Use of relevant principal components to define a simplified multivarate test procedure of optimal clustering

Clustering is the problem of partitioning data into a finite number, k, of homogeneous and separate groups, called clusters. A good choice of k is essential for obtaining meaningful clusters. The intraclass correlation coefficient r is frequently used to measure the degree of intragroup resemblance (for example of characteristics such as blood pressure, weight and height). The theory concerning r is well established for single variables analysis (Sheff`e, 1959; Rao, 1973). In this paper, this task is addressed by means of a multiple test procedure defining the optimal cluster solution under normality assumption of the involved variables. Relevant principal components are used to define a simplified multivariate test of null intraclass correlation procedure and the proposal of a new statistical stopping rule is evaluated.