Alternative fuzzy c-lines and local principal component extraction

Authors:
Katsuhiro Honda;Sakuya Nakao;Akira Notsu;Hidetomo Ichihashi
Affiliations:
Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan.;Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan.;Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan.;Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka, 599-8531, Japan
Venue:
International Journal of Knowledge Engineering and Soft Data Paradigms
Year:
2011

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Abstract

Alternative c-means is an extension of k-means-type clustering for robustifying cluster estimation, in which a modified distance measure instead of the conventional Euclidean distance is used based on the robust M-estimation concept. In this paper, alternative c-means is further extended to linear clustering models with line-shape prototypes, in which the clustering criteria of distances between data samples and linear prototypes are calculated by the lower rank approximation concept. The iterative updating scheme is derived in a pseudo-M-estimation procedure with a weight function for the modified distance measure and is demonstrated to be useful for extracting linear substructures from noisy datasets. In numerical experiments, the model is applied to POS transaction data analysis based on local PCA-like data summarisation.