JACIII Vol.21 No.3 pp. 534-542
doi: 10.20965/jaciii.2017.p0534


Families of Triangular Norm-Based Kernel Functions and Their Application to Kernel k-Means

Kazushi Okamoto

Department of Informatics, Graduate School of Informatics and Engineering, The University of Electro-Communications
1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan

August 4, 2016
February 27, 2017
Online released:
May 19, 2017
May 20, 2017
adjusted rand index, k-means, kernel method, positive-definite kernel, t-norm

This study proposes the concept of families of triangular norm (t-norm)-based kernel functions, and discusses their positive-definite property and the conditions for applicable t-norms. A clustering experiment with kernel k-means is performed in order to analyze the characteristics of the proposed concept, as well as the effects of the t-norm and parameter selections. It is evaluated that the clusters obtained in terms of the adjusted rand index and the experimental results suggested the following : (1) the adjusted rand index values obtained by the proposed method were almost the same or higher than those produced using the linear kernel for all of the data sets; (2) the proposed method slightly improved the adjusted rand index values for some data sets compared with the radial basis function (RBF) kernel; (3) the proposed method tended to map data to a higher dimensional feature space than the linear kernel but the dimension was lower than that using the RBF kernel.

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Last updated on May. 24, 2017