Entropy regularization for unsupervised clustering with adaptive neighbors

Abstract

Graph-based clustering has been considered as an effective kind of method in unsupervised manner to partition various items into several groups, such as Spectral Clustering (SC). However, there are three species of drawbacks in SC: (1) The effects of clustering is sensitive to the affinity matrix that is fixed by original data. (2) The input affinity matrix is simply based on distance measurement, which lacks of clear physical meaning under probabilistic prediction. (3) Additional discretization procedures still need to be operated. To cope with these issues, we propose a new clustering model, which refers to Entropy Regularization for unsupervised Clustering with Adaptive Neighbors (ERCAN), to dynamically and simultaneously update affinity matrix and clustering results. Firstly, the maximized entropy regularization term is introduced in probability model to avoid trivial similarity distributions. Additionally, we newly introduce the Laplacian rank constraint with ℓ0-norm to construct adaptive neighbors for sparsity and strength segmentation ability without extra discretization process. Finally, we present a novel monotonic function optimization method, which reveals the consistence between graph sparsity and neighbor assignment, to address the ℓ0-norm constraint in alternative optimization process. Comprehensive experiments show the superiority of our method with promising results.