Correntropy spectral density for voices with edema andnodules obtained for a kernel size equal to 00129
problemsTheobtained results are presented inTables 1 and 2The average success rate is determined considering 100 trials
Based on Table 1 it is possible to observe that the archi-tecture based on correntropy is able to distinguish betweenhealthy and pathological voices with a success rate between9122 and 9565 and average rate of 9381 while thestandard deviation is 130 On the other hand when anarchitecture based on correlation is used the success rate ofthe classifier is reduced considerably Besides it can be statedthat the standard deviation of the recognition rate for theproposed architecture is much lower if compared to that forthe architecture based on correlation thus indicating higherreliability of the classifier with correntropy
From Table 2 it can be seen that the recognition ratebetween the voices with edema and nodules is considerablyhigher in the architecture based on correntropy Once againthe success rate of the proposed architecture is within anacceptable range of values and with low standard deviation
43 Comparison with Existing Methods Several methods forthe detection of vocal pathologies have been proposed inthe literature With the aim of better assessing the classifierdeveloped in this work the obtained results are comparedwith those regarding the works in [6 8 10] which were alsoobtained using the MEEI database [20]
Feature extractor
Decision 01Euclidean distance
Healthy Pathological
Decision 02
NoduleEdema
Voice signal
Feat
ures
Feat
ures
Step 1
Step 2
Euclidean distance
P0P1
P2P3
Figure 5 Automatic classification process of pathological voices
4 6 8 10 12 14 16
06507
07508
08509
0951
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 6 Influence of the kernel size and amount of samples on thesuccess rates between healthy and pathological voices
Table 2 Performance of classification for edemas and nodules withkernel size of 177 and 1300 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9555 9643 9823 143Correlation 7783 7975 8312 643
The work in [6] considers a transform initially appliedto the voice signal to obtain a space of smaller dimensionby using the decomposition in singular values that ishigher-order singular value decomposition (HOSVD) In theclassification stage measure of mutual information and a
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
edema nodule
Edemavoices
features
Nodulevoices
features
ProposedArchitecture
P3
P3
P2
P2
Figure 2 Extractor for the characteristics of voices with edema andnodules
the success rate between healthy and pathological voicesThen the success rate is assessed among 43 voices with edemaand 20 voices with nodules
The only adjustable parameter in the architecture is thevariance of the Gaussian kernel that is the kernel sizeMany systems use a heuristic known as Silvermanrsquos ruleto determine such variance [21] However this work hasemployed a numerical evaluation method to determine theinfluence of the kernel size on the accurate classification ratefor the proposed architecture The performed experimentsare represented in Figures 6 and 7
From the aforementioned experiments it is possible todetermine suboptimal values for the kernel width associatedwith each class of vocal disease The kernel size was tested byusing a logarithmic scale with values ranging from 001 to 10The kernel adjustment has provided an effective mechanismto eliminate outliers The right choice of its size may increasethe success rate considerably The amount of samples is alsoa fundamental factor in the classification rates according tothe results given in Figures 6 and 7
The results shown in Figure 6 demonstrate that theindependently of the kernel size the classifier for healthy andpathological voices represents an unsatisfactory result whenonly a few samples are used However when the kernel isequal to 077 and about 1000 signal samples are used theclassifier has presented a success rate of 93
One of the goals of this work is to reduce the complexityassociated with the architecture while a classifier based onthe Euclidean distance is used However it is sensitive to
6000
5000
4000
3000
2000
1000
0
6000
5000
4000
3000
2000
1000
0
10 20 30 40 50
50 100 150 200 250 300
Frequency (Hz)
HealthyPathological
Cor
rent
ropy
Descriptors
Figure 3 Correntropy spectral density for healthy and pathologicalvoices obtained for a kernel size equal to 0003
Table 1 Performance of classification for healthy and pathologicalclasses with kernel size of 077 and 1000 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9122 9381 9565 130Correlation 6042 7143 8233 912
the sample size as it is necessary optimize such parameterThus it is possible to state that amounts of samples higherthan 1000 affect success rates between healthy and patholog-ical voices
The success rate in the classification between voices withedema and nodules varied from 65 (when the kernel sizeis 031 and the number of samples is 700) to 98 (when thekernel size is 177 and 1300 samples are adopted) accordingto Figure 7
After adjusting the architecture with the adequate valuesfor the kernel size and number of samples the correntropymeasure was investigated regarding its capability of classify-ing and characterizing the statistical independencies of theconsidered voice signals Accordingly correlation is adoptedas a reference measure since it can be seen as a particularcase of correntropy and is very often used in classification
Mathematical Problems in Engineering 5
3500
3000
2500
2000
1500
1000
500
010 20 30 40 50
3500
3000
2500
2000
1500
1000
500
050 100 150 200 250 300
Frequency (Hz)
EdemaNodule
Cor
rent
ropy
Descriptors
Figure 4 Correntropy spectral density for voices with edema andnodules obtained for a kernel size equal to 00129
problemsTheobtained results are presented inTables 1 and 2The average success rate is determined considering 100 trials
Based on Table 1 it is possible to observe that the archi-tecture based on correntropy is able to distinguish betweenhealthy and pathological voices with a success rate between9122 and 9565 and average rate of 9381 while thestandard deviation is 130 On the other hand when anarchitecture based on correlation is used the success rate ofthe classifier is reduced considerably Besides it can be statedthat the standard deviation of the recognition rate for theproposed architecture is much lower if compared to that forthe architecture based on correlation thus indicating higherreliability of the classifier with correntropy
From Table 2 it can be seen that the recognition ratebetween the voices with edema and nodules is considerablyhigher in the architecture based on correntropy Once againthe success rate of the proposed architecture is within anacceptable range of values and with low standard deviation
43 Comparison with Existing Methods Several methods forthe detection of vocal pathologies have been proposed inthe literature With the aim of better assessing the classifierdeveloped in this work the obtained results are comparedwith those regarding the works in [6 8 10] which were alsoobtained using the MEEI database [20]
Feature extractor
Decision 01Euclidean distance
Healthy Pathological
Decision 02
NoduleEdema
Voice signal
Feat
ures
Feat
ures
Step 1
Step 2
Euclidean distance
P0P1
P2P3
Figure 5 Automatic classification process of pathological voices
4 6 8 10 12 14 16
06507
07508
08509
0951
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 6 Influence of the kernel size and amount of samples on thesuccess rates between healthy and pathological voices
Table 2 Performance of classification for edemas and nodules withkernel size of 177 and 1300 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9555 9643 9823 143Correlation 7783 7975 8312 643
The work in [6] considers a transform initially appliedto the voice signal to obtain a space of smaller dimensionby using the decomposition in singular values that ishigher-order singular value decomposition (HOSVD) In theclassification stage measure of mutual information and a
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
3500
3000
2500
2000
1500
1000
500
010 20 30 40 50
3500
3000
2500
2000
1500
1000
500
050 100 150 200 250 300
Frequency (Hz)
EdemaNodule
Cor
rent
ropy
Descriptors
Figure 4 Correntropy spectral density for voices with edema andnodules obtained for a kernel size equal to 00129
problemsTheobtained results are presented inTables 1 and 2The average success rate is determined considering 100 trials
Based on Table 1 it is possible to observe that the archi-tecture based on correntropy is able to distinguish betweenhealthy and pathological voices with a success rate between9122 and 9565 and average rate of 9381 while thestandard deviation is 130 On the other hand when anarchitecture based on correlation is used the success rate ofthe classifier is reduced considerably Besides it can be statedthat the standard deviation of the recognition rate for theproposed architecture is much lower if compared to that forthe architecture based on correlation thus indicating higherreliability of the classifier with correntropy
From Table 2 it can be seen that the recognition ratebetween the voices with edema and nodules is considerablyhigher in the architecture based on correntropy Once againthe success rate of the proposed architecture is within anacceptable range of values and with low standard deviation
43 Comparison with Existing Methods Several methods forthe detection of vocal pathologies have been proposed inthe literature With the aim of better assessing the classifierdeveloped in this work the obtained results are comparedwith those regarding the works in [6 8 10] which were alsoobtained using the MEEI database [20]
Feature extractor
Decision 01Euclidean distance
Healthy Pathological
Decision 02
NoduleEdema
Voice signal
Feat
ures
Feat
ures
Step 1
Step 2
Euclidean distance
P0P1
P2P3
Figure 5 Automatic classification process of pathological voices
4 6 8 10 12 14 16
06507
07508
08509
0951
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 6 Influence of the kernel size and amount of samples on thesuccess rates between healthy and pathological voices
Table 2 Performance of classification for edemas and nodules withkernel size of 177 and 1300 samples
Method Recognition rate ()Minimum Average Maximum Standard deviation
Correntropy 9555 9643 9823 143Correlation 7783 7975 8312 643
The work in [6] considers a transform initially appliedto the voice signal to obtain a space of smaller dimensionby using the decomposition in singular values that ishigher-order singular value decomposition (HOSVD) In theclassification stage measure of mutual information and a
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
4 6 8 10 12 14 16
0506070809
1
Kernel size
Succ
ess r
ate
101
100
10minus1
10minus2
Sample sizes (lowast100)
Figure 7 Influence of the kernel size and amount of samples on thesuccess rates between voices with edema and nodule
SVM network are usedThe success rate is around 941 withan interval of reliability of 028
The classification architecture in [8] is developed fromeleven characteristics extracted by means of nonlinear analy-sis of temporal series where two are based on conventionalnonlinear statistics other two are based on the analysisof recurrence and fractal scheduling and the rest of themare obtained from different estimations of the entropy Theachieved success rate is 98 by using a SVM and Gaussianmixture models (GMM) in the classification stage
Information measures are employed in [10] for exampleShannon entropy correlation entropy approximate entropyTsallis entropy Hurst exponent maximal Lyapunov expo-nent and the first minimum of the mutual informationfunction in addition to LPC (linear prediction coding)coefficients [10] In the classification process a quadraticdiscriminant analysis (QDA) is applied with a success rateequal to about 9650
Thus it is possible to state that all aforementionedmethods employ a complex stage for the extraction ofcharacteristics with the calculation of a large set of variablesthat in general are sent to a neural network for classificationpurposes
On the other hand the architecture proposed in thispaper uses only one extractor defined by the CSD and also avery simple classification stage based on Euclidian distanceTherefore the introduced strategy presents low computa-tional complexity which implies simple implementation inreal-time embedded systems Besides the proposed systempresents high success rate that is about 97
5 Conclusion
This paper has presented a novel method of automatic classi-fication for pathological voices based on correntropy spectraldensity (CSD) It has been demonstrated that CSD is adequateto characterize dynamic interdependencies among the voicesignal samples being able to extract distinct characteristicsbetween healthy and pathological voices Among the maincharacteristics of such method it is worth mentioning thatthe classification stage becomes simpler by the use of Euclid-ian distance which effectively reduces its computationalcomplexity From the obtained results it has been shown
that the proposed classifier presents high recognition ratewhich is achieved after a simple adjustment in the kernelsize employed by the feature extractorThe proposed methodcan be used as a valuable tool by researchers and speechpathologists Future work aims at the development of exper-iments using other databases and also the implementation ofan online diagnosing system
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] B G Aguiar Neto S C Costa J M Fechine and M MuppaldquoFeature estimation for vocal fold edema detection using short-term cepstral analysisrdquo in Proceedings of the 7th IEEE Interna-tional Conference on Bioinformatics and Bioengineering (BIBErsquo07) pp 1158ndash1162 January 2007
[2] J I Godino-Llorente P Gomez-Vilda and M Blanco-VelascoldquoDimensionality reduction of a pathological voice qualityassessment system based on gaussian mixture models andshort-term cepstral parametersrdquo IEEE Transactions on Biomed-ical Engineering vol 53 no 10 pp 1943ndash1953 2006
[3] G Muhammad and M Melhem ldquoPathological voice detec-tion and binary classification using MPEG-7 audio featuresrdquoBiomedical Signal Processing and Control vol 11 pp 1ndash9 2014
[4] R T S Carvalho C C Cavalcante and P C Cortez ldquoWavelettransform and artificial neural networks applied to voice dis-orders identificationrdquo in Proceedings of the 3rd World Congresson Nature and Biologically Inspired Computing (NaBIC rsquo11) pp371ndash376 IEEE October 2011
[5] E S Fonseca R C Guido A C Silvestre and J C Pereira ldquoDis-crete wavelet transform and support vector machine applied topathological voice signals identificationrdquo in Proceedings of the7th IEEE International Symposium onMultimedia (ISM rsquo05) pp785ndash789 December 2005
[6] M Markaki and Y Stylianou ldquoVoice pathology detection anddiscrimination based on modulation spectral featuresrdquo IEEETransactions on Audio Speech and Language Processing vol 19no 7 pp 1938ndash1948 2011
[7] E S Fonseca and J C Pereira ldquoNormal versus pathologicalvoice signalsrdquo IEEE Engineering in Medicine and Biology Maga-zine vol 28 no 5 pp 44ndash48 2009
[8] J D Arias-Londono J I Godino-Llorente N Saenz-Lechon VOsma-Ruiz and G Castellanos-Domınguez ldquoAutomatic detec-tion of pathological voices using complexity measures noiseparameters and mel-cepstral coefficientsrdquo IEEE Transactionson Biomedical Engineering vol 58 no 2 pp 370ndash379 2011
[9] S Jothilakshmi ldquoAutomatic system to detect the type of voicepathologyrdquo Applied Soft Computing vol 21 pp 244ndash249 2014
[10] W C A Costa S L N C Costa F M Assis and B G AguiarldquoHealthy and pathological voice assessment by means of non-linear dynamic analysis measures and linear predictive codingrdquoBrazilian Journal of Biomedical Engineering vol 29 no 1 pp3ndash14 2013
[11] L Salhi and A Cherif ldquoRobustness of auditory teager energycepstrum coefficients for classification of pathological andnormal voices in noisy environmentsrdquo The Scientific WorldJournal vol 2013 Article ID 435729 8 pages 2013
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
[12] I Santamarıa P P Pokharel and J C Principe ldquoGeneralizedcorrelation function definition properties and application toblind equalizationrdquo IEEE Transactions on Signal Processing vol54 no 6 I pp 2187ndash2197 2006
[13] A Gunduz and J C Principe ldquoCorrentropy as a novel measurefor nonlinearity testsrdquo Signal Processing vol 89 no 1 pp 14ndash232009
[14] I Park and J C Prıncipe ldquoCorrentropy based Granger causal-ityrdquo in Proceedings of the IEEE International Conference onAcoustics Speech and Signal Processing (ICASSP rsquo08) pp 3605ndash3608 April 2008
[15] K JeongW Liu S Han E Hasanbelliu and J C Principe ldquoThecorrentropyMACE filterrdquo Pattern Recognition vol 42 no 5 pp871ndash885 2009
[16] R LiW Liu and J C Principe ldquoA unifying criterion for instan-taneous blind source separation based on correntropyrdquo SignalProcessing vol 87 no 8 pp 1872ndash1881 2007
[17] A I R Fontes L A Pasa V A De Sousa Jr F M AbinaderJr J A F Costa and L F Q Silveira ldquoAutomatic modulationclassification using information theoretic similarity measuresrdquoinProceedings of the 76th IEEEVehicular Technology Conference(VTC rsquo12) pp 1ndash5 September 2012
[18] J C Principe Information Theoretic Learning Renyirsquos Entropyand Kernel Perspectives Springer 2010
[19] J Xu Nonlinear signal processing based on reproducing KernelHilbert space [PhD thesis] University of Florida 2007
[20] M Eye and E Infirmary Elemetrics Disordered Voice Database(Version 103) Voice and Speech Lab Boston Mass USA 1994
[21] B W Silverman ldquoDensity estimation for statistics and dataanalysisrdquo Technometrics vol 37 1986
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
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