2 Introduction Chap.1 The last two definitions assume that the objects to be clustered are represented as points in the measurement space.We recognize a cluster when we see it in the plane,although it is not clear how we do it.While it is easy to give a functional definition of a cluster,it is very difficult to give an operational definition of a cluster.This is due to the fact that objects can be grouped into clusters with different purposes in mind.Data can reveal clusters of differing"shapes"and "sizes."To compound the problem further,cluster membership can change over time,as is the case with star clusters(Dewdney,1986),and the number of clusters often depends on the resolution (fine versus coarse)with which we view the data. Figure 1.I illustrates some of these concepts for two-dimensional point clusters. How many clusters are there in Figure 1.1?At the global or higher level of similarity,we perceive four clusters in these data,but at the local level or a 88 w89888」 0 o98 oo o 8 8 8 0o0 00 8 8 8 8 85% c8A88 00 8 00°°。000° 00 0 0 Figure 1.1 Clusters of point patterns in two dimensions