Biomedical Engineering Reference
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(wake.Q3 >= 50) => cluster=cluster2 (10.0/0.0)
(SWS.Q1 >= 30) => cluster=cluster3 (41.0/2.0)
(SWS.Q1 >= 17) and (6 >= wake.Q3 >= 4) => cluster=cluster3 (13.0/3.0)
=> cluster=cluster1 (180.0/37.0)
Fig. 4.
JRIP rules for
3
clusters using wake.Q3 and SWS.Q1 only. Coverage/errors in parentheses
rules do not apply. This particular model attains an accuracy of
0
.
77
and a mean area
under the ROC plot of
0
.
76
. Although the classification performance of the model in
Fig. 4 is unremarkable, it provides an easily understood rough description of the clus-
ters in the case
k
=3
. In particular, it suggests that cluster
2
is associated with high
wake bout durations. This is consistent with Fig. 3. More detailed characterizations of
the various clusters are discussed in section 3.3.
3.3
Statistical Properties of the Bout Duration Clusters
Cluster Sizes and Membership.
The sizes of the EM bout duration clusters appear in
Table 3. Relationships among the three families of clusterings
k
=2
,
3
,
4
are derived
from the detailed membership lists of the various clusters. A simplified description of
the relationships among clusterings for different values of
k
is the following. Additional
characteristics of individual clusters are given in Table 4 and section 3.3.
Relationships between
k
=2
and
k
=3
Clusters.
Cluster
1
in the
k
=2
family splits
into the two
k
=3
clusters labeled
1
and
3
. As discussed in section 3.3 below, the
k
=3
cluster
3
portion is characterized by higher SWS bout duration quartiles than the
k
=3
cluster
1
portion. Two-thirds of the
k
=2
cluster
2
- with higher wake and lower SWS
and REM bout duration quartiles - retains its identity in the
k
=3
family; the remaining
one-third of the
k
=2
cluster
2
joins the
k
=3
cluster
3
. The only inaccuracy in this
description is that
3
of the
33
instances in the
k
=2
cluster
2
join the
k
=3
cluster
1
.
Relationships between
k
=3
and
k
=4
Clusters.
In the transition between
k
=3
and
k
=4
,cluster
1
remains largely unchanged (with only
12
of
148
instances leaving
cluster
1
and joining cluster
4
). Cluster
2
remains mainly within cluster
2
(with
4
of
19
instances joining cluster
4
, which has higher mean REM bout duration quartiles than
cluster
2
; see section 3.3). Two-thirds of the
k
=3
cluster
3
joins the
k
=4
cluster
2
,
and the remaining one-third of
k
=3
cluster
3
remains within the
k
=4
cluster
3
(
8
instances join
k
=4
cluster
4
). However, the
k
=4
cluster
3
retains the characteristic,
shared with
k
=3
cluster
3
, of having the highest SWS bout duration quartiles among
clusters.
Cluster Bout Duration Summary Statistics.
The mean, standard deviation, median,
and mean absolute deviation of the
15
descriptive variables were computed for each of
the EM clusters, with a view toward establishing statistical differences among clusters.
Table 4 provides numerical values of the bout duration quartile means of the different
clusters for
k
=2
,
3
,
4
. Fig. 5, 6, 7 show the mean values of the
15
clustering variables
in the cases
k
=2
,
3
,
4
, respectively. These figures suggest that each cluster is charac-
terized by different bout duration quartiles for one or more of the sleep stages than the
other clusters (e.g., cluster
2
by higher wake duration quartiles).
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