Section 5.2.1 defined a pattern distance measure between closed patterns \(P_{1}\) and \(P_{2}\) as

\[\text { Pat_Dist }\left(P_{1}, P_{2}ight)=1-\frac{\left|T\left(P_{1}ight) \cap T\left(P_{2}ight)ight|}{\left|T\left(P_{1}ight) \cup T\left(P_{2}ight)ight|}\]

where \(T\left(P_{1}ight)\) and \(T\left(P_{2}ight)\) are the supporting transaction sets of \(P_{1}\) and \(P_{2}\), respectively. Is this a valid distance metric? Show the derivation to support your answer.

Section 5.2.1

Pattern compression can be achieved by pattern clustering. Clustering techniques are described in detail in Chapters 8 and 9. In this section, it is not necessary to know the fine details of clustering. Rather, you will learn how the concept of clustering can be applied to compress frequent patterns. Clustering is the automatic process of grouping similar objects together, so that objects within a cluster are similar to one another and dissimilar to objects in other clusters. In this case, the objects are frequent patterns. The frequent patterns are clustered using a tightness measure called δ-cluster. A representative pattern is selected for each cluster, thereby offering a compressed version of the set of frequent patterns.....