Determining the Number of Component Clusters in the Standard Multivariate Normal Mixture Model Using Model-Selection Criteria.

摘要

The problem of clustering individuals is considered within the context of a multivariate normal mixture using model-selection criteria. Often, the number K of components in the mixture is not known. In practical problems, the question arises as to the appropriate choice of k. The problem is to decide how many components are in the mixture, a difficult multiple decision problem. What the null distribution of the criterion is if the data acutally contain k clusters is not known, and remains largely unresolved still. Two well known model-selection criteria, namely Akike's Information Criterion (AIC) and Schwarz's Criterion are proposed for the first time as two new approaches to the problem of what the appropriate choice of k in the mixture multinormal model should be. The forms of these two model-selection criteria are obtained in the standard multivariate normal mixture model. The results are obtained when data initially partitioned into equal size groups; when data initially reordered; when data initialized by k-means algorithm; when data initialized by special initialization scheme; and when special initialization scheme is used on reordered data.