Multi-layer networks treat various types of interactions at each level to model complex systems in nature and society, and clustering of them is of great significance for revealing mechanisms of systems. Vast majority of current algorithms focus on identifying the common communities in clear multi-layer networks, and few attempt has been devoted to the detection of layer-specific communities in noised ones. To address these issues, a joint learning algorithm withGraphDenoising andStructureLearning (calledGDSL) for the detection of layer-specific communities in noised multi-layer networks is proposed, which simultaneously integrates graph denoising, structure learning, and module detection. To remove noise of networks, GDSL re-constructs affinity graphs for the original ones by preserving community structure. To enhance robustness and discriminative of features, GDSL explores the relations of features among various layers with the Hilbert-Schmidt Independence Criterion and structure learning. Finally, GDSL joins all these procedures with an objective function, and deduces optimization rules. The results show that GDSL not only significantly outperforms baselines but also enhances the robustness of the algorithm, providing an effective model for community detection in noised multi-layer networks.

Traffic prediction is the core task of intelligent transportation system (ITS) and accurate traffic prediction can greatly improve the utilization of public resources. Dynamic interaction of multiple spatial relationships will influence the accuracy of traffic prediction. However, many existing methods only consider static spatial relationships, which restricts the accuracy of the prediction. To address the above problem, in this article, we propose the Dynamic Multi-Graph Fusion Network (DMGF-Net) to model the spatial-temporal correlations in traffic network. In the DMGF-Net, the fusion graph is designed to leverage and extract the various spatial correlations between different regions by fusing spatial graph, semantic graph, and spatial-semantic graph. Further, to dynamically learn the importance of different neighbors, we design the Dynamic Spatial-Temporal Unit (DSTU), which can adjust the aggregation weights of different neighbors by combining the convolution operation and the attention mechanism. It can selectively aggregate spatial-temporal features from different neighbors. Extensive experiments on three datasets demonstrate that effectiveness of our model, especially on PEMS08, our model achieves an increase of about 8.55% and 7.55% in terms of MAE and RMSE than the static model STGCN.

Dynamic pricing plays an important role in solving the problems such as traffic load reduction, congestion control, and revenue improvement. Efficient dynamic pricing strategies can increase capacity utilization, total revenue of service providers, and the satisfaction of both passengers and drivers. Many proposed dynamic pricing technologies focus on short-term optimization and face poor scalability in modeling long-term goals for the limitations of solution optimality and prohibitive computation. In this article, a deep reinforcement learning framework is proposed to tackle the dynamic pricing problem for ride-hailing platforms. A soft actor-critic (SAC) algorithm is adopted in the reinforcement learning framework. First, the dynamic pricing problem is translated into a Markov Decision Process (MDP) and is set up in continuous action spaces, which is no need for the discretization of action space. Then, a new reward function is obtained by the order response rate and the KL-divergence between supply distribution and demand distribution. Experiments and case studies demonstrate that the proposed method outperforms the baselines in terms of order response rate and total revenue.

Many complex systems derived from nature and society consist of multiple types of entities and heterogeneous interactions, which can be effectively modeled as heterogeneous information network (HIN). Structural analysis of heterogeneous networks is of great significance by leveraging the rich semantic information of objects and links in the heterogeneous networks. And, clustering heterogeneous networks aims to group vertices into classes, which sheds light on revealing the structure–function relations of the underlying systems. The current algorithms independently perform the feature extraction and clustering, which are criticized for not fully characterizing the structure of clusters. In this study, we propose a learning model by joint Graph Embedding and Nonnegative Matrix Factorization (aka GEjNMF ), where feature extraction and clustering are simultaneously learned by exploiting the graph embedding and latent structure of networks. We formulate the objective function of GEjNMF and transform the heterogeneous network clustering problem into a constrained optimization problem, which is effectively solved by l 0 -norm optimization. The advantage of GEjNMF is that features are selected under the guidance of clustering, which improves the performance and saves the running time of algorithms at the same time. The experimental results on three benchmark heterogeneous networks demonstrate that GEjNMF achieves the best performance with the least running time compared with the best state-of-the-art methods. Furthermore, the proposed algorithm is robust across heterogeneous networks from various fields. The proposed model and method provide an effective alternative for heterogeneous network clustering.

Many complex systems are composed of coupled networks through different layers, where each layer represents one of many possible types of interactions. A fundamental question is how to extract communities in multi-layer networks. The current algorithms either collapses multi-layer networks into a single-layer network or extends the algorithms for single-layer networks by using consensus clustering. However, these approaches have been criticized for ignoring the connection among various layers, thereby resulting in low accuracy. To attack this problem, a quantitative function (multi-layer modularity density) is proposed for community detection in multi-layer networks. Afterward, we prove that the trace optimization of multi-layer modularity density is equivalent to the objective functions of algorithms, such as kernel$K$-means, nonnegative matrix factorization (NMF), spectral clustering and multi-view clustering, for multi-layer networks, which serves as the theoretical foundation for designing algorithms for community detection. Furthermore, aSemi-SupervisedjointNonnegativeMatrixFactorization algorithm (S2-jNMF) is developed by simultaneously factorizing matrices that are associated with multi-layer networks. Unlike the traditional semi-supervised algorithms, the partial supervision is integrated into the objective of the S2-jNMF algorithm. Finally, through extensive experiments on both artificial and real world networks, we demonstrate that the proposed method outperforms the state-of-the-art approaches for community detection in multi-layer networks.

Discovering evolving communities in dynamic networks is essential to important applications such as analysis for dynamic web content and disease progression. Evolutionary clustering uses the temporal smoothness framework that simultaneously maximizes the clustering accuracy at the current time step and minimizes the clustering drift between two successive time steps. In this paper, we propose two evolutionary nonnegative matrix factorization (ENMF) frameworks for detecting dynamic communities. To address the theoretical relationship among evolutionary clustering algorithms, we first prove the equivalence relationship between ENMF and optimization of evolutionary modularity density. Then, we extend the theory by proving the equivalence between evolutionary spectral clustering and ENMF, which serves as the theoretical foundation for hybrid algorithms. Based on the equivalence, we propose a semi-supervised ENMF (sE-NMF) by incorporating a priori information into ENMF. Unlike the traditional semi-supervised algorithms, a priori information is integrated into the objective function of the algorithm. The main advantage of the proposed algorithm is to escape the local optimal solution without increasing time complexity. The experimental results over a number of artificial and real world dynamic networks illustrate that the proposed method is not only more accurate but also more robust than the state-of-the-art approaches.