Fuzzyc-Means Algorithms Using Kullback-Leibler Divergence and Helliger Distance Based on Multinomial Manifold
Ryo Inokuchi, Sadaaki Miyamoto · Journal of Advanced Computational Intelligence and Intelligent Informatics · 2008
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 fuzzyc-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.