An information-theoretic fuzzy C-spherical shells clustering algorithm

In this paper, we shall investigate source compression coding theorem from the perspective of robust fuzzy clustering that is derived from the basic fuzzy C-spherical shells (FCSS) algorithm. The proposed information fuzzy C-spherical shells (IFCSS) algorithm tackles the intertwined robust fuzzy clustering problems of outlier detection, prototype initialization and cluster validity in a unified framework of information clustering. The IFCSS addresses fuzzy membership and typicality issues separately through the minimum number and the sensitivity of hyper-parameters in the clustering objective function. We use the basic FCSS algorithm for the clustering phase to minimize the number of hyper-parameters and reduce the difficulty of prototype initialization, especially for spherical shells data. The robustness of IFCSS against noisy points (outliers) is obtained by the maximizing the mutual information (MI), which also provides a good criterion for prototype initialization. The clustering validity criterion for the IFCSS is proposed based on the structural risk minimization principle to achieve an optimal trade-off between the empirical risk (clustering) and model complexity control (cluster number). The effectiveness of the proposed algorithms for clustering spherical shells is supported by experimental results.