  An Undirected Weighted Network (UWN) is frequently encountered in a
big-data-related application concerning the complex interactions among numerous
nodes, e.g., a protein interaction network from a bioinformatics application. A
Symmetric High-Dimensional and Incomplete (SHDI) matrix can smoothly illustrate
such an 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 symmetric-topology for describing an UWN's
intrinsic symmetry. Representation learning to an 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 rigorously. 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 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 precisely 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 stronger representation learning ability to an SHDI matrix than
state-of-the-art models do.
