Class-dependent features and multicategory classification

Abstract

The problem of pattern classification is considered for the case of multicategory classification where the number of classes, k, is greater than two. Many classification algorithms are in fast 2-class classifiers and are generalised to solve k-class problems. Which classifiers are naturally multicategory and the nature of the generalisation of a 2-class classifier to k classes is not often investigated. A thorough analysis of multicategory classification is given in this thesis which provides a new taxonomy of popular classification algorithms, and goes on to derive these from a probabilistic viewpoint. A clear distinction is made between classifiers that partition the input space and those that partition the set of k classes. Of the classifiers which partition the set of classes, the one-of-n, pairwise, and hierarchical methods of decomposition are shown to be equivalent in the knowledge of the true data distributions. The scaling properties of these algorithms are analysed for increasing k. The effects of learning models on finite data are then investigated to show the practical differences between each decomposition.

In classification problems with many classes it is commonly the case that different classes exhibit wildly different properties. In this case it is unreasonable to expect to be able to summarise these properties by using features designed to represent all the classes. In contrast, features should be designed to represent subsets of classes that exhibit common properties without regard to any class outside the subset. The value for classes outside the subset may be meaningless, or simply undefined. The multicategory classification schemes proposed explicitly deal with such class-dependent features, and attractive properties of these classifiers are demonstrated for a real-world handwritten digit recognition application.

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