Yang-type and Extended Q-type Fuzzy Clustering for Series Data

Abstract

Various fuzzification techniques have been applied to clustering algorithms for vectorial data, such as Yang-type fuzzification and extended q-divergence-regularization, whereas only a few such techniques have been applied to fuzzy clustering algorithms for series data. In this regard, this study presents four fuzzy clustering algorithms for series data. The first two algorithms are obtained by penalizing each optimization problem in the two conventional algorithms: Bezdek-type fuzzy dynamic-time-warping (DTW) c-means and Bezdek-type fuzzy c-shape, with the cluster-size controller fixed. The other two algorithms are obtained from a conventional algorithm, q-divergence-based fuzzy DTW c-means or q-divergence-based fuzzy c-shape, by distinguishing two fuzzificators for membership from those for cluster-size controllers. Numerical experiments are conducted to evaluate the performance of the proposed algorithms.