A comparative study on cluster validity criteria in linear fuzzy clustering and pareto optimality analysis

Cluster validation is an important issue in cluster analysis. In this paper, a comparative study on validity criteria is performed with linear fuzzy clustering that can be identified with a local PCA technique. Besides the standard fuzzification approach, the entropy regularization approach is responsible for fuzzification of data partition and the approach implies a close relation between FCM-type linear fuzzy clustering and probabilistic PCA models. This comparative study reveals mutual differences between two fuzzification approaches from the view point of cluster validation using several cluster validity criteria. Additional characteristics are shown in a pareto analysis, in which the effect of noise sensitivity is also discussed.