Clustering Methodology for Symbolic Data

4Dissimilarity, Similarity, and Distance Measures: Modal Data

In Chapter 3 , the basic principles and properties of dissimilarity/similarity and distance measures were introduced. Detailed measures for multi‐valued list observations and interval‐valued observations were described and illustrated. In this chapter, we discuss dissimilarity/similarity and distance measures for modal data, i.e., modal multi‐valued data in section 4.1 and histogram‐valued data in section 4.2.

4.1 Dissimilarity/Distance Measures: Modal Multi‐valued List Data

As in Chapter 3 , we suppose our sample space consists of objects , and suppose the realization of each object contains modal multi‐valued list values for the ‐dimensional random variable in the form

(4.1.1)

where is the th th category observed from the ...