Nonparametric fisher kernel using fuzzy clustering

Abstract

The Fisher kernel, which refers to the inner product in the feature space of the Fisher score, has been known to be a successful tool for feature extraction using a probabilistic model. If an appropriate probabilistic model for given data is known, the Fisher kernel provides a discriminative classifier such as support vector machines with good generalization. However, if the distribution is unknown, it is difficult to obtain an appropriate Fisher kernel. In this paper, we propose a new nonparametric Fisher-like kernel derived from fuzzy clustering instead of a probabilistic model, noting that fuzzy clustering methods such as a family of fuzzy c-means are highly related to probabilistic models, e.g., entropy-based fuzzy c-means and a Gaussian mixture distribution model. The proposed kernel is derived from observing the last relationship. Numerical examples show the effectiveness of the proposed method. © Springer-Verlag Berlin Heidelberg 2006.