Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme

Abstract Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, sparsity only side effect cannot be explicitly controlled without additional regularization. In this paper, we investigated CANDECOMP/PARAFAC (NCP) with sparse regularization item using $$l_1$$ l 1 -norm (sparse NCP). When high imposed, factor matrices will contain more zero not of full column rank. Thus, NCP prone to rank deficiency, algorithms may converge. proposed novel model proximal algorithm. The subproblems in new strongly convex block coordinate descent (BCD) framework. Therefore, provides condition guarantees converge stationary point. addition, an inexact BCD scheme NCP, where each subproblem updated multiple times speed up computation. order prove effectiveness efficiency algorithm, employed two optimization solve model, including alternating quadratic programming hierarchical least squares. We evaluated methods experiments on synthetic, real-world, small-scale, large-scale data. experimental results demonstrate that our can efficiently impose matrices, extract meaningful components, outperform state-of-the-art methods.