Robust collaborative clustering approach with adaptive local structure learning

Abstract

Different from one-sided clustering technique based on sample similarity, collaborative clustering captures the sample clustering structure and feature clustering structure by mining the duality between samples and features. Non-negative Matrix Tri-Factorization (NMTF) has become one of the most commonly used frameworks for collaborative clustering due to its excellent geometric significance. Unfortunately, NMTF-based approaches generally suffer from the following drawbacks: (1) Based on a fixed and fallible affinity matrix to explore the spatial intrinsic geometry structure, which limits the spatial exploration ability of the model. (2) Based on the L2 loss function to measure the reconstruction error, which weakens the robustness of the model. (3) Based on strict constraints to preserve the orthogonality of the factor matrix, which increases the burden of model solving. To overcome the aforementioned shortcomings, we propose a novel NMTF-based unsupervised collaborative clustering approach. In particular, we first propose a new adaptive local structure learning strategy to enhance the spatial exploration ability of the model. Secondly, we adopt the L1 loss function to improve the robustness of the model. Thirdly, we relax the orthogonal constraints of the factor matrix as a regularization term to reduce the burden of model solving. Finally, we propose a special four-step iterative algorithm to solve the corresponding model, and prove the convergence of the algorithm. The numerical performance on 3 synthetic data sets and 8 benchmark databases demonstrates that the proposed approach outperforms the state-of-the-art collaborative clustering algorithm.