Community detection is a popular yet thorny issue in social network analysis. A symmetric and nonnegative matrix factorization (SNMF) model based on a nonnegative multiplicative update (NMU) scheme is frequently adopted to address it. Current research mainly focuses on integrating additional information into it without considering the effects of a learning scheme. This study aims to implement highly accurate community detectors via the connections between an SNMF-based community detector's detection accuracy and an NMU scheme's scaling factor. The main idea is to adjust such scaling factor via a linear or nonlinear strategy, thereby innovatively implementing several scaling-factor-adjusted NMU schemes. They are applied to SNMF and graph-regularized SNMF models to achieve four novel SNMF-based community detectors. Theoretical studies indicate that with the proposed schemes and proper hyperparameter settings, each model can: 1) keep its loss function nonincreasing during its training process and 2) converge to a stationary point. Empirical studies on eight social networks show that they achieve significant accuracy gain in community detection over the state-of-the-art community detectors.

Symmetric Nonnegative Matrix Factorization-Based Community Detection Models and Their Convergence Analysis.

Community detection, aiming at determining correct affiliation of each node in a network, is a critical task of complex network analysis. Owing to its high efficiency, Symmetric and Non-negative Matrix Factorization (SNMF) is frequently adopted to handle this task. However, existing SNMF models mostly focus on a network's first-order topological information described by its adjacency matrix without considering the implicit associations among involved nodes. To address this issue, this study proposes a Pointwise mutual information-incorporated and Graph-regularized SNMF (PGS) model. It uses a) Pointwise Mutual Information to quantify implicit associations among nodes, thereby completing the missing but crucial information among critical nodes in a uniform way; b) graph-regularization to achieve precise representation of local topology, and c) SNMF to implement efficient community detection. Empirical studies on eight real-world social networks generated by industrial applications demonstrate that a PGS model achieves significantly higher accuracy gain in community detection than state-of-the-art community detectors.

Highly-Accurate Community Detection via Pointwise Mutual Information-Incorporated Symmetric Non-Negative Matrix Factorization

A dynamically weighted directed network (DWDN) is frequently encountered in various big data-related applications like a terminal interaction pattern analysis system (TIPAS) concerned in this study. It consists of large-scale dynamic interactions among numerous nodes. As the involved nodes increase drastically, it becomes impossible to observe their full interactions at each time slot, making a resultant DWDN High Dimensional and Incomplete (HDI). An HDI DWDN, in spite of its incompleteness, contains rich knowledge regarding involved nodes various behavior patterns. To extract such knowledge from an HDI DWDN, this paper proposes a novel Alternating direction method of multipliers (ADMM)-based Nonnegative Latent-factorization of Tensors (ANLT) model. It adopts three-fold ideas: a) building a data density-oriented augmented Lagrangian function for efficiently handling an HDI tensors incompleteness and nonnegativity; b) splitting the optimization task in each iteration into an elaborately designed subtask series where each one is solved based on the previously solved ones following the ADMM principle to achieve fast convergence; and c) theoretically proving that its convergence is guaranteed with its efficient learning scheme. Experimental results on six DWDNs from real applications demonstrate that the proposed ANLT outperforms state-of-the-art models significantly in both computational efficiency and prediction accuracy. 

A Novel Approach to Large-Scale Dynamically Weighted Directed Network Representation

A non-negative latent factor (NLF) model with a single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) algorithm is frequently adopted to extract useful knowledge from non-negative data represented by high-dimensional and sparse (HiDS) matrices arising from various service applications. However, its convergence rate is rather slow. To address this issue, this study proposes a Generalized Nesterov's acceleration-incorporated, Non-negative and Adaptive Latent Factor (GNALF) model. It results from a) incorporating a generalized Nesterov's accelerated gradient (NAG) method into an SLF-NMU algorithm, thereby achieving an NAG-incorporated and element-oriented non-negative (NEN) algorithm to perform efficient parameter update; and b) making its regularization and acceleration hyper-parameters self-adaptive via incorporating the principle of a particle swarm optimization algorithm into the training process, thereby implementing a highly adaptive and practical model. Empirical studies on six large sparse matrices from different recommendation service applications show that a GNALF model achieves very high convergence rate without the need of hyper-parameter tuning, making its computational efficiency significantly higher than state-of-the-art models. Meanwhile, such efficiency gain does not result in accuracy loss, since its prediction accuracy is comparable with its peers. Hence, it can better serve practical service applications with real-time demands.

Generalized Nesterov's Acceleration-incorporated Non-negative and Adaptive Latent Factor Analysis

CARM: Confidence-aware recommender model via review representation learning and historical rating behavior in the online platforms

A recommender system (RS) relying on latent factor analysis usually adopts stochastic gradient descent (SGD) as its learning algorithm. However, owing to its serial mechanism, an SGD algorithm suffers from low efficiency and scalability when handling large-scale industrial problems. Aiming at addressing this issue, this study proposes a momentum-incorporated parallel stochastic gradient descent (MPSGD) algorithm, whose main idea is two-fold: a) implementing parallelization via a novel data-splitting strategy, and b) accelerating convergence rate by integrating momentum effects into its training process. With it, an MPSGD-based latent factor (MLF) model is achieved, which is capable of performing efficient and high-quality recommendations. Experimental results on four high-dimensional and sparse matrices generated by industrial RS indicate that owing to an MPSGD algorithm, an MLF model outperforms the existing state-of-the-art ones in both computational efficiency and scalability.

Efficient and High-quality Recommendations via Momentum-incorporated Parallel Stochastic Gradient Descent-Based Learning

A Fast Deep AutoEncoder for High-Dimensional and Sparse Matrices in Recommender Systems

Exploration of single Fe atom supported on anatase TiO2(001) for methane oxidation: A DFT study

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Efficient and High-quality Recommendations via Momentum-incorporated Parallel Stochastic Gradient Descent-Based Learning

A Fast Deep AutoEncoder for High-Dimensional and Sparse Matrices in Recommender Systems

Exploration of single Fe atom supported on anatase TiO2(001) for methane oxidation: A DFT study