Improved Symmetric and Nonnegative Matrix Factorization Models for Undirected, Sparse and Large-Scaled Networks: A Triple Factorization-Based Approach

Undirected, sparse and large-scaled networks existing ubiquitously in practical engineering are vitally important since they usually contain rich information in various patterns. Matrix factorization (MF) technique is an efficient method to extract the useful latent factors (LFs) from the LF model, which directly gives rise to the so-called MF model. However, most MF models cannot maintain some frequently encountered constraints such as nonnegativity of LFs and the symmetry of the target network. In addition, in spite of its potential capability of obtaining the effectiveness of both the computation and the storage, the currently developed double factorization (DF)-based model still suffers from the problem of the low prediction accuracy due to the limited amount of LFs. To address the above problems, a novel MF model is proposed in terms of the triple-factorization (TF) technique, thereby leading to TF-based symmetric and nonnegative latent factor (SNLF) models. Compared with the traditional DF-based SNLF model, the proposed TF-based SNLF model is equipped with: 1) constraints on symmetry and nonnegativity; 2) desirable performance with high accuracy; 3) the convergence of the algorithm; and 4) fairly low storage and computational complexity. Furthermore, in order to reduce overfitting so as to further improve the model performance, regularization is precisely considered into the proposed TF-based SNLF model. Experiments on real datasets show that the proposed TF-based SNLF model has a whelming ability of improving the estimation accuracy for the missing data as well as guaranteeing the symmetry of the target network and the nonnegativity of LFs at a little expense of the computation and storage burden. Moreover, it is easy to be implemented for the data analysis.