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Large-scale undirected weighted networks are usually found in bigdata-related research fields. It can naturally be quantified as a symmetrichigh-dimensional and incomplete (SHDI) matrix for implementing big dataanalysis tasks. A symmetric non-negative latent-factor-analysis (SNL) model isable to efficiently extract latent factors (LFs) from an SHDI matrix. Yet itrelies on a constraint-combination training scheme, which makes it lackflexibility. To address this issue, this paper proposes an unconstrainedsymmetric nonnegative latent-factor-analysis (USNL) model. Its main idea istwo-fold: 1) The output LFs are separated from the decision parameters viaintegrating a nonnegative mapping function into an SNL model; and 2) Stochasticgradient descent (SGD) is adopted for implementing unconstrained model trainingalong with ensuring the output LFs nonnegativity. Empirical studies on fourSHDI matrices generated from real big data applications demonstrate that anUSNL model achieves higher prediction accuracy of missing data than an SNLmodel, as well as highly competitive computational efficiency.

An Unconstrained Symmetric Nonnegative Latent Factor Analysis for Large-scale Undirected Weighted Networks