Probability Models of Classification

Abstract

Applying a clustering algorithm to a set of data results in a classification of objects whether the data exhibit a true or “natural” grouping structure or not. This is no problem if clustering is done for obtaining a practical stratification of a given set of objects for organisational purposes. Such purposes justify even purely artificial groupings (random clusters). In exploratory data analysis however, interest lies in uncovering an unknown clustering structure of the data. Here, the result of a clustering procedure should reflect the real structure (real or natural clusters). From the group structure of the objects of a sample S,we usually derive probability models on a population. Here, an artificial clustering is not acceptable. The classes resulting from the algorithm must, in addition, be investigated for their relevance and their validity.