sleep dynamics and sleep disorders: a syntactic approach ... · classifications is achieved....
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1.8.3.02
Sleep Dynamics and Sleep Disorders: a SyntacticApproach to Hypnogram Classification
Ana L. N. Fred* T. Paiva*** Instituto de TelecomunicaEöes, DEEC, Instituto Superior Tdcnico
IST - Torre Norte, Av. Rovisco Pais, 1096 Lisboa Codex PORTUGAL** Centro de Estudos Egas Moniz, Hospital de Santa Maria, Lisboa PORTUGAL
ABSTRACT: This paper addresses the problem of au-
tomatic classification of sleep macrostmcture, as given bythe hypnogram. The proposed approach is based on themodeling of sleep dynamics in terms of stochastic context-free grammars, automatically inferred from the existinghypnogram data. These grammars are then applied in thediscrimination between a control group and six patholog-ical populations. A global performance of 84Vo of correctclassifications is achieved.
INTRODUCTIONSleep macrostructure is composed of patterns in
physiological variables. These patterns are usu-
ally classified into sleep stages, according to the
Rechtschaffen and Kales (R&K) criteria tl] Thehypnogram is the graphical representation of the evo-
lution of sleep stages along the night. The existenceof a typical organization of sleep stages is well known.Some authors have characterized it in terms of statis-tics of transitions between stages, latencies and du-rations. Markovian models have been applied to de-
scribe the transition mechanisms [2]. Concerning the
assessment of sleep quality, tests are usually based onsleep efficiency parameters (global statistics) derived
from the hypnogram.Our perspective is to view the hypnogram as expres-
sion of a language, modeled and analysed in termsof stochastic grammars. We have shown, in previ-ous work [3, 4], the adequacy of syntactic modelingin automatic sleep analysis. Reference [3] concerns
the application of this approach to the comparison ofa population of normals with a population of psychi-
atric (dysthymic) patients. From the structural pointof view, grammars proved to be a natural way of representation, being able to describe the tendencies ofsleep cyclicity and having higher discriminating capac-
ity than statistical tests based on sleep efficiency pa-
rameters. This methodology has been further refinedby the introduction of a priori information in the pro'cess of grammar inference [5] and by modeling stage
duration in terms of attributed grammars [4]. This ad-
Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 1, 1996The 1Oth Nordic-Baltic Conference on Biomedical Engineering, June 9-13, 1996, Tampere, Finland
ditional information has been useful in the classifica-
tion of borderline situations, leading to reduced errorprobability. In this paper stochastic grammars are ap-
plied in the discrimination between seven populations:normal; dysthymia; sleep apnea; generalized anxiety;fibromyalgia; panic disorder; Parkinson disease.
METHODFigure 1 describes schematically the methodology
used.Hypnogram data are translated into string descrip-
tion by selecting as symbols of the language the set
{W, 1,2,3,4, R}, in correspondence with the sleep
stages: wakefulness, stage I,2,3, and 4 non-REM, and
stage REM - Rapid Eyes Movements. Seven popula-
tions were used: normals (39 samples), dysthymic (22
samples), apnea (53 samples), anxiety (21), fibromyal-gia (29), panic (12) and parkinson (20 samples).
For each population, a stochastic context-free gram-mar was inferred using Crespi-Reghizzi's method [6].The estimation of rules probabilities was based on the
method of stochastic presentation. Arbitrary samples
r were then classified using Bayes decision rule:
Decide r€ Population;if Pr(G;lt) > Pr(G1lr), i *i
with
Pr(G ;l') = P r(xl9;) P'r(G i)
Pr(r)
where Pr(xlGt) is the probability of r according tothe rules in the grammar representing population i,and Pr(G;) is the a priori probability of population i'
RESULTSTable 1 shows the results of classifications obtained.
The value in row f , column j represent the percentage
of elements of population i classified as 7. The last
column gives the total error rate for the population ofthe corresponding row.
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Hlpnograns
'w12w123234313131 ...
Stochaslic Grammarc
Figure 1: Methodology in hypnogram analysis andclassification.
Results show clear differences in the temporal or-ganization of sleep stages for the several populationsunder study, as error rates for each population pairare lower than 13%. When considering the discrimi-nation between the seven populations simultaneously,the highest error rate is obtained for the normal pop-ulation (28.2%\, which corresponds to false alarms.
CONCLUSIONS
A fully automatic approach for the modeling andclassification of sleep macrostructure, as given by thehypnogram, was described and applied in the clas-sification of six pathological populations and a con-trol group. According to the proposed methodology,sleep dynamics were modeled by stochastic context-free grammars, inferred from the hypnogram data byan automatic procedure. No a priori informationwas introduced. Using a Bayesian decision criterion,hypnograms from the several populations were classi-fied by determining the probability of being generatedby each of the candidate grammars representing theseveral groups. The inferred grammars showed cleardifferences between the populations under study, be-ing able to discriminate between them.
References
[1] A. Rechtschaffen and A. Kales. A Manual ofStandardized Terminology, Techniques and Scor-ing System for Sleep Stages of Human Subjects.U. S. Government Printing Office, WashingtonDC. 1968.
[2] B Kemp and H. A. Kamphuisen. Simulation ofhuman hypnograms using a markov chain model.Sleep, 9:405-414, 1986.
[3] A. L. N. Fred and J. M. N. Leitäo. Use of stochas-tic grammars for hypnogram analysis. In Proc, ofthe 1lth IAPR Int'l Conference on Pcttern Recog-nition, pages 242-245, August L992.
[4] A. L. N. Fred and J. M. N. Leitåo. AttriburtedGrammars in Hypnogram Analysis. ln Proc, ofthe Int'l Conference on Systems, Man and Cyber-netics, Vancouver, October 1995.
[5] A. L. N. Fred and J. M. N. Leitäo. Solomonoffcoding as a means of introducing prior informa-tion in syntactic pattern recognition. In Proc, ofthe 12th IAPR Int'l Conference on Pattern Recog-nition, Jerusalem, October 1994.
[6] K. S. Fu and T. L. Booth. Grammatical inference:Introduction and survey. IEEE Trans. Sgstems,Man and Cybernetics, SMC-5, January 1975.
Medical & Biological Engineering & Computing Vol. 34, Supplement 1, Part 1, 1996The 1Oth Nordic-Baltic Conference'on Biomedical Engineering, June 9-13, 1996, Tampere, Finland
Classif ication Probability
Norm. Lryst. Apn. Anx. .F'rbr. I,an. Park. .tirr.N ormalDysthymiaApneaAnxietyFibromyalgiaPanic disorderParkinson
/ I.ö4.5D./4.86.90
10.0
81.8J./4.83.48.35.0
62. 5.10
86.80
10.30
10.0
10.39.11.9
90.53.40
5.0
12.80
D./0
86.20
5.0
2.60000
9t.75.0
2.60
1.9000
85.0
28.213.6L3.29.513.88.315.0
Table 1: Classification results (in percentage).
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