As an important and challenging problem, knowledge representation and inference are typically carried out in a knowledge embedding framework over a multi-relational knowledge graph, and thus have a wide range of applications such as semantic retrieval and question answering. In this paper, we propose a bilinear learning framework which performs cross-entity knowledge relation analysis in the continuous vector space (derived from knowledge embedding). In the framework, we effectively model the intrinsic correlations among different types of knowledge relations within a max-margin multi-relational ranking scheme, which jointly optimizes the tasks of entity embedding and cross-entity relation prediction in terms of multi-relational structures of the knowledge graph. Specifically, we devise a bilinear scoring function that aims to evaluate the confidence degree of semantic relation prediction for entity pairs through a multi-relational learning-to-rank pipeline. In essence, the pipeline formulates the problem of relation prediction for entity pairs as that of learning relation-specific ranking functions by max-margin optimization. Experimental results demonstrate the effectiveness of the proposed framework on two common benchmark datasets.

As the monoplex network has its limitations in describing the real world, a new framework called the multiplex network is put forward and has received much attention in recent years. This paper focuses on synchronization of the multiplex network with multiple delays and stochastic perturbations. Due to the complexity, pinning control of the multiplex network is of particular interest. Based on the LaSalle-type invariance principle for stochastic differential delay equations and the Lyapunov stability theory, some control schemes and synchronization criteria are obtained. It is concluded that under some mild conditions, one can determine which nodes should be pinned in a multiplex network. In addition, it is found that the number of pinned nodes increases with the varying interval of noise and time delay, and decreases with the varying interval of intralayer coupling strength. Some two-layer and three-layer networks are employed to validate the effectiveness of the proposed algorithm.

In the study of complex networks, identifying important nodes in propagation contributes a lot to the control of diffusion. Since real-world networks are often closely interacted, it seems promising to generalize the ranking algorithms of nodes to multi-layer networks. In this paper, the iterative resource allocation method is extended to interconnected networks for the identification of influential spreaders. The new method is verified by the SIR model in interconnected networks. Simulations show that the proposed model performs more accurately comparing the original IRA in monoplex networks.

In this paper, the critical point that is a coupling strength at which the model changes from desynchronization to synchronization is solved by the mean field method theoretically and the phenomenon that with the increase of the mean value in the Gaussian distribution, the corresponding critical point is reduced is explained. Based on simulation and the theoretical results, the threshold of the mean value at which the model changes from the first order phase transition to the second order phase transition can be predicted and it's found that the threshold is linearly proportional to the variance in the Gaussian distribution.

As a joint-optimization problem which simultaneously fulfills two different but correlated embedding tasks (i.e., entity embedding and relation embedding), knowledge embedding problem is solved in a joint embedding scheme. In this embedding scheme, we design a joint compatibility scoring function to quantitatively evaluate the relational facts with respect to entities and relations, and further incorporate the scoring function into the max-margin structure learning process that explicitly learns the embedding vectors of entities and relations using the context information of the knowledge base. By optimizing the joint problem, our design is capable of effectively capturing the intrinsic topological structures in the learned embedding spaces. Experimental results demonstrate the effectiveness of our embedding scheme in characterizing the semantic correlations among different relation units, and in relation prediction for knowledge inference.

We study content-based learning to rank from the perspective of learning distance functions. Standardly, the two key issues of learning to rank, feature mappings and score functions, are usually modeled separately, and the learning is usually restricted to modeling a linear distance function such as the Mahalanobis distance. However, the modeling of feature mappings and score functions are mutually interacted, and the patterns underlying the data are probably complicated and nonlinear. Thus, as a general nonlinear distance family, the Bregman distance is a suitable distance function for learning to rank, due to its strong generalization ability for distance functions, and its nonlinearity for exploring the general patterns of data distributions. In this paper, we study learning to rank as a structural learning problem, and devise a Bregman distance function to build the ranking model based on structural SVM. To improve the model robustness to outliers, we develop a robust structural learning framework for the ranking model. The proposed model Robust Structural Bregman distance functions Learning to Rank (RSBLR) is a general and unified framework for learning distance functions to rank. The experiments of data ranking on real-world datasets show the superiority of this method to the state-of-the-art literature, as well as its robustness to the noisily labeled outliers.

As an important and challenging problem in machine learning and computer vision, multilabel classification is typically implemented in a max-margin multilabel learning framework, where the inter-label separability is characterized by the sample-specific classification margins between labels. However, the conventional multilabel classification approaches are usually incapable of effectively exploring the intrinsic inter-label correlations as well as jointly modeling the interactions between inter-label correlations and multilabel classification. To address this issue, we propose a multilabel classification framework based on a joint learning approach called label graph learning (LGL) driven weighted Support Vector Machine (SVM). In principle, the joint learning approach explicitly models the inter-label correlations by LGL, which is jointly optimized with multilabel classification in a unified learning scheme. As a result, the learned label correlation graph well fits the multilabel classification task while effectively reflecting the underlying topological structures among labels. Moreover, the inter-label interactions are also influenced by label-specific sample communities (each community for the samples sharing a common label). Namely, if two labels have similar label-specific sample communities, they are likely to be correlated. Based on this observation, LGL is further regularized by the label Hypergraph Laplacian. Experimental results have demonstrated the effectiveness of our approach over several benchmark data sets.

Visual feature learning, which aims to construct an effective feature representation for visual data, has a wide range of applications in computer vision. It is often posed as a problem of nonnegative matrix factorization (NMF), which constructs a linear representation for the data. Although NMF is typically parallelized for efficiency, traditional parallelization methods suffer from either an expensive computation or a high runtime memory usage. To alleviate this problem, we propose a parallel NMF method called alternating least square block decomposition (ALSD), which efficiently solves a set of conditionally independent optimization subproblems based on a highly parallelized fine-grained grid-based blockwise matrix decomposition. By assigning each block optimization subproblem to an individual computing node, ALSD can be effectively implemented in a MapReduce-based Hadoop framework. In order to cope with dynamically varying visual data, we further present an incremental version of ALSD, which is able to incrementally update the NMF solution with a low computational cost. Experimental results demonstrate the efficiency and scalability of the proposed methods as well as their applications to image clustering and image retrieval.

Many existing learning-to-rank approaches are incapable of effectively modeling the intrinsic interaction relationships between the feature-level and ranking-level components of a ranking model. To address this problem, we propose a novel joint learning-to-rank approach called Deep Latent Structural SVM (DL-SSVM), which jointly learns deep neural networks and latent structural SVM (connected by a set of latent feature grouping variables) to effectively model the interaction relationships at two levels (i.e., feature-level and ranking-level). To make the joint learning problem easier to optimize, we present an effective auxiliary variable-based alternating optimization approach with respect to deep neural network learning and structural latent SVM learning. Experimental results on several challenging datasets have demonstrated the effectiveness of the proposed learning to rank approach in real-world information retrieval.

Multimedia information retrieval usually involves two key modules including effective feature representation and ranking model construction. Most existing approaches are incapable of well modeling the inherent correlations and interactions between them, resulting in the loss of the latent consensus structure information. To alleviate this problem, we propose a learning to rank approach that simultaneously obtains a set of deep linear features and constructs structure-aware ranking models in a joint learning framework. Specifically, the deep linear feature learning corresponds to a series of matrix factorization tasks in a hierarchical manner, while the learning-to-rank part concentrates on building a ranking model that effectively encodes the intrinsic ranking information by structural SVM learning. Through a joint learning mechanism, the two parts are mutually reinforced in our approach, and meanwhile their underlying interaction relationships are implicitly reflected by solving an alternating optimization problem. Due to the intrinsic correlations among different queries (i.e., similar queries for similar ranking lists), we further formulate the learning-to-rank problem as a multi-task problem, which is associated with a set of mutually related query-specific learning-to-rank subproblems. For computational efficiency and scalability, we design a MapReduce-based parallelization approach to speed up the learning processes. Experimental results demonstrate the efficiency, effectiveness, and scalability of the proposed approach in multimedia information retrieval.

Due to the ubiquitous existence of large-scale data in today's real-world applications including learning on cross media data, we propose a semi-supervised learning method named Multiple Binary Subspace Regression (MBSR) for cross media data classification. In order to mine the common features among the data with multiple modalities, we project the original cross-media data into the same low-rank representation simultaneously by mapping to the corresponding subspaces for dimension reduction. All the subspaces are set to be binary, which only involve the addition operations and omit the multiplication operations in the subsequent computation owing to the good property of the binary values. The dimension reduction to a binary subspace and the classification on this subspace are also optimized simultaneously leading to a semi-supervised model. For dealing with large-scale data, our learning method is easily implemented to run in a MapReduce-based Hadoop system. Empirical studies demonstrate its competitive performance on convergence, efficiency, and scalability in comparison with the state-of-the-art literature.