In this paper we present Collaborative Low-Rank Subspace Clustering. Given multiple observations of a phenomenon we learn a unified representation matrix. This unified matrix incorporates the features from all the observations, thus increasing the discriminative power compared with learning the representation matrix on each observation separately. Experimental evaluation shows that our method outperforms subspace clustering on separate observations and the state of the art collaborative learning algorithm.
The work most closely related and which inspires our work is the so called Multi-Task Low-rank Affinity Pursuit (MLAP) @cite_41 . MLAP adopts the low-rank representation model for each individual observation and fuses them together by seeking sparsity consistent low-rank coefficients. The MLAP objective is the following where @math , @math and @math are observation data, the fitting error and coefficient matrices for the @math th observation respectively, @math is the number of observations, the @math norm is defined as @math , @math and @math is the vectorisation operator such that @math .
@cite_41
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In this paper, we explore the problem of multiview subspace clustering. We introduce a low-rank tensor constraint to explore the complementary information from multiple views and, accordingly, establish a novel method called Low-rank Tensor constrained Multiview Subspace Clustering (LT-MSC). Our method regards the subspace representation matrices of different views as a tensor, which captures dexterously the high order correlations underlying multiview data. Then the tensor is equipped with a low-rank constraint, which models elegantly the cross information among different views, reduces effectually the redundancy of the learned subspace representations, and improves the accuracy of clustering as well. The inference process of the affinity matrix for clustering is formulated as a tensor nuclear norm minimization problem, constrained with an additional L2,1-norm regularizer and some linear equalities. The minimization problem is convex and thus can be solved efficiently by an Augmented Lagrangian Alternating Direction Minimization (AL-ADM) method. Extensive experimental results on four benchmark datasets show the effectiveness of our proposed LT-MSC method.