On Mahalanobis distance based fuzzy c-means clustering for uncertain data using penalty vector regularization

This paper presents Mahalanobis distance based fuzzy c-means clustering for uncertain data using penalty vector regularization. When we handle a set of data, data contains inherent uncertainty e.g., errors, ranges or some missing value of attributes. In order to handle such uncertain data as a point in a pattern space the concept of penalty vector has been proposed. Some significant clustering algorithms based on it have been also proposed. In conventional clustering algorithms, Mahalanobis distance have been used as dissimilarity as well as squared L₂ and L₁-norm. From the viewpoint of the guideline of dissimilarity, Mahalanobis distance based fuzzy c-means clustering for uncertain data should be considered. In this paper, we introduce fuzzy c-means clustering for uncertain data using penalty vector regularization as our conventional works. Next, we propose Mahalanobis distance based one. Moreover, we show the effectiveness of proposed method through numerical examples.