This article presents a two-timescale duplex neurodynamic approach to mixed-integer optimization, based on a biconvex optimization problem reformulation with additional bilinear equality or inequality constraints. The proposed approach employs two recurrent neural networks operating concurrently at two timescales. In addition, particle swarm optimization is used to update the initial neuronal states iteratively to escape from local minima toward better initial states. In spite of its minimal system complexity, the approach is proven to be almost surely convergent to optimal solutions. Its superior performance is substantiated via solving five benchmark problems.

This paper presents a two-timescale duplex neurodynamic system for constrained biconvex optimization. The two-timescale duplex neurodynamic system consists of two recurrent neural networks (RNNs) operating collaboratively at two timescales. By operating on two timescales, RNNs are able to avoid instability. In addition, based on the convergent states of the two RNNs, particle swarm optimization is used to optimize initial states of the RNNs to avoid local minima. It is proven that the proposed system is globally convergent to the global optimum with probability one. The performance of the two-timescale duplex neurodynamic system is substantiated based on the benchmark problems. Furthermore, the proposed system is applied for L1 -constrained nonnegative matrix factorization.

Multi-view data processing is an effective tool to differentiate the levels of consumers on electronics. Recently, the graph based multi-view clustering methods have attracted widespread attention because they can obtain the relationships of multi-view data points efficiently. However, there exist several shortcomings on most existing graph based clustering methods. Firstly, the mostly adopted Euclidean distance can not extract the nonlinear manifold structure. Secondly, graph based methods are mainly hard clustering methods, which means that each data point belongs to only the one cluster exactly. Thirdly, the high-dimension information between multiple views are not taken into account. Thus, a low-rank tensor regularized graph fuzzy learning (LRTGFL) method for multi-view data processing is proposed. In LRTGFL, Jensen-Shannon divergence is adopted to replace the Euclidean distance for obtaining more completely nonlinear structures. In addition, fuzzy learning is adopted to make graph clustering be a soft clustering method. Furthermore, a tensor nuclear norm based on the tensor singular value decomposition (t-SVD) is adopted to take advantage of the high-dimension information. Then, alternating direction method of multipliers (ADMM) is adopted to solve the LRTGFL model. Finally, the effectiveness and superiority of LRTGFL are demonstrated by comparing with various state-of-the-art algorithms on eight real-world datasets.

Social media has a significant influence, which greatly facilitates people to stay up-to-date with information. Unfortunately, a great deal of fake news on social media misleads people and causes a lot of losses. Therefore, fake news detection is necessary to address this issue. Recently, social content category-based methods have become a crucial component of fake news detection. Different from news context-based category, which focuses on word embedding, it tends to explore the potential relationships and structures between users and news. In this article, a third-order tensor, which obtains massive information and connections, is constructed by the social links and engagements of social networks. Then, a sparse and graph-regularized CANDECOMP/PARAFAC (SGCP) tensor decomposition learning method is proposed for fake news detection on social network. In SGCP, a news factor matrix is constructed by CP decomposition of the tensor, which reflects the complex connections among users and news. Furthermore, SGCP retains sparsity of the news factor matrix and preserves the manifold structures from the original space. In addition, an efficient optimization algorithm, which is proven to be monotonically nonincreasing, is proposed to solve SGCP. Finally, abundant experiments are conducted on real-world datasets and demonstrate the effectiveness of the proposed SGCP.