Robust Fuzzy K-Means Clustering With Shrunk Patterns Learning

Fuzzy K-Means (FKM) clustering regards each cluster as a fuzzy set and assigns each sample to multiple clusters with a certain degree of membership. However, conventional FKM methods perform clustering on the basis of original data directly where the intrinsic structure of data may be corrupted by the noise or other factors. According, the performance of these methods would be challenged. In this paper, we present a novel fuzzy K-Means clustering model to conduct clustering tasks on the flexible manifold. Technically, we perform fuzzy clustering based on the shrunk patterns which have desired manifold structure. The shrunk patterns can be viewed as an approximation to the original data; and a penalty term is employed to measure the mismatch between them. Moreover, we integrate the learning of shrunk patterns and the learning of membership degree between shrunk patterns and clusters into a unified framework. Consider traditional projected FKM methods usually project samples into a linear subspace, which is overstrict. We further extend the proposed model for projected FKM clustering to find a suitable subspace to fit the non-linear manifold structure of data, reduce the interference of the noise and redundant features and gather homogeneous samples together simultaneously. Two alternating iterative algorithms are derived to solve these models, respectively. Extensive experimental results demonstrate the feasibility and effectiveness of our proposed clustering algorithms.