a hierarchical gaussian mixture model for continuous high...
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A Hierarchical Gaussian Mixture Model for Continuous High-Resolution Sleep Analysis
Roman Rosipal1, Stefan Neubauer2, Peter Anderer3,4 Georg Gruber3, Silvia Parapatics3, Michael Woertz1, Georg Dorffner1,2,3
1Austria Research Institute for Artificial Intelligence, Vienna, Austria; 2Institute of Medical Cybernetics and Artificial Intelligence, Center for Brain
Research, Medical University of Vienna, Vienna, Austria; 3The Siesta Group Schlafanalyse GmbH, Vienna, Austria;
4Department of Psychiatry, Medical University of Vienna, Vienna, Austria
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Limits of R&K x Limits of R&K x Probabilistic Continuous Representation of Probabilistic Continuous Representation of
SleepSleep
coarse time resolution (20 or 30 sec) x 3 sec - up to the sampling frequency
limitation to the central electrodes (C3,C4) x multi-electrodes model
amplitude dependent delta waves rule for SWS x AR representation of the power spectra
discrete clustering/classification x continuous probability curves of sleep stages
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0 5 10 15 20 25 30 35 40 45 50-20
-15
-10
-5
0
5
10
15
20
Frequency (Hz)
Pow
er/fr
eque
ncy
(dB
/Hz)
wakes1s2s3s4
Example 1: mean AR(10)Example 1: mean AR(10)--based power spectrumbased power spectrum
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Example 2: 2Example 2: 2--D projection of AR(10) coefficients D projection of AR(10) coefficients -- GTMGTM
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Top-Level Visualization
S2 vs deep (S3+S4)S1 vs S2
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subject b0042, 2nd night, age 74, female, healthy control, filter 15 time points
0 50 100 150 200 250 300 350 400 4500
1
time [min]
deep
0
1
s2
0
1
s1
0
1
wak
e
C4
C3
undefwake
s1s2s3s4
REM
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Gaussian Mixture Model (GMM)Gaussian Mixture Model (GMM)
( ) ( | )k kk K
p x p xα θ∈
=∑ 1, 0k kk K
α α∈
= ≥∑
( ) ( ) ( ) ( )11/ 2/ 2 / 2| 2T
k k kd x xk kp x e µ µθ π
−−− − − Σ −= Σ
where
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group priors, i = 1 ...C
number of componentsmixing proportionsmeans, covariances
Step1: train mixtures of individual classes, set group priors
Step2: unsupervised (semi-supervised) reshuffling, keep structure
p(gC)p(g1) …p(g2)
αi, µi, Σii ∈ G1
αi, µi, Σii ∈ G2
αi, µi, Σii ∈ GC…
Structure of a Hierarchical GMMStructure of a Hierarchical GMM
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Data flow of the model building process
Data flow of the model building process
Spindle process
Artifacts detection
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subject b0042, 2nd night, age 74, female, healthy control, filter 3 time points
0 50 100 150 200 250 300 350 400 4500
1
time [min]
deep
0
1
s2
0
1
s1
0
1
wak
e
C4
C3
undefwake
s1s2s3s4
REM
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subject b0042, 2nd night, age 74, female, healthy control, filter 3 time points
10 20 30 40 50 600
1
time [min]
deep
0
1
s2
0
1
s1
0
1
wak
e
C4
C3
undefwake
s1s2s3s4
REM
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subject b0042, 2nd night, age 74, female, healthy control, filter 15 time points
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ResultsResults
Normal Healthy Subjects (PSQI < 5)
• 176 healthy subjects (83 males and 93 females) aged between 20 and 95 years.
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A) Night differences (pA) Night differences (p--values < 0.01)values < 0.01)
Sleep Quality Index (SSA-1)(Saletu et al. 1987) Mood (VAS score)
c_eff -0.538 rk_eff -0.542
c_wake_tsp 0.527 rk_wake_tsp 0.517
c_rAUC_wake 0.529
c_s1_tst 0.328 rk_s1_tst 0.332
c_rAUC1_s1 0.336
c_s2 -0.303 rk_s2 -0.325
c_rAUC_s2 -0.311
rk_s4 -0.245
c_rAUC2_deep -0.401
c_rAUC1_deep -0.396
c_rAUC_deep -0.289
c_fw 0.300 rk_fw 0.213
0.250c_rAUC_s2
0.201rk_s2_tst0.201c_s2_tst
0.258rk_s20.244c_s2
Drowsiness (VAS score)
-0.197c_AUC1_deep
0.205c_AUC_wake
0.219rk_wake_tsp0.196c_wake_tsp
-0.229rk_eff-0.201c_eff
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B) Individual Nights (pB) Individual Nights (p--values < 0.01)values < 0.01)
c_eff 0.291 rk_eff 0.223
c_AUC1_s2 -0.374
c_wake_tsp -0.387 rk_wake_tsp -0.312
c_AUC1_tsp_wake -0.458
c_AUC2_tsp_wake -0.458
c_fw -0.457 rk_fw -0.307
c_fs -0.423 rk_fs -0.280
c_AUC_s1 -0.337
Fine motor activity test (Grunberger 1977)
0.299rk_s4
-0.277rk_fw-0.354c_fw
0.281rk_eff0.297c_eff
-0.250c_AUC_s2
-0.340c_AUC1_s1
-0.211rk_s1_tst
-0.381c_AUC1_tsp_wake
-0.296rk_wake_tsp-0.307c_wake_tsp
Alphabetical cross-out test (Grunberger 1977)
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ConclusionsConclusions
Continuous probabilistic sleep modeling shows higher flexibility to model several characteristics of sleep (sleep arousals, sleep stages transitions, delta process)
The continues sleep model has shown the same or a higher level of informationabout the sleep process in the investigated correlation and discrimination (not presented here) tasks
The continuous sleep model can successfully complement the R&K standard for a more comprehensive description of sleep
The probabilistic approach allows principled sensor and different processes fusion(spindle process, EOG or EMG modeling) and a new sleep process interpretation