Nonconvex Low-Rank Tensor Representation for Multi-View Subspace Clustering with Insufficient Observed Samples

Multi-view subspace clustering (MVSC) separates the data with multiple views into multiple clusters, and each cluster corresponds to one certain subspace. Existing tensor-based MVSC methods construct self-representation subspace coefficient matrices of all views as a tensor, and introduce the tensor nuclear norm (TNN) to capture the complementary information hidden in different views. The key assumption is that the data samples of each subspace must be sufficient for subspace representation. This work proposes a nonconvex latent transformed low-rank tensor representation framework for MVSC. To deal with the insufficient sample problem, we study the latent low-rank representation in the multi-view case to supplement underlying observed samples. Moreover, we propose to use data-driven transformed TNN (TTNN), resulting from the intrinsic structure of multi-view samples, to preserve the consensus and complementary information in the transformed domain. Meanwhile, the proposed unified nonconvex low-rank tensor representation framework can better learn the high correlation among different views. To resolve the proposed nonconvex optimization model, we propose an effective algorithm under the framework of the alternating direction method of multipliers and theoretically prove that the iteration sequences converge to the critical point. Experiments on various datasets showcase outstanding performance.