Fuzzy Clustering Algorithm Extracting Principal Components Independent of Subsidiary Variables

Fuzzy c-varieties (FCV) is one of the clustering algorithms in which the prototypes are multi-dimensional linear varieties. The linear varieties are represented by some local principal component vectors and the FCV clustering algorithm can be regarded as a simultaneous algorithm of fuzzy clustering and principal component analysis. However, obtained principal components are sometimes strongly influenced by the dominant factors which are already known as common knowledge. To diminish the influences, we propose a new method of fuzzy clustering algorithm which extracts principal components independent of subsidiary variables. In the algorithm, the dominant factors are used as subsidiary variables. We apply the proposed method to a POS (Point of Sales) transaction data set in order to discover associations among items without being influenced by the explicit dominant factors.