A Fine-Grained Regularization Scheme for Non-negative Latent Factorization of High-Dimensional and Incomplete Tensors

A Dynamically Weighted Directed Network (DWDN) fundamentally illustrates the complex interactions among massive nodes from a big-data-oriented application, like the dynamic interactions among numerous terminals in a metropolitan network management system (MNMS). A High-Dimensional and Incomplete (HDI) tensor is able to flexibly quantize it, where lots of entries are missing primarily due to the impossibility in discovering the full interactions among numerous nodes. Such an HDI tensor can be effectively represented by a Latent Factorization of Tensors (LFT) model for extracting useful knowledge like potential links from it, while existing LFT models commonly adopt general regularization schemes without considering an HDI tensor's imbalanced known data, which impairs their generality. To address this issue, this paper develops an Fine-grained Regularized Nonnegative Latent factorization of tensors (FRNL) model based on two-fold ideas: a) innovatively proposing an Swish-p-based and fine-grained regularization scheme where the regularization effects acting on individual latent feature is proportional to its related instance count for precisely representing the imbalanced distribution of an HDI tensor's known data; b) implementing the self-adaptation of the model hyper-parameters via a fuzzy controller to achieve high practicability. The convergence ability of FRNL is justified theoretically. Experimental studies on eight DWDNs emerging from a real MNMS illustrate that compared with state-of-the-art LFT models, the proposed FRNL model obtains significantly higher learning accuracy and computational efficiency in representing a DWDN.