Consider the (relative distance) K-means scheme for outlier detection de- scribed in Section 10.5 and the accompanying figure, Figure 10.10.

Question

(a) The points at the bottom of the compact cluster shown in Figure 10.10
have a somewhat higher outlier score than those points at the top of
the compact cluster. Why?
(a) The points at the bottom of the compact cluster shown in Figure 10.10
have a somewhat higher outlier score than those points at the top of
the compact cluster. Why?
(c) The use of relative distance adjusts for differences in density. Give an
example of where such an approach might lead to the wrong conclusion.

Answer 1

(a) The mean of the points is pulled somewhat upward from the center of
the compact cluster by point D.
(b) No. This point would become a cluster by itself.
(c) If absolute distances are important. For example, consider heart rate
monitors for patients. If the heart rate goes above or below a specified
range of values, then this has an physical meaning. It would be incorrect
not to identify any patient outside that range as abnormal, even though
there may be a group of patients that are relatively similar to each other
and all have abnormal heart rates.