Clustering of Human Sleep Recordings Using a Quantile Representation of Stage Bout Durations - Biomedical Engineering Systems and Technologies - page 350

p -values p 1 <p 2 < <p n , and a desired overall level of significance ( p -value) p ,

the Benjamini-Hochberg procedure declares as significant the first k findings, where k
is the largest index i , 1

···

n ,forwhich p i i/n < p . This approach provides rigorous
control of the false discovery rate, the expected proportion of multiple null hypotheses
that are incorrectly rejected due to multiple comparisons. In the present paper, control
of the false discovery rate is performed at the significance level p< 0 . 05 .

≤ i ≤

3R su s

This section describes the results of clustering that were obtained using the hypnogram
data of section 2.1 represented in terms of the quartiles of the stage bout duration dis-
tributions (section 2.2, q =4 ), utilizing EM clustering (section 2.3). In passing, we
note that variants of the bout duration quartile data representation that use more than 4
quantiles were also considered for the present work. The advantage of using a greater
number of quantiles is the ability to describe finer details in the bout duration distribu-
tions. However, clustering stability was considerably lower with such representations,
and so the decision was made to use quartiles only (see section 2.2).

3.1 Clustering Stability

The mean observed value of the adjusted Rand Index (section 2.3) for EM is at least
0 . 87 for the values k =2 , 3 , 4 . The high values of the adjusted Rand Index show that
the EM clustering is only slightly influenced by the initial parameter values, and rep-
resents a stable grouping of the hypnograms. In contrast, the adjusted Rand index of
k -means stays between 0 . 36 and 0 . 53 over the range k =2 , 3 , 4 . For this reason, EM
was selected as the clustering algorithm for the work discussed in the present paper.
The seed value 8 was found to provide an EM clustering of maximum mean adjusted
Rand Index as compared to the other 49 seed values considered, for each k =2 , 3 , 4 .
All results discussed subsequently in this paper utilize the EM clustering resulting from
the seed value 8 .

3.2 Cluster Separation

Visualization of Cluster Separation. The visualization technique of multidimensional
scaling (MDS) provides a low-dimensional nonlinear projection of a dataset in a way
that minimizes distortion of the distances between pairs of data instances [5]. Fig. 3
shows a two-dimensional MDS projection of the set of data instances used in the present
paper. The results of EM clustering did not enter into the generation of the MDS projec-
tion itself. The EM cluster labels for k =3 were used to determine the glyph (marker)
for each instance in the visualization shown. The MDS results show only moderate sep-
aration among the EM clusters in two dimensions, which indicates that more than two
variables are likely to be needed in order to achieve high separation. See section 3.2.