A Nonnegative Latent Factor Model for Large-Scale Sparse Matrices in Recommender Systems via Alternating Direction Method

Abstract

Nonnegative matrix factorization (NMF)-based models possess fine representativeness of a target matrix, which is critically important in collaborative filtering (CF)-based recommender systems. However, current NMF-based CF recommenders suffer from the problem of high computational and storage complexity, as well as slow convergence rate, which prevents them from industrial usage in context of big data. To address these issues, this paper proposes an alternating direction method (ADM)-based nonnegative latent factor (ANLF) model. The main idea is to implement the ADM-based optimization with regard to each single feature, to obtain high convergence rate as well as low complexity. Both computational and storage costs of ANLF are linear with the size of given data in the target matrix, which ensures high efficiency when dealing with extremely sparse matrices usually seen in CF problems. As demonstrated by the experiments on large, real data sets, ANLF also ensures fast convergence and high prediction accuracy, as well as the maintenance of nonnegativity constraints. Moreover, it is simple and easy to implement for real applications of learning systems.

An Effective Scheme for QoS Estimation via Alternating Direction Method-Based Matrix Factorization

“…The principle of ADM [21,22] is to decompose the original optimization task into tiny sub-ones, and then solve each subtask sequentially. The optimization process of a subtask relies on the updated status of those previously solved ones, thereby leading to fast convergence.…”

“…With (8), the original optimization task is divided into (|U|+|S|)×(f+1) subtasks. To achieve a highly-efficient ADM-based training process, it is necessary to arrange them into a properly designed solving-sequence [21,22]. By carefully investigating the ALS-based update rule (8), we have the following results: a) The update of parameters inside B/C is independent, e.g., for users u and v, the update of b u does not affect that of b v .…”

“…Note that the incompleteness of Q makes (1) not solvable. Nevertheless, according to [16][17][18][19][20][21][22], to expand (1) into a singleelement-dependent form enables the optimization process to focus on Q K rather than on Q, thereby resulting in the following problem:…”

“…Another widely-adopted kind of approaches to CFbased QoS estimation is via matrix factorization (MF) [16][17][18][19][20][21][22]. A QoS estimator of this kind generally works by a) modeling the historical QoS data on a given QoS metric, i.e., request time, with a user-service matrix.…”

GNMFLMI: Graph Regularized Nonnegative Matrix Factorization for Predicting LncRNA-MiRNA Interactions

“…The predictive effect of interactions between molecules can be improved by integrating biological information from different sources [35][36][37]. In fact, prediction of lncRNA-miRNA interactions can be considered as a recommender system problem [38,39]. Accumulated studies have shown that matrix factorization is an effective method which has been successfully used in recommender system for data representation，and already widely applied in the field of bioinformatics [40][41][42].…”