A Nonconvex Low Rank and Sparse Constrained Multiview Subspace Clustering via $l_{\frac{1}{2}}$-Induced Tensor Nuclear Norm

In the realm of clustering of multi-view data, many of the clustering methods, generate view-specific representations for individual views and conjoin them for final grouping. However, in most of the cases,such methods fail to effectively discover the underlying complementary information and higher order correlations present in a multi-view data. Unlike many of the existing works, this paper proposes a nonconvex low rank tensor approximation based clustering framework for multi-view data, relying on the self-expressiveness property of free submodules. Instead of creating individual representation for each view, the proposed method creates a single optimal representation tensor for all the submodules, with a low tensor rank and an f-diagonal structure. The
$l_{\frac{1}{2}}$
-induced Tensor Nuclear Norm (TNN) incorporated as a low tensor rank constraint, improves the low rankness of the representation tensor. In addition, a structural constraint is integrated into the proposed method by means of a dissimilarity matrix with
$l_{\frac{1}{2}}$
regularization. Furthermore, the proposed dissimilarity matrix is capable of extracting complementary information and higher order correlations underneath each lateral slice more effectively. The clustering efficiency of the proposed method was evaluated using popular evaluation measures on several challenging multi-view datasets. Experimental results of the proposed method were compared to state-of-the-art single-view and multi-view clustering methods. The compared results demonstrate the improved performance of the proposed method over the existing clustering methods.