Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization
This addresses the challenge of clustering multiarray data without losing structural information, which is important for fields like data analysis, but it appears incremental as it builds on existing tensor factorization methods.
The paper tackles the problem of tensor clustering by proposing a subspace clustering algorithm that avoids vectorization, using a novel heterogeneous Tucker decomposition model with a trust-region method for optimization. Numerical experiments show it competes effectively with state-of-the-art tensor factorization-based clustering algorithms.
Tensors or multiarray data are generalizations of matrices. Tensor clustering has become a very important research topic due to the intrinsically rich structures in real-world multiarray datasets. Subspace clustering based on vectorizing multiarray data has been extensively researched. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model. In contrast to existing techniques, we propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the so-called multinomial manifold, for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization.