Twin Tensor Learning for Consistency and Inconsistency: A Unified Affinity Learning Framework for Multi-View Clustering

Due to the efficiency of discovering the high-order correlations of multiple views, tensorized multi-view clustering (TMVC) has been extensively investigated and achieve impressive performance. However, previous TMVC studies merely emphasize on exploring the multi-view consistency, but rarely consider the cross-view inconsistency that may be caused by noise, corruptions or view-specific properties, rendering the abundant information contained in multiple features cannot be comprehensively detected. To this end, this paper proposes aTwin tensOrized affinity learning framewOrk for mulTi-view cluStering (TOOTS), which seamlessly integrates multi-view consistency and cross-view inconsistency into a unified framework. Specifically, the TOOTS model employs the self-representation mechanism to learn two sets of affinity matrices, which are reorganized into twin tensors (i.e., consistent tensor and diverse tensor). Meanwhile, tensor low-rank constraint and exclusive lasso with$\ell _{21}$regularization are imposed on consistent part and diverse part respectively, leading to the intra-view spatial structure and the inter-view inconsistency be exploited simultaneously. Furthermore, the multiple consistent factors are manipulated by a connectivity constraint and fused into a consensus graph with different weights, making the explicit clusters structural and the salient difference between views effectively leveraged. Substantial experimental results demonstrate that the proposed TOOTS model outperforms state-of-the-arts.