Inductive and non-inductive methods of clustering

This paper aims to overview a variety of methods of clustering by introducing the concepts of inductive and non-inductive clustering. These concepts are in parallel with the concepts of inductive and transductive learning in the studies of semi-supervised classification. When the result of clustering naturally induces functions for classification on the whole space of interest, the method is called that of inductive clustering. In contrast, a method is called non-inductive, if it does not induce such a function. Typical examples in the inductive class are crisp and fuzzy c-means, while one of the non-inductive class is agglomerative hierarchical clustering. We show how differences of the two classes of methods of clustering occur in the theoretical consideration of clustering algorithms, in particular two concepts are clearly contrasted when positive-definite kernel functions are employed. Moreover semi-supervised classification is considered for the two classes.