Algorithms of nonlinear document clustering based on fuzzy multiset model

Fuzzy multiset is applicable as a model of information retrieval because it has the mathematical structure which expresses the number and the degree of attribution of an element simultaneously. Therefore fuzzy multisets can be used also as a suitable model for document clustering. This paper aims at developing clustering algorithms based on a fuzzy multiset model for document clustering. The standard proximity measure of the cosine correlation is generalized in the multiset model and two nonlinear clustering techniques are applied to the existing clustering methods. One introduces a variable for controlling cluster volume sizes; the other one is a kernel trick used in Support Vector Machines. Moreover clustering by competitive learning is also studied. When the kernel trick has been used the classification configuration of data in a high-dimensional feature space is visualized by Self-Organizing Maps. Two numerical examples which use an artificial data and real document data are shown and effects of the proposed methods are discussed.