research article prediction research of red tide based on ...red tide, statistical prediction method...

Research ArticlePrediction Research of Red Tide Based on Improved FCM

Xiaomei Hu1 Dong Wang1 Hewei Qu1 and Xinran Shi2

1The Key Laboratory of Intelligent Manufacturing and Robotics School of Mechatronic Engineering and AutomationShanghai University Mailbox 232 No 149 Yanchang Road Shanghai 200072 China2Department of Mechanical Engineering College of Engineering University of Michigan Ann Arbor MI 48105 USA

Correspondence should be addressed to Xiaomei Hu sufeimasohxm163com

Received 21 September 2015 Revised 15 December 2015 Accepted 17 December 2015

Academic Editor Daniela Boso

Copyright copy 2016 Xiaomei Hu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Red tides are caused by the combination effects of many marine elements The complexity of the marine ecosystem makes it hardto find the relationship between marine elements and red tides The algorithm of fuzzy 119888-means (FCM) can get clear classificationof things and expresses the fuzzy state among different things Therefore a prediction algorithm of red tide based on improvedFCM is proposed In order to overcome the defect of FCM which is overdependent on the initial cluster centers and the objectivefunction this paper gains the initial cluster centers through the principle of regionalminimumdata density and theminimummeandistance The feature weighted cluster center is added to the objective function Finally the improved FCM algorithm is appliedin the prediction research of red tide and the results show that the improved FCM algorithm has good denoising ability and highaccuracy in the prediction of red tides

1 Introduction

Ocean as the cradle of human beings provides humans withabundant biological resources and mineral resources Alongwith the rapid growth of population and economic societyin the 21st century we march into the sea to alleviate theshortage of resources followed by the marine ecologicalenvironment pollution and destruction Because of a largeamount of untreated waste water directly discharged into theocean and global climate change harmful red tide speciesincreased dramatically The cause of the red tides is morecomplex Although the occurrencemechanism of red tide hasnot yet been determined most scholars believe that red tideoccurrence is closely related to water eutrophication [1 2]

There have been some studies on the red tide predictionUsing numerical method Gibson et al established NPZecological dynamic model and analyzed five kinds of sestonfeeding functions [3] Zhang et al combined the multifactorincluding the meteorological and hydrological data to fore-cast the red tide [4] Wang et al established a multivariateadaptive spline regression model to forecast the red tide [5]However the accuracy of the traditional red tide prediction isflawed With the rapid rise of artificial intelligence artificial

neural network (ANN) has been applied to the red tideprediction andhasmade a lot of achievements [6 7] Artificialneural network also has many defects such as low learningefficiency and unstable network learning and memory

In this paper a fuzzy 119888-means clustering algorithmis proposed for the red tide prediction The algorithm isoptimized from the initial cluster center selection and theimprovement of the objective function As the experimentshows the prediction of red tide based on improved FCMalgorithm has better clustering results converging speed androbustness to noise and outliers

2 Related Research

21 Research on the Prediction Method of Red Tide Red tideis caused by the comprehensive action of multiple factorssuch as the sudden proliferation and accumulation of someplankton [8] It has the characteristics of common naturaldisasters namely inhomogeneity diversity difference burstreproducibility disorder randomness and predictability intime and space [9] As one of the most serious marinedisasters the scale of the red tide and the loss of the economyare increasing year by year Red tide also has a negative

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9618706 8 pageshttpdxdoiorg10115520169618706

2 Mathematical Problems in Engineering

effect on the marine economy sustainable development inour country therefore the prediction research of red tidehas an important meaning in environmental protection andreducing the economic loss [10ndash12]

According to the research on the prediction of red tidethere are alreadymany predictionmethods such as empiricalprediction method statistical prediction method numericalmodel prediction method and artificial neural network [13ndash15]

(1) Empirical Prediction Method There is a certain regularitybetween the occurrence of red tide and the changes ofenvironmental factors such as meteorological conditionsoceanographic processes and ecological factors Empiricalprediction method is based on the certain regularity

(2) Statistical Prediction Method The empirical predictionmethod only depends on the change of a certain environmen-tal factor However red tide in fact is caused by many factorsThe statistical prediction method can have comprehensiveanalysis on the factors therefore it has stronger predictiveability Its main method includes principal component anal-ysis discriminant analysis and stepwise regression method

(3) Numerical Model Prediction Method Due to the lackof detailed understanding of the occurrence mechanism ofred tide statistical prediction method is to a certain degreesubjective and blind Numerical model prediction methoduses a variety of mathematical tools to analyze solve andsimulate the model based on various physical and chemicalbiological coupling factors

(4) Artificial Neural Network With the rapid development ofcomputer technology artificial intelligence technology andbiotechnology artificial neural network has been applied tothe prediction of the red tide However the research of thismethod has been a certain constraint because it has the slowconvergence speed and it is easy to fall into local minimumvalues

22 Research on the Fuzzy 119888-Means Clustering AlgorithmClustering is one of the most basic activities of humanunderstanding of the world The purpose of clustering isto make the same class of things as similar as possibleand different categories of things as different as possibleAccording to the different values of membership degreethe clustering method can be divided into hard clusteringmethod and fuzzy clustering method As for the hard clus-tering method 0 means that the sample must not fall intothis category and 1 means that the sample must belong to thiscategory Fuzzy clustering method is a combination of fuzzytheory and clustering analysisThe fuzzy clustering algorithmproposed by Dunn and extended by Bezdek is the mostwell-known and the most frequently used method [16] Themajor algorithms include transitive closure method based onfuzzy equivalence relation the method based on similarityrelation and fuzzy relation and most tree method based onfuzzy graph theory However these methods have the high

complexity of calculation and are not suitable for large datatherefore they have been gradually reduced in research Thefuzzy clustering algorithm based on objective function iswidely studied Within-Groups Sum of Squared Error is usedto construct the objective function This algorithm is simpleand effective also supported by classical theory Fuzzy 119888-means clustering algorithm is the most widely used fuzzyclustering algorithm based on objective function [17]

Let 119883 = 1199091 1199092 119909

119899 be sample dataset with 119899

samples and each sample 119909119896has 119904 properties namely 119909

119896=

1199091198961 1199091198962 119909

119896119904 then the matrix of the sample dataset can

be expressed as follows

119883 = (119909119899119904) 119899 = 1 2 119899 119904 = 1 2 119904 (1)

The objective function of FCM clustering algorithm119869119898(119880 119881) is defined as [18ndash20]

119869119898(119880 119881) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894) (2)

where 119888 is clustering category 2 le 119888 le 119899 119880 is matrix ofmembership degree 119880 = 120583

119894119896 119894 = 1 2 119888 119896 = 1 2 119899

119881 is matrix of cluster center 119881 = V119894 119894 = 1 2 119888 120583

119894119896is

membership degree of the 119896th element in the 119894th clusteringcategory V

119894is cluster center of the 119894th clustering category

V119894= V1198941 V1198942 V

119894119904 119894 = 1 2 119888 119898 is weighting exponent

and empirical value is 15 le 119898 le 25 119889119894119896(119909119896 V119894) is the

Euclidean distance of target data between 119909119896and V119894

The basic idea of FCM algorithm is to find fuzzymatrix ofmembership degree and cluster center making the objectivefunction minimum

Membership degree function satisfies the following equa-tions

119888

sum

119894=1

(120583119894119896)119898

= 1 forall119896

119899

sum

119896=1

(120583119894119896)119898

ge 0 forall119894

120583119894119896isin [0 1] forall119894 119896

(3)

According to the Lagrange multiplier optimization algo-rithm the update formulas ofmembership degree and clustercenter are expressed as

120583119894119896=

1

sum119888

119897=1[119889119894119896(119909119896 V119894) 119889119897119896(119909119896 V119897)]2(119898minus1)

119894 = 1 2 119888 119896 = 1 2 119899

(4)

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896

sum119899

119896=1(120583119894119896)119898

119894 = 1 2 119888 (5)

FCM algorithm is described as follows

Step 1 Give the number of clustering categories 119888 (2 le 119888 le 119899)Set the number of iterations 119896 = 1 weighting exponent 119898and stop parameters 120576

Mathematical Problems in Engineering 3

Step 2 Randomly select cluster centers V119894(119896) 119894 = 1 2 119888

Step 3 According to formula (4) update the subjectionfunction

Step 4 According to formula (5) update the cluster centerand set the updated cluster center V

119894(119896 + 1)

Step 5 If V119894(119896+1)minus V

119894(119896) gt 120576 then turn to Step 3 119896 = 119896+1

otherwise quit the loop and get the clustering results

Although FCM clustering algorithm as a classical algo-rithm is widely applied in a variety of key areas [21ndash23] ithas its own shortcomings and deficiencies On one hand theinitial cluster centers are randomly selected which leads toa possible local convergence rather than the global optimalsolution on the other hand the objective function of FCMalgorithm considers only the distance between sample dataand cluster centers but it ignores the effect of the distancebetween cluster centers on the solution To solve the problemabove a variety of different improved algorithms are pro-posed [24ndash26] In this paper an improved FCM algorithm isproposed and applied to make a red tide prediction

3 An Improved Fuzzy 119888-MeansClustering Algorithm

31 Selection of the Initial Cluster Centers The selectionprinciple of the initial cluster center is to make the initialcluster center within a certain threshold contain more dataThis not only ensures that the clustering algorithm findsthe cluster centers in a number of feasible regions but alsoeffectively reduces the impact of the noise and outliers on theobjective function

Let 119883 = 1199091 1199092 119909

119899 be the sample dataset the

regional minimum threshold 119886 and regional minimum datadensity 119887 according to the principle above the selection stepsof initial cluster centers are as follows

Step 1 Calculate Euclideandistance between any two samplesin the dataset to generate distance matrix119860 According to thedistance matrix 119860 choose the nearest two samples

Step 2 With the center of the two samples as center and theregional threshold 119886 as radius plan 119886 circular region If thedata density in the region is equal or greater than minimumdata density 119887 in this region this center is chosen as a kind ofinitial cluster center otherwise the region is removed

Step 3 Choose the nearest two samples in the remainingsamples outside the region Repeat Step 2 until 119888 classes arefound If the selected classes are less than 119888 the criteria of 119886and 119887 will be relaxed

Figure 1 shows the selection process of the initial clustercenter According to the distance matrix the two red sampleshave the nearest distance among all the samples Howeverthe data density in its region is small so the red samples areremoved from the sample data In the rest of the sample data

cluster centerThe first initial

Figure 1 The selection of the initial cluster centers through theprinciple of regional minimum data density

Class 2Class 1

radius is rThe regional

Figure 2 The selection of the initial cluster centers through theprinciple of the minimum mean distance

the initial cluster centers are continued to look for until 119888classes are found

According to formula (4) the membership degree of theelement 119909

119894in the 119894th clustering category is determined by the

relative radio of 119889119894119895and 119889

119888119895(119888 = 119894) but the real distance 119889

119894119895is

not reflected in the solution of subjection functionAs shown in Figure 2 the red data point is located on

the bisecting line of two datasets below it It is obviouslydifficult to distinguish the class of the red data point usingthe traditional FCM subjection functionThe principle of themean distanceminimum is proposed to classify the boundarydata firstly with the boundary red data point as center119903 as radius plan 119886 circular region secondly respectivelycalculate the mean value of the distance between the pointsin the circular region and the two cluster centers finally theboundary red data point is assigned to the class where themean value of the distance is smaller

32 Improvement of the Objective Function As the mostcommon analysismethod of FCM fuzzy clustering algorithm


based on dissimilar objective function only considers weight-ing Euclidean distance between sample data and clustercenters without taking into account the distance betweeneach cluster center [27] Therefore a weighting fuzzy 119888-means based on dissimilar objective function (DWFCM) isproposed and weighted distance between cluster centers isadded to dissimilar objective function according to the effectof the distance between cluster centers on clustering results

Dissimilar objective function with distance between clus-ter centers is defined as [28]

119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(6)

where 120578119894119895= 120573(min119889

119894119896(V119894 119909119896) 119889119895119896(V119895 119909119896)max119889

119886119887(V119886 V119887))

0 le 120573 le 1 119886 119887 isin 119888 119889119894119895(V119894 V119895) is the Euclidean distance

between cluster centers V119894and V119895

According to the Lagrange multiplier optimization algo-rithm under the constraint conditions of formula (3) theupdate formulas of cluster center andmembership degree areexpressed as

120597119869119898

120597V119894

= 0 997904rArr

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1(120578119894119895)

119898

(7)

120583119894119896

=

(119889119894119896

2(119909119896 V119894))

minus1(119898minus1)

sum119888

119895=1(119889119895119896

2(119909119896 V119895))

minus1(119898minus1)119889119894119896

2(119909119896 V119894) gt 0 (1 le 119895 le 119888)

1 119889119894119896

2(119909119896 V119894) = 0 (1 le 119895 le 119888)

0 119895 = 119894 119889119895119896

2(119909119896 V119895) = 0

(8)

Formula (6) adds the effect of the cluster centers onclustering results This optimization obtains the minimumweighting Euclidean distance between sample data and clus-ter centers and the maximum Euclidean distance betweencluster centers However this optimization does not considerthe effect of the distance between cluster centers on clusteringresultsTherefore DWFCM algorithm adds feature weight toEuclidean distance among cluster centers

In order to obtain the feature weight the similarity coef-ficient 119903

119894119895between the cluster centers should be calculated

There are several common methods as follows [29](1) The correlation coefficient method is defined as

119903119894119895=

sum119904

119901=1

10038161003816100381610038161003816V119894119901minus V119894

10038161003816100381610038161003816

10038161003816100381610038161003816V119895119901minus V119895

10038161003816100381610038161003816

[sum119904

119901=1(V119894119901minus V119894)

2

sum119904

119901=1(V119895119901minus V119895)

2

]

12 (9)

where V119894= (1119904)sum

119904

119901=1V119894119901 V119895= (1119904)sum

119904

119901=1V119895119901 1 le 119894 119895 le 119888 V

119894119901

V119895119901are the 119901th attribute of the 119894th 119895th cluster center

(2) The least arithmetic average method is defined as

119903119894119895=

2sum119904

119901=1min (V

119894119901 V119895119901)

sum119904

119901=1(V119894119901+ V119895119901)

(10)

(3) The angle cosine method is defined as

119903119894119895=

sum119904

119901=1V119894119901V119895119901

radicsum119904

119901=1V119894119901

2radicsum119904

119901=1V119895119901

2

(11)

The correlation coefficientmethod is used to calculate thesimilarity coefficient 119903

119894119895in the DWFCM algorithm

The feature weight 119871119894119895is defined as

119871119895=

119888

sum

119875=1

119903119901119895

119871119894119895=

119903119894119895

119871119895

(12)

The objective function of DWFCM is defined as

119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

119871119894119895(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(13)

According to the Lagrange multiplier optimization algo-rithmunder the constraint conditions of formula (3) formula(7) is modified as follows

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1119871119894119895(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1119871119894119895(120578119894119895)

119898 (14)

Considering the unit of sample data is not unified andthe data is not complete the data are normalized before thesample is classified The normalized functions are as follows

1199091015840

119899119904=

119909119899119904minus 119909119899

119904119899

(15)

where 119909119899= (1119904)sum

119904

119895=1119909119899119904 119904119899= radic(1(119904 minus 1))sum

119904

119895=1(119909119899119904minus 119909119899)2

33 The Description of Improved FCM Algorithm The stepsof improved FCM algorithm are as follows

Step 1 Set the regional threshold 119886 regional density 119887regional radius 119903 category number 119888 iteration 119896 = 1weighting exponent119898 and stop parameters 120576

Step 2 According to the number of regional thresholdsregional density and regional radius accomplish the selec-tion of 119888 initial cluster centers

Step 3 Calculate the correlation coefficient 119903119894119895and feature

weight 119871119894119895among cluster centers


Step 4 According to formulas (8) and (14) update thesubjection function and the cluster center and set the updatedcluster center V

119894(119896 + 1) Normalize the original sample

Step 5 If V119894(119896+1)minus V


otherwise quit the loop and get the subjection function 120583119894119896

Step 6 The samples are classified according to the followingmethods

119889119894119896(V119894 119909119896) le 119889119895119896(V119895 119909119896)

119896 = 1 2 119899 119894 119895 = 1 2 119888

(16)

In this case the sample 119909119896is classified into the 119894th class

4 Red Tide Prediction Analysis Based onImproved FCM Algorithm

Example 1 Some changes of the marine environment factorsaccompany the process of the red tide from happening toextinction The original sample set is composed of marineenvironment factors which have a great influence on thered tide FCM possibilistic fuzzy 119888-mean algorithm (PCM)and DWFCM are used to classify the original sample setConsidering that the increase of nitrogen concentration isthe key factor of eutrophication of the seawater meanwhilethe eutrophication of the seawater is the primary conditionof the occurrence of red tide and the change of phytoplank-ton density is also an important indicator to measure theoccurrence of red tide nitrogen concentration (120583molL) andphytoplankton density (104cubic meter) are chosen as theresearch factors 21 original samples from the State OceanicAdministration are shown in Table 1 where the last sampleis used for forecasting and other samples are used for clusteranalysis

Before clustering the normalized processing of origi-nal samples is completed If the horizontal axis representsnitrogen concentration and the vertical axis represents thephytoplankton density the simulation results of three dif-ferent algorithms are shown in Figures 3 4 and 5 and thecomparison of clustering results is shown in Table 2

In Figures 3 4 and 5 the samples where red tide occursare marked as the inverted triangle The samples where redtide will occur are marked as the asterisk The samples wherered tide does not occur are marked as rhombic The red dotsrepresent cluster centers of samples In Table 2 the errorscore is the number of the misclassified data pieces and theerror rate is the percentage of the error score in the totaldata From Figures 3 4 and 5 and Table 1 DWFCM hasthe best performance among three algorithms the selectionof clustering center is the most reasonable the number ofiterations is also the least the accuracy is also the best

Example 2 In order to sufficiently demonstrate superiorityof the proposed optimization model in this paper thisexample chooses another original sample set which alsohave a great influence on the red tide Considering that thewater temperature is the key factor of plankton growth speedand the transparency can be used to evaluate the density

Table 1 The original sample set with 21 elements

SampleNitrogen

concentration(120583molL)

Phytoplankton density(104cubic meter)

1 04 1482 054 1093 01 7154 007 3185 054 1096 031 837 042 11318 021 9339 018 31110 021 97211 04 74512 036 12513 056 18714 039 14615 007 3216 047 20517 043 13618 043 14719 026 16020 032 105421 037 1037

070603 04 08 090201 050Nitrogen concentration

0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity

Figure 3 The clustering results of FCM algorithm in Example 1

of plankton water temperature (∘C) and transparency (m)are chosen as the research factors 32 original samples areshown in Table 3 where the last sample is used for forecastingand other samples are used for cluster analysis The specificclustering results and the analysis of clustering results areshown in Tables 3 and 4 and Figures 6 7 and 8

As to the FCM algorithm the sum of the membershipdegree of the same sample belonging to all categories is 1


Table 2 The comparison of clustering results in Example 1

FCM PCM DWFCM

Clustering center(055 084) (056 081) (054 086)(078 050) (085 043) (081 055)(018 012) (016 019) (017 018)

Iteration number 11 13 8Error score 4 3 1Error rate 20 15 5

01 02 03 04 05 06 07 090 08Nitrogen concentration

0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity

Figure 4 The clustering results of PCM algorithm in Example 1


0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity

Figure 5The clustering results of DWFCMalgorithm in Example 1

which makes FCM algorithm sensitive to noise and outliers[30] Figure 6 shows that FCM algorithm makes the wrongclustering division for some boundary samples In PCMalgorithm the value of the membership degree reflects thereal Euclidean distance between sample data and clustercenters which makes PCM algorithm have good robustnessto noise and outliers Figure 7 shows that PCM algorithmmakes the right clustering division for boundary samplesbut there are still a large number of overlapping clusters


Sample Water temperature (∘C) Transparency (m)1 2647 152 2622 123 2447 124 242 355 2515 126 242 257 237 228 266 099 265 0410 265 0511 261 0612 262 1513 265 0914 249 1815 250 2516 250 2517 258 1118 261 1819 262 1520 254 1221 274 5022 276 2123 270 2024 268 4025 268 5026 268 4527 266 0928 265 0429 265 0530 261 0631 262 1532 275 39


FCM PCM DWFCM



Because DWFCM algorithm uses the principle of regionalminimum data density and the minimum mean distance toselect the fixed initial cluster centers which can effectivelyavoid the influence of noise and outliers it also consideredthe influence of the weighted cluster center on the objectivefunction which makes the clustering results more accurateAfter the last set is added to the clustering sample the lastset is clustered to the red tides cluster using the DWFCM


01 02 03 04 05 06 07 08 090Water temperature

0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency



algorithm and the fact is that the last set is indeed thesamplewhen red tide occursThe simulation results show thatDWFCM algorithm can effectively achieve the prediction ofred tide disaster

From Figures 6 7 and 8 and Table 4 FCM algorithm andPCM algorithm randomly select the initial cluster centerswhich make the number of iterations and the clusteringresults very different from each other However DWFCMalgorithm has selected the fixed initial cluster centers beforethe iteration so the number of iterations is significantlyreduced and the clustering results are unified

5 Conclusion

In view of the complexity of the red tide disaster and theshortage of the previous prediction algorithm a DWFCMalgorithm is proposed to predict red tide The initial clustercenters are chosen by the principle of regional minimumdatadensity and the minimum mean distance and the objective

0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


Figure 8The clustering results ofDWFCMalgorithm inExample 2

function is optimized by using the weighted cluster centerThe simulation results show that DWFCMalgorithm has bet-ter denoising ability and can optimize the prediction modelof red tide disaster and get more accurate predictive resultsHowever DWFCM algorithm introduces many parametersIn order to get accurate parameter values a lot of experimentshave to be doneTherefore the study of combining DWFCMalgorithm with other algorithms to overcome the defects inthe DWFCM algorithm is the focus of study in the future

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the Grand Science amp TechnologyProgram Shanghai China (no 14DZ1100700)

References

[1] W Hong-Li and F Jian-li Ecological Dynamics and Prediction ofRed Tide Tianjin University Press Tianjin China 2006

[2] S-Z Feng F-Q Li and S-Q Li Introduction toMarine ScienceHigher Education Press Beijing China 1999

[3] G A Gibson D L Musgrave and S Hinckley ldquoNon-lineardynamics of a pelagic ecosystem model with multiple predatorand prey typesrdquo Journal of Plankton Research vol 27 no 5 pp427ndash447 2005

[4] J F Zhang Y Bai J Yu et al ldquoForecast of red tide in theSouth China Sea by using the variation trend of hydrologicaland meteorological factorsrdquoMarine Science Bulletin vol 8 no2 pp 60ndash74 2006

[5] H-L Wang J-P Xiang and G Ge ldquoMultivariate adaptivespline regression prediction of total phytoplanktonrdquo MarineTechnology vol 25 no 3 pp 7ndash9 2006


[6] R Zhang H Yan and L P Du ldquoResearch on prediction of redtide based on fuzzy neural networkrdquo Bulletin of Marine Sciencevol 8 no 1 pp 83ndash91 2006

[7] HWilson and F Recknagel ldquoTowards a generic artificial neuralnetwork model for dynamic predictions of algal abundance infreshwater lakesrdquo Ecological Modelling vol 146 no 1ndash3 pp 69ndash84 2001

[8] W-L Huang and D-W Ding Prediction Mechanism and Tech-nology of Red Tide Disaster Ocean Press Beijing China 2004

[9] F Jin-Qing ldquoAttention to the complexity of science andresearchrdquo Nature Magazine vol 24 no 1 pp 7ndash14 2002

[10] F Jian-Feng Study on the Nonlinear Dynamics of the PlanktonicEcosystem and the Prediction of Red Tide Engineering Mechan-ics of Tianjin University 2005

[11] D-M Guan and X-W Zhan ldquoRed tide disasters in the coastalwaters in China and its countermeasuresrdquoMarine Environmen-tal Science no 2 pp 60ndash63 2003

[12] C-S Wang S-M Tang and P-Q Song ldquoEconomic lossassessment of red tide disaster in ChinardquoMarine EnvironmentalScience no 3 pp 428ndash431 2011

[13] X-L Wang P-Y Sun and Z-H Gao ldquoThe status and progressof the prediction of red tide in Chinardquo Progress in MarineScience vol 21 no 1 pp 93ndash98 2003

[14] H L Wang J F Feng S P Li and F Shen ldquoStatistical analysisand prediction of the concentration of harmful algae in bohaibayrdquo Transactions of Tianjin University vol 11 no 4 pp 308ndash312 2005

[15] X Wei-Yi and Z De-Di ldquoNumerical simulation of the processof the red tide in the real sea areardquo Oceanologia vol 32 no 6pp 598ndash604 2001

[16] K-L Wu and M-S Yang ldquoAlternative c-means clusteringalgorithmsrdquo Pattern Recognition vol 35 no 10 pp 2267ndash22782002

[17] N YongThe application of data mining to marine environmentonline monitoring and HVB prediction system [MS thesis]Shandong University Jinan China 2008

[18] M N Ahmed S M Yamany N Mohamed A A Farag andT Moriarty ldquoAmodified fuzzy C-means algorithm for bias fieldestimation and segmentation of MRI datardquo IEEE Transactionson Medical Imaging vol 21 no 3 pp 193ndash199 2002

[19] N R Pal K Pal J M Keller and J C Bezdek ldquoA possibilisticfuzzy c-means clustering algorithmrdquo IEEE Transactions onFuzzy Systems vol 13 no 4 pp 517ndash530 2005

[20] H Timm and R Kruse ldquoAmodification to improve possibilisticfuzzy cluster analysisrdquo in Proceedings of the IEEE InternationalConference on Fuzzy Systems (FUZZ-IEEE rsquo02) vol 2 pp 1460ndash1465 IEEE Honolulu Hawaii USA May 2002

[21] X Li X Lu J Tian P Gao H W Kong and G W XuldquoApplication of fuzzy c-means clustering in data analysis ofmetabolomicsrdquo Analytical Chemistry vol 81 no 11 pp 4468ndash4475 2009

[22] H-K Xu J-H Chuai Z-H Zhang and H-W Fan ldquoDatamining of traffic flow in road tunnelrdquo Journal of ChangrsquoanUniversity vol 25 no 4 pp 66ndash69 2005

[23] F Yu H Xu L Wang and X Zhou ldquoAn improved automaticFCM clustering algorithmrdquo in Proceedings of the 2nd Inter-national Workshop on Database Technology and Applications(DBTA rsquo10) pp 1ndash4 IEEE Wuhan China November 2010

[24] J Yu and H Huang ldquoA new weighting fuzzy c-means algo-rithmrdquo in Proceedings of the IEEE International Conference onFuzzy System (FUZZ rsquo03) pp 896ndash901 May 2003

[25] JM Leski ldquoGeneralizedweighted conditional fuzzy clusteringrdquoIEEE Transactions on Fuzzy Systems vol 11 no 6 pp 709ndash7152003

[26] J Li X-B Gao and L-C Jiao ldquoNew fuzzy clustering algorithmbased on feature weightingrdquo Electronic Journal vol 34 no 1 pp89ndash92 2006

[27] W Zebing and C Baozhen ldquoThe study of an improved FCMclustering algorithmrdquo in Proceedings of the 2nd InternationalConference on Signal Processing Systems (ICSPS rsquo10) vol 2 ppV2-96ndashV2-100 IEEE Dalian China July 2010

[28] J F Zhang Y Bai J Yu et al ldquoForecast of red tide in theSouth China sea by using the variation trend of hydrologicaland meteorological factorsrdquoMarine Science Bulletin vol 8 no2 pp 60ndash74 2006

[29] W Jin-Pei and S De-Shan Modern Data Analysis MachineryIndustry Press Beijing China 2006


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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


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Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


effect on the marine economy sustainable development inour country therefore the prediction research of red tidehas an important meaning in environmental protection andreducing the economic loss [10ndash12]

According to the research on the prediction of red tidethere are alreadymany predictionmethods such as empiricalprediction method statistical prediction method numericalmodel prediction method and artificial neural network [13ndash15]

(1) Empirical Prediction Method There is a certain regularitybetween the occurrence of red tide and the changes ofenvironmental factors such as meteorological conditionsoceanographic processes and ecological factors Empiricalprediction method is based on the certain regularity

(2) Statistical Prediction Method The empirical predictionmethod only depends on the change of a certain environmen-tal factor However red tide in fact is caused by many factorsThe statistical prediction method can have comprehensiveanalysis on the factors therefore it has stronger predictiveability Its main method includes principal component anal-ysis discriminant analysis and stepwise regression method

(3) Numerical Model Prediction Method Due to the lackof detailed understanding of the occurrence mechanism ofred tide statistical prediction method is to a certain degreesubjective and blind Numerical model prediction methoduses a variety of mathematical tools to analyze solve andsimulate the model based on various physical and chemicalbiological coupling factors

(4) Artificial Neural Network With the rapid development ofcomputer technology artificial intelligence technology andbiotechnology artificial neural network has been applied tothe prediction of the red tide However the research of thismethod has been a certain constraint because it has the slowconvergence speed and it is easy to fall into local minimumvalues

22 Research on the Fuzzy 119888-Means Clustering AlgorithmClustering is one of the most basic activities of humanunderstanding of the world The purpose of clustering isto make the same class of things as similar as possibleand different categories of things as different as possibleAccording to the different values of membership degreethe clustering method can be divided into hard clusteringmethod and fuzzy clustering method As for the hard clus-tering method 0 means that the sample must not fall intothis category and 1 means that the sample must belong to thiscategory Fuzzy clustering method is a combination of fuzzytheory and clustering analysisThe fuzzy clustering algorithmproposed by Dunn and extended by Bezdek is the mostwell-known and the most frequently used method [16] Themajor algorithms include transitive closure method based onfuzzy equivalence relation the method based on similarityrelation and fuzzy relation and most tree method based onfuzzy graph theory However these methods have the high

complexity of calculation and are not suitable for large datatherefore they have been gradually reduced in research Thefuzzy clustering algorithm based on objective function iswidely studied Within-Groups Sum of Squared Error is usedto construct the objective function This algorithm is simpleand effective also supported by classical theory Fuzzy 119888-means clustering algorithm is the most widely used fuzzyclustering algorithm based on objective function [17]

Let 119883 = 1199091 1199092 119909

119899 be sample dataset with 119899

samples and each sample 119909119896has 119904 properties namely 119909

119896=

1199091198961 1199091198962 119909

119896119904 then the matrix of the sample dataset can

be expressed as follows

119883 = (119909119899119904) 119899 = 1 2 119899 119904 = 1 2 119904 (1)

The objective function of FCM clustering algorithm119869119898(119880 119881) is defined as [18ndash20]

119869119898(119880 119881) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894) (2)

where 119888 is clustering category 2 le 119888 le 119899 119880 is matrix ofmembership degree 119880 = 120583

119894119896 119894 = 1 2 119888 119896 = 1 2 119899

119881 is matrix of cluster center 119881 = V119894 119894 = 1 2 119888 120583

119894119896is

membership degree of the 119896th element in the 119894th clusteringcategory V

119894is cluster center of the 119894th clustering category

V119894= V1198941 V1198942 V

119894119904 119894 = 1 2 119888 119898 is weighting exponent

and empirical value is 15 le 119898 le 25 119889119894119896(119909119896 V119894) is the

Euclidean distance of target data between 119909119896and V119894

The basic idea of FCM algorithm is to find fuzzymatrix ofmembership degree and cluster center making the objectivefunction minimum

Membership degree function satisfies the following equa-tions

119888

sum

119894=1

(120583119894119896)119898

= 1 forall119896

119899

sum

119896=1

(120583119894119896)119898

ge 0 forall119894

120583119894119896isin [0 1] forall119894 119896

(3)

According to the Lagrange multiplier optimization algo-rithm the update formulas ofmembership degree and clustercenter are expressed as

120583119894119896=

1

sum119888

119897=1[119889119894119896(119909119896 V119894) 119889119897119896(119909119896 V119897)]2(119898minus1)

119894 = 1 2 119888 119896 = 1 2 119899

(4)

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896

sum119899

119896=1(120583119894119896)119898

119894 = 1 2 119888 (5)

FCM algorithm is described as follows

Step 1 Give the number of clustering categories 119888 (2 le 119888 le 119899)Set the number of iterations 119896 = 1 weighting exponent 119898and stop parameters 120576





119894(119896 + 1)

Step 5 If V119894(119896+1)minus V






Let 119883 = 1199091 1199092 119909









Class 2Class 1








119894119895is







119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(6)

where 120578119894119895= 120573(min119889

119894119896(V119894 119909119896) 119889119895119896(V119895 119909119896)max119889

119886119887(V119886 V119887))




120597119869119898

120597V119894

= 0 997904rArr

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1(120578119894119895)

119898

(7)

120583119894119896

=

(119889119894119896

2(119909119896 V119894))


sum119888

119895=1(119889119895119896

2(119909119896 V119895))

minus1(119898minus1)119889119894119896

2(119909119896 V119894) gt 0 (1 le 119895 le 119888)

1 119889119894119896

2(119909119896 V119894) = 0 (1 le 119895 le 119888)

0 119895 = 119894 119889119895119896

2(119909119896 V119895) = 0

(8)





119903119894119895=

sum119904

119901=1

10038161003816100381610038161003816V119894119901minus V119894

10038161003816100381610038161003816

10038161003816100381610038161003816V119895119901minus V119895

10038161003816100381610038161003816

[sum119904

119901=1(V119894119901minus V119894)

2

sum119904

119901=1(V119895119901minus V119895)

2

]

12 (9)

where V119894= (1119904)sum

119904

119901=1V119894119901 V119895= (1119904)sum

119904

119901=1V119895119901 1 le 119894 119895 le 119888 V

119894119901



119903119894119895=

2sum119904

119901=1min (V

119894119901 V119895119901)

sum119904

119901=1(V119894119901+ V119895119901)

(10)


119903119894119895=

sum119904

119901=1V119894119901V119895119901

radicsum119904

119901=1V119894119901

2radicsum119904

119901=1V119895119901

2

(11)




119871119895=

119888

sum

119875=1

119903119901119895

119871119894119895=

119903119894119895

119871119895

(12)


119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

119871119894119895(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(13)


V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1119871119894119895(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1119871119894119895(120578119894119895)

119898 (14)


1199091015840

119899119904=

119909119899119904minus 119909119899

119904119899

(15)

where 119909119899= (1119904)sum

119904

119895=1119909119899119904 119904119899= radic(1(119904 minus 1))sum

119904

119895=1(119909119899119904minus 119909119899)2









Step 5 If V119894(119896+1)minus V




119889119894119896(V119894 119909119896) le 119889119895119896(V119895 119909119896)

119896 = 1 2 119899 119894 119895 = 1 2 119888

(16)








SampleNitrogen



1 04 1482 054 1093 01 7154 007 3185 054 1096 031 837 042 11318 021 9339 018 31110 021 97211 04 74512 036 12513 056 18714 039 14615 007 3216 047 20517 043 13618 043 14719 026 16020 032 105421 037 1037


0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity






FCM PCM DWFCM




0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity



0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity






FCM PCM DWFCM






0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency





5 Conclusion


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119894(119896 + 1)

Step 5 If V119894(119896+1)minus V






Let 119883 = 1199091 1199092 119909









Class 2Class 1








119894119895is







119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(6)

where 120578119894119895= 120573(min119889

119894119896(V119894 119909119896) 119889119895119896(V119895 119909119896)max119889

119886119887(V119886 V119887))




120597119869119898

120597V119894

= 0 997904rArr

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1(120578119894119895)

119898

(7)

120583119894119896

=

(119889119894119896

2(119909119896 V119894))


sum119888

119895=1(119889119895119896

2(119909119896 V119895))

minus1(119898minus1)119889119894119896

2(119909119896 V119894) gt 0 (1 le 119895 le 119888)

1 119889119894119896

2(119909119896 V119894) = 0 (1 le 119895 le 119888)

0 119895 = 119894 119889119895119896

2(119909119896 V119895) = 0

(8)





119903119894119895=

sum119904

119901=1

10038161003816100381610038161003816V119894119901minus V119894

10038161003816100381610038161003816

10038161003816100381610038161003816V119895119901minus V119895

10038161003816100381610038161003816

[sum119904

119901=1(V119894119901minus V119894)

2

sum119904

119901=1(V119895119901minus V119895)

2

]

12 (9)

where V119894= (1119904)sum

119904

119901=1V119894119901 V119895= (1119904)sum

119904

119901=1V119895119901 1 le 119894 119895 le 119888 V

119894119901



119903119894119895=

2sum119904

119901=1min (V

119894119901 V119895119901)

sum119904

119901=1(V119894119901+ V119895119901)

(10)


119903119894119895=

sum119904

119901=1V119894119901V119895119901

radicsum119904

119901=1V119894119901

2radicsum119904

119901=1V119895119901

2

(11)




119871119895=

119888

sum

119875=1

119903119901119895

119871119894119895=

119903119894119895

119871119895

(12)


119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

119871119894119895(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(13)


V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1119871119894119895(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1119871119894119895(120578119894119895)

119898 (14)


1199091015840

119899119904=

119909119899119904minus 119909119899

119904119899

(15)

where 119909119899= (1119904)sum

119904

119895=1119909119899119904 119904119899= radic(1(119904 minus 1))sum

119904

119895=1(119909119899119904minus 119909119899)2









Step 5 If V119894(119896+1)minus V




119889119894119896(V119894 119909119896) le 119889119895119896(V119895 119909119896)

119896 = 1 2 119899 119894 119895 = 1 2 119888

(16)








SampleNitrogen



1 04 1482 054 1093 01 7154 007 3185 054 1096 031 837 042 11318 021 9339 018 31110 021 97211 04 74512 036 12513 056 18714 039 14615 007 3216 047 20517 043 13618 043 14719 026 16020 032 105421 037 1037


0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity






FCM PCM DWFCM




0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity



0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity






FCM PCM DWFCM






0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency





5 Conclusion


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(6)

where 120578119894119895= 120573(min119889

119894119896(V119894 119909119896) 119889119895119896(V119895 119909119896)max119889

119886119887(V119886 V119887))




120597119869119898

120597V119894

= 0 997904rArr

V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1(120578119894119895)

119898

(7)

120583119894119896

=

(119889119894119896

2(119909119896 V119894))


sum119888

119895=1(119889119895119896

2(119909119896 V119895))

minus1(119898minus1)119889119894119896

2(119909119896 V119894) gt 0 (1 le 119895 le 119888)

1 119889119894119896

2(119909119896 V119894) = 0 (1 le 119895 le 119888)

0 119895 = 119894 119889119895119896

2(119909119896 V119895) = 0

(8)





119903119894119895=

sum119904

119901=1

10038161003816100381610038161003816V119894119901minus V119894

10038161003816100381610038161003816

10038161003816100381610038161003816V119895119901minus V119895

10038161003816100381610038161003816

[sum119904

119901=1(V119894119901minus V119894)

2

sum119904

119901=1(V119895119901minus V119895)

2

]

12 (9)

where V119894= (1119904)sum

119904

119901=1V119894119901 V119895= (1119904)sum

119904

119901=1V119895119901 1 le 119894 119895 le 119888 V

119894119901



119903119894119895=

2sum119904

119901=1min (V

119894119901 V119895119901)

sum119904

119901=1(V119894119901+ V119895119901)

(10)


119903119894119895=

sum119904

119901=1V119894119901V119895119901

radicsum119904

119901=1V119894119901

2radicsum119904

119901=1V119895119901

2

(11)




119871119895=

119888

sum

119875=1

119903119901119895

119871119894119895=

119903119894119895

119871119895

(12)


119869119898(119880 119881 120578) =

119899

sum

119896=1

119888

sum

119894=1

(120583119894119896)119898

119889119894119896

2(119909119896 V119894)

minus

1

119888 (119888 minus 1)

119888

sum

119894=1

119888

sum

119895=1

119871119894119895(120578119894119895)

119898

119889119894119895

2(V119894 V119895)

(13)


V119894=

sum119899

119896=1(120583119894119896)119898

119909119896minus (1119888 (119888 minus 1))sum

119888

119895=1119871119894119895(120578119894119895)

119898

V119895

sum119899

119896=1(120583119894119896)119898

minus (1119888 (119888 minus 1))sum119888

119895=1119871119894119895(120578119894119895)

119898 (14)


1199091015840

119899119904=

119909119899119904minus 119909119899

119904119899

(15)

where 119909119899= (1119904)sum

119904

119895=1119909119899119904 119904119899= radic(1(119904 minus 1))sum

119904

119895=1(119909119899119904minus 119909119899)2









Step 5 If V119894(119896+1)minus V




119889119894119896(V119894 119909119896) le 119889119895119896(V119895 119909119896)

119896 = 1 2 119899 119894 119895 = 1 2 119888

(16)








SampleNitrogen



1 04 1482 054 1093 01 7154 007 3185 054 1096 031 837 042 11318 021 9339 018 31110 021 97211 04 74512 036 12513 056 18714 039 14615 007 3216 047 20517 043 13618 043 14719 026 16020 032 105421 037 1037


0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity






FCM PCM DWFCM




0

01

02

03

04

05

06

07

08

09

1

Phyt

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nsity



0

01

02

03

04

05

06

07

08

09

1

Phyt

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nkto

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FCM PCM DWFCM






0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency





5 Conclusion


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Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Step 5 If V119894(119896+1)minus V




119889119894119896(V119894 119909119896) le 119889119895119896(V119895 119909119896)

119896 = 1 2 119899 119894 119895 = 1 2 119888

(16)








SampleNitrogen



1 04 1482 054 1093 01 7154 007 3185 054 1096 031 837 042 11318 021 9339 018 31110 021 97211 04 74512 036 12513 056 18714 039 14615 007 3216 047 20517 043 13618 043 14719 026 16020 032 105421 037 1037


0

01

02

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04

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06

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08

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FCM PCM DWFCM




0

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01

02

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FCM PCM DWFCM






0

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1

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0

01

02

03

04

05

06

07

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09

1

Tran

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ency





5 Conclusion


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











FCM PCM DWFCM




0

01

02

03

04

05

06

07

08

09

1

Phyt

opla

nkto

n de

nsity



0

01

02

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04

05

06

07

08

09

1

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n de

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FCM PCM DWFCM






0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency





5 Conclusion


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency


0

01

02

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07

08

09

1

Tran

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ency





5 Conclusion


0

01

02

03

04

05

06

07

08

09

1

Tran

spar

ency






Acknowledgment


References







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article prediction research of red tide based on ...red tide, statistical prediction method...

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