Cauchy loss induced block diagonal representation for robust multi-view subspace clustering

With the rapid emergence of data that can be described by different feature sets or different "views", multi-view subspace clustering has attracted considerable research attention. To uncover the common latent structure shared by multiple views, existing models usually impose the sparse or/and low-rank constraint on the coefficients of each view data, and use Frobenius norm or '1-norm based metric to measure the residuals of multi-view data. However, the intuition behind the sparse or low-rank regularization is implicit. Besides, the Frobenius norm or '1-norm based metric is suitable to handle either Gaussian noise or sparse noise, which are very sensitive to larger noise or outliers. When the data is contaminated by large noise or densely corrupted, performance of existing models is degraded dramatically. In this article, we propose a novel multi-view subspace clustering method to provide superior robustness against large noise or outliers embedded in multi-view data. Our method adopts a more direct and intuitive block diagonal regularization to preserve the underlying structure of each view, and meantime introduces the cauchy loss function to deal with large noise. The derived consensus representation matrix can effectively preserve the underlying common structure of multi-view data and be robust to large noise and data corruptions. Experimental results show that our method outperforms the state-of-the-arts on both synthetic and real-world benchmark datasets. (c) 2020 Elsevier B.V. All rights reserved.