Applying the Possibilistic c-Means Algorithm in Kernel-Induced Spaces
Maurizio Filippone, Francesco Masulli and Stefano Rovetta
IEEE Transactions on Fuzzy Systems Volume 18, Number 3, pp. 572-584, 2011.

Abstract

In this paper, we study a kernel extension of the classic possibilistic clustering. 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 SVM 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 data sets. The results show high stability and good performances in terms of accuracy.

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