Neural Nonnegative Latent Factorization of Tensors Model With Acceleration and Unconstraint

The traditional nonnegative latent factorization of tensors (NLFTs) models can effectively represent high-dimensional and incomplete (HDI) tensors, but they currently face two main problems: 1) existing models are linear and cannot capture the nonlinear features of HDI tensors and 2) they rely on random initialization of nonnegative parameter and constraint-combined training schemes. To address these issues, this article proposes a neural NLFTs model with acceleration and unconstraint. The main ideas are given as follows: 1) utilizing a neural network (NN) structure and a nonlinear activation function to capture the nonlinear features within the HDI tensor accurately; 2) constructing a nonnegative mapping domain that transfers nonnegativity constraints from latent factors (LFs) to output decision parameters via a single-element-dependent mapping function, enabling an unconstrained optimization framework; and 3) utilizing the highly compatible momentum-incorporated stochastic gradient descent (SGD) algorithm as the backward propagation (BP) learning scheme of the model, which not only ensures training effectiveness and scalability but also accelerates convergence. Empirical studies on ten HDI tensors demonstrate that the proposed model achieves impressive estimation accuracy and per-iteration time cost compared to state-of-the-art models.