Inductive vs. transductive clustering using kernel functions and pairwise constraints

In parallel with the inductive and transductive learning, we introduce the concepts of inductive and transductive clustering: when the result of clustering induces a function for classification on the entire space of interest, the method is called that of inductive clustering, whereas a method does not induce such a function, it is called transductive. Typical examples in the former class are crisp and fuzzy c-means, while one of the latter is agglomerative hierarchical clustering. These two concepts are clearly contrasted when kernel functions are employed. We show differences of the two classes of methods of clustering, in particular the latter class has what we call explicit mappings for kernel functions, while the former does not. Moreover pairwise constraints are considered for two methods, one from each class, and investigate effects of the constraints by typical examples.