Graph Regularized Nonnegative Tensor Ring Decomposition for Multiway Representation Learning
This work addresses the need for more interpretable and effective representation learning in multiway data analysis, though it is incremental as it builds upon existing tensor ring decomposition.
The authors tackled the problem of multiway representation learning by proposing nonnegative tensor ring (NTR) decomposition and its graph-regularized variant (GNTR) to extract interpretable parts-based features from tensor data, resulting in improved performance over state-of-the-art tensor methods in clustering and classification tasks.
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition and graph regularized NTR (GNTR) decomposition are proposed, where the former equips TR decomposition with local feature extraction by imposing nonnegativity on the core tensors and the latter is additionally able to capture manifold geometry information of tensor data, both significantly extend the applications of TR decomposition for nonnegative multiway representation learning. Accelerated proximal gradient based methods are derived for NTR and GNTR. The experimental result demonstrate that the proposed algorithms can extract parts-based basis with rich colors and rich lines from tensor objects that provide more interpretable and meaningful representation, and hence yield better performance than the state-of-the-art tensor based methods in clustering and classification tasks.