Applying the possibilistic C-means algorithm in kernel-induced spaces

Filippone, M., Masulli, F. and Rovetta, S. (2010) Applying the possibilistic C-means algorithm in kernel-induced spaces. IEEE Transactions on Fuzzy Systems, 18(3), pp. 572-584. (doi: 10.1109/TFUZZ.2010.2043440)

Abstract

In this paper, we study a kernel extension of the classic possibilistic c-means. In the proposed extension, we implicitly map input patterns into a possibly high-dimensional space by means of positive semidefinite kernels. In this new space, we model the mapped data by means of the possibilistic clustering algorithm. We study in more detail the special case where we model the mapped data using a single cluster only, since it turns out to have many interesting properties. The modeled memberships in kernel-induced spaces yield a modeling of generic shapes in the input space. We analyze in detail the connections to one-class support vector machines and kernel density estimation, thus, suggesting that the proposed algorithm can be used in many scenarios of unsupervised learning. In the experimental part, we analyze the stability and the accuracy of the proposed algorithm on some synthetic and real datasets. The results show high stability and good performances in terms of accuracy.

• Item Type: Articles
• Additional Information: (c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting / republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Filippone, Dr Maurizio
• Authors: Filippone, M., Masulli, F., and Rovetta, S.
• Subjects: Q Science > QA Mathematics; Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: IEEE Transactions on Fuzzy Systems
• Publisher: IEEE
• ISSN: 1063-6706
• Copyright Holders: Copyright © 2010 IEEE
• First Published: First published in IEEE Transactions on Fuzzy Systems 18(3):572-584
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher