Clustering of Human Sleep Recordings Using a Quantile Representation of Stage Bout Durations - Biomedical Engineering Systems and Technologies - page 356

paralysis =
-0.015 wake.Q1 + 0.012 wake.Q2 + 0.0037 wake.Q3
-0.22 NREM1.Q1 + 0.07 NREM1.Q3
+0.03 NREM2.Q1 + 0.018 NREM2.Q2
-0.0045 REM.Q1 - 0.012
Fig. 9. Least squares linear regression model of paralysis ( r 2 < 0 . 01 )

a sensation of muscular weakness or paralysis during laughter, anger, or emotional situ-
ations, and the recollection of vivid dreams and nightmares, differ significantly among
clusters for k =2 , 3 , and are highest in cluster 2 for k =2 , 3 ( p< 0 . 05 ); an un-
comfortable crawly sensation in the legs that is relieved by walking differs significantly
( p< 0 . 05 ) among clusters for k =3 , 4 , and is lowest in cluster 2 .

Comparison with Multivariate Linear Regression. Given the significant differences
in health variables in section 3.4, it is natural to ask if linear regression can provide
good predictions of one of these variables, such as a muscle weakness or paralysis in
emotional situations, based on bout duration statistics. For k =3 , least squares linear
regression yields the model in Fig. 9 (coefficients to two significant digits).
Although terms involving wake bout duration quartiles, which as discussed in sec-
tion 3.3 differentiate cluster 2 from the others, and in which paralysis attains its max-
imum value as discussed in section 3.4, appear in the regression model of Fig. 9, the
linear correlation between paralysis and the predictions of the least squares linear re-
gression model is less than 0 . 06 . Thus, this model explains a fraction that is less than
0 . 06 2 , much less than 1% , of the variance in paralysis. Nonlinear predictive models ob-
tained through regression based on the machine learning technique of Support Vector
Machines (SVM) provide slightly improved performance here. In any case, the fact that
paralysis differs significantly among the bout duration-based groupings found through
clustering, shows that machine learning can uncover structure in health-related data that
is not clearly identified by traditional statistical techniques such as linear regression.

4 Conclusions and Future Work

The durations of maximal uninterrupted periods in a given sleep stage are important in
the description of sleep structure. This paper has applied unsupervised machine learning
to the discovery of patterns in human sleep data based on stage bout durations, utilizing
a compressed representation in terms of the quantiles of the stage bout duration distri-
butions. The results identify groups of hypnograms with statistically distinct differences
in bout durations among groups ( p< 0 . 05 ), even after a Benjamini-Hochberg correc-
tion for increased type I error due to multiple comparisons. Each group is characterized
by bout duration features for specific sleep stages.
Sleep latency, a variable not among those used for clustering, is also shown to differ
significantly among the bout duration groups. Significant differences are also found for
several variables corresponding to items on the Epworth Daytime Sleepiness question-
naire, such as muscular weakness or paralysis associated with emotional situations,
the recollection of vivid dreams or nightmares after waking, and an uncomfortable