Distance metric learning for soft subspace clustering in composite kernel space

• The composite kernel space is constructed based on a set of basis kernels.
• The general form of soft subspace clustering in CKS is presented.
• CKS-EWFC-K and CKS-EWFC-F are proposed under the framework of CKS-SSC.
• The properties of CKS-EWFC-K and CKS-EWFC-F are investigated.
• Both CKS-EWFC-K and CKS-EWFC-F are immune to ineffective kernels.

Soft subspace clustering algorithms have been successfully used for high dimensional data in recent years. However, the existing algorithms often utilize only one distance function to evaluate the distance between data items on each feature, which cannot deal with datasets with complex inner structures. In this paper, a composite kernel space (CKS) is constructed based on a set of basis kernels and a novel framework of soft subspace clustering is proposed by integrating distance metric learning in the CKS. Two soft subspace clustering algorithms, i.e., entropy weighting fuzzy clustering in CKS for kernel space (CKS-EWFC-K) and feature space (CKS-EWFC-F) are thus developed. In both algorithms, the prototype in the feature space is mapped into the CKS by multiple simultaneous mappings, one mapping for each cluster, which is distinct from existing kernel-based clustering algorithms. By evaluating the distance on each feature in the CKS, both CKS-EWFC-K and CKS-EWFC-F learn the distance function adaptively during the clustering process. Experimental results have demonstrated that the proposed algorithms in general outperform classical clustering algorithms and are immune to ineffective kernels and irrelevant features in soft subspace.