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Tensor ring (TR) decomposition is a powerful tool for exploiting the low-ranknature of multiway data and has demonstrated great potential in a variety ofimportant 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 byimposing nonnegativity on the core tensors and the latter is additionally ableto capture manifold geometry information of tensor data, both significantlyextend the applications of TR decomposition for nonnegative multiwayrepresentation learning. Accelerated proximal gradient based methods arederived for NTR and GNTR. The experimental result demonstrate that the proposedalgorithms can extract parts-based basis with rich colors and rich lines fromtensor objects that provide more interpretable and meaningful representation,and hence yield better performance than the state-of-the-art tensor basedmethods in clustering and classification tasks.

Graph Regularized Nonnegative Tensor Ring Decomposition for Multiway Representation Learning