Low-Rank Regularized Heterogeneous Tensor Decomposition Algorithm for Subspace Clustering

Tensor decomposition is a powerful computational tool for analyzing multi-dimensional data. The traditional Tucker decomposition models arc generally proposed based on the isotropy hypothesis, meaning that the factor matrices arc learned in an equivalent way for all modes (such as orthogonal or non-negative constraints), which is not suitable for the heterogeneous tensor data. We propose a low-rank regularized heterogeneous tensor decomposition (LRRHTD) model for subspace clustering. The core idea of LRRHTD is that we seek a set of orthogonal factor matrices for all but the last mode to map the high-dimensional tensor into a low-dimensional latent subspace. In the meantime, we seek the lowest-rank representation of the original tensor by imposing a low-rank constraint on the last mode, in order to reveal the global structure of samples for the purpose of clustering. We also develop an effective optimization algorithm based on augmented Lagrangian multiplier to solve our proposed model. Experiments on two public datasets demonstrate that the proposed method reaches convergence within a small number of iterations and achieves promising clustering results in comparison with state-of-the-art methods.