Enhanced subspace clustering with limited prior knowledge using tensor low-rank representation

In this paper, we introduce a new subspace clustering model based on tensor low-rank representation to improve clustering performance under the condition of limited prior knowledge. The proposed model, namely, enhanced and versatile subspace clustering (EVSC), operates in two stages. In the first stage, it augments prior knowledge by employing pairwise constraint propagation to construct a discriminative graph matrix that integrates both prior knowledge and the local geometric structure of the data. In the second stage, this discriminate graph guides the learning of the affinity matrix through a tensor low-rank representation. Specifically, both discriminate graph matrix and affinity matrix are concatenated into a 3D tensor with additional low-rank constraint. Through optimizing this constraint, the discriminate graph matrix complements the affinity matrix, whose discriminate power is improved, and thus boosting clustering performance. EVSC can directly deal with multiview setting, termed MvEVSC. A key feature of MvEVSC is the natural integration of limited prior knowledge and local structural information into the traditional subspace clustering framework, eliminating the need for difficult-to-tune balancing penalty parameters. Furthermore, both EVSC and MvEVSC can be formulated as a convex low-rank tensor representation model, which is efficiently solved using the alternating direction method of multipliers (ADMM). Comprehensive experimental results on eight benchmark datasets demonstrate the superiority of both EVSC and MvEVSC compared to the state-of-the-art methods.