Fuzzy c-Means Algorithms Using Kullback-Leibler Divergence and Helliger Distance Based on Multinomial Manifold
Ryo Inokuchi* and Sadaaki Miyamoto**
*Doctoral Program in Risk Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
**Department of Risk Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
In this paper, we discuss fuzzy clustering algorithms for discrete data. Data space is represented as a statistical manifold of the multinomial distribution, and then the Euclidean distance are not adequate in this setting. The geodesic distance on the multinomial manifold can be derived analytically, but it is difficult to use it as a metric directly. We propose fuzzy c-means algorithms using other metrics: the Kullback-Leibler divergence and the Hellinger distance, instead of the Euclidean distance. These two metrics are regarded as approximations of the geodesic distance.
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