Multi-Constrained Symmetric Nonnegative Latent Factor Analysis for Accurately Representing Undirected Weighted Networks.

An Undirected Weighted Network (UWN) is frequently encountered in a big-data-related application concerning the complex interactions among numerous nodes. A Symmetric High-Dimensional and Incomplete (SHDI) matrix can smoothly illustrate such a UWN, which contains rich knowledge like node interaction behaviors and local complexes. To extract desired knowledge from an SHDI matrix, an analysis model should carefully consider its topology for describing a UWN's intrinsic symmetry precisely. Representation learning to a UWN borrows the success of a pyramid of symmetry-aware models like a Symmetric Nonnegative Matrix Factorization (SNMF) model whose objective function utilizes a sole Latent Factor (LF) matrix for representing SHDI's symmetry precisely. However, they suffer from the following drawbacks: 1) their computational complexity is high; and 2) their modeling strategy narrows their representation features, making them suffer from low learning ability. Aiming at addressing the above critical issues, this paper proposes a Multi-constrained Symmetric Nonnegative Latent-factor-analysis (MSNL) model with two-fold ideas: 1) introducing multi-constraints composed of multiple LF matrices, i.e., inequality and equality ones into a data-density-oriented objective function for precisely representing the intrinsic symmetry of an SHDI matrix with broadened feature space; and 2) implementing an alternating direction method of multipliers (ADMM)-incorporated learning scheme for efficiently solving such a multi-constrained model. Empirical studies on three SHDI matrices from a real bioinformatics or industrial application demonstrate that the proposed MSNL model achieves higher representation accuracy than state-of-the-art models do, as well as promising computational efficiency.