Graph data have become increasingly important, and graph node clustering has emerged as a fundamental task in data analysis. In recent years, graph node clustering has gradually moved from traditional shallow methods to deep neural networks due to the powerful representation capabilities of deep learning. In this article, we review some representatives of the latest graph node clustering methods, which are classified into three categories depending on their principles. Extensive experiments are conducted on real-world graph datasets to evaluate the performance of these methods. Four mainstream evaluation performance metrics are used, including clustering accuracy, normalized mutual information, adjusted rand index, and F1-score. Based on the experimental results, several potential research challenges and directions in the field of deep graph node clustering are pointed out. This work is expected to facilitate researchers interested in this field to provide some insights and further promote the development of deep graph node clustering.

Multiview learning aims to learn beneficial patterns from heterogeneous data sources and has captured growing attention in recent years. Most of the previous research studies focused on searching for an effective feature embedding of downstream tasks using diverse optimization algorithms, however, very limited work has been conducted to explore the connection between multiview learning and deep neural networks of structure sharing hidden layers. In this article, we propose a multiview deep matrix factorization model to learn a shared compact representation from multiview data. First, the proposed model constructs a multiview auto-encoder architecture with one shared encoder and multiple decoders, where each view corresponds to a factorization and the shared encoder leads to a common hidden layer. Accordingly, matrix factorizations from multiview data share the last hidden layer for a high-level semantic representation. Second, the nonnegativity constraint of the learned representation is transformed to the projection operation, which can be easily achieved by activating weights of the shared encoder network. Third, this network is trained with a joint loss of the reconstruction error and the compactness loss. By employing the clustering layer, the proposed method serves as an end-to-end multiview clustering method. Finally, comprehensive experiments on nine real-world datasets demonstrate the superiority of the proposed method against state-of-the-art multiview clustering methods.

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.

The reinforcement learning (RL) problem is typically formalized as the Markov Decision Process (MDP), where an agent interacts with the environment to maximize the long-term expected reward. As an important branch of RL, Lifelong RL requires the agent to consecutively solve a series of tasks modeled as MDPs, each of which is drawn from some distribution. A crucial issue in Lifelong RL is how best to utilize the knowledge from the previous tasks for improving the performance in the current task. As a pioneering work in this field, MaxQInit takes the maximum over action-values learned from previous tasks’ environmental rewards as the initial action-value of the current task. In this way, MaxQInit improves the initial performance in the current task and reduces the sample complexity of learning. However, the rewards obtained in the learning process are usually delayed and sparse, dramatically decreasing the learning efficiency. In this paper, we propose a new method, Shaping Rewards for Lifelong RL (SR-LLRL), to speed up the lifelong learning process by shaping timely and informative rewards for each task. Critically, we construct the Lifetime Reward Shaping (LRS) function based on the knowledge of optimal trajectories collected in previous tasks, providing additional reward information for the current task. Compared with MaxQInit, our method exhibits higher learning efficiency and superior performance in Lifelong RL experiments.

Social image colocalization locates the objects belonging to the same category from a set of images. Its goal is to explore the consistent relationship among social entities in the social system, which is conducive to promoting the development of social scene understanding. In a social relationship, consistency is easy to be ignored but is useful for many fields, e.g., natural language processing and computer vision. The social image colocalization aims to utilize the consistent relationship to discover the objects belonging to the same category and locate them by rectangle bounding boxes. The consistency is principally reflected in the category of objects, which can be achieved by a similar appearance or a uniform structure. Currently, state-of-the-art colocalization methods mainly focus on three solving strategies: candidate region proposal selection, saliency maps-based methods, and deep descriptor transformation. In this article, we sort out several kinds of the present mainstream methods and provide a comprehensive review of their fundamentals and performance. We expect that the overview of colocalization would be helpful for the researchers who are new to this area and provide them enlightenments.

High dimensionality is quite commonly encountered in data mining problems, and hence dimensionality reduction becomes an important task in order to improve the efficiency of learning algorithms. As a widely used technique of dimensionality reduction, feature selection is about selecting a feature subset being guided by certain criterion. In this paper, three unsupervised feature selection algorithms are proposed and addressed from the viewpoint of sparse graph embedding learning. First, using the self-characterization of the given data, we view the data themselves as a dictionary, conduct sparse coding and propose the sparsity preserving feature selection (SPFS) algorithm. Second, considering the locality preservation of neighborhoods for the data, we study a special case of the SPFS problem, namely, neighborhood preserving feature selection problem, and come up with a suitable algorithm. Third, we incorporate sparse coding and feature selection into one unified framework, and propose a neighborhood embedding feature selection (NEFS) criterion. Drawing support from nonnegative matrix factorization, the corresponding algorithm for NEFS is presented and its convergence is proved. Finally, the three proposed algorithms are validated with the use of eight publicly available real-world datasets from machine learning repository. Extensive experimental results demonstrate the superiority of the proposed algorithms over four compared state-of-the-art unsupervised feature selection methods.

In this paper, bipartite graphs and their adjacency matrices are applied to equivalently represent covering-based rough sets through three sides, which are approximation operators, properties and reducible elements. Firstly, a bipartite graph is constructed through a covering. According to the constructed bipartite graph, two equivalent representations of a pair of covering upper and lower approximation operators are presented. And an algorithm is designed for computing the pair of covering approximation operators from the viewpoint of these equivalent representations. Some properties and reducible elements of covering-based rough sets are also investigated through the constructed bipartite graph. Finally, an adjacency matrix of the constructed bipartite graph is proposed, and reducible elements in the covering are obtained through the proposed adjacency matrix. Moreover, an equivalent representation of the covering upper approximation operator is presented through the proposed adjacency matrix. In a word, these results show two interesting views, which are graphs and matrices, to investigate covering-based rough sets.

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

The existing approaches for trajectory prediction (TP) are primarily concerned with discovering frequent trajectory patterns (FTPs) from historical movement data. Moreover, most of these approaches work by using a linear TP model to depict the positions of objects, which does not lend itself to the complexities of most real-world applications. In this research, we propose a three-in-one TP model in road-constrained transportation networks called TraPlan. TraPlan contains three essential techniques: 1) constrained network R-tree (CNR-tree), which is a two-tiered dynamic index structure of moving objects based on transportation networks; 2) a region-of-interest (RoI) discovery algorithm is employed to partition a large number of trajectory points into distinct clusters; and 3) a FTP-tree-based TP approach, called FTP-mining, is proposed to discover FTPs to infer future locations of objects moving within RoIs. In order to evaluate the results of the proposed CNR-tree index structure, we conducted experiments on synthetically generated data sets taken from real-world transportation networks. The results show that the CNR-tree can reduce the time cost of index maintenance by an average gap of about 40% when compared with the traditional NDTR-tree, as well as reduce the time cost of trajectory queries. Moreover, compared with fixed network R-Tree (FNR-trees), the accuracy of range queries has shown an on average improvement of about 32%. Furthermore, the experimental results show that the TraPlan demonstrates accurate and efficient prediction of possible motion curves of objects in distinct trajectory data sets by over 80% on average. Finally, we evaluate these results and the performance of the TraPlan model in regard to TP by comparing it with other TP algorithms.

Trajectory prediction of objects in moving objects databases (MODs) has garnered wide support in a variety of applications and is gradually becoming an active research area. The existing trajectory prediction algorithms focus on discovering frequent moving patterns or simulating the mobility of objects via mathematical models. While these models are useful in certain applications, they fall short in describing the position and behavior of moving objects in a network-constraint environment. Aiming to solve this problem, a hidden Markov model (HMM)-based trajectory prediction algorithm is proposed, called Hidden Markov model-based Trajectory Prediction (HMTP). By analyzing the disadvantages of HMTP, a self-adaptive parameter selection algorithm called HMTP* is proposed, which captures the parameters necessary for real-world scenarios in terms of objects with dynamically changing speed. In addition, a density-based trajectory partition algorithm is introduced, which helps improve the efficiency of prediction. In order to evaluate the effectiveness and efficiency of the proposed algorithms, extensive experiments were conducted, and the experimental results demonstrate that the effect of critical parameters on the prediction accuracy in the proposed paradigm, with regard to HMTP*, can greatly improve the accuracy when compared with HMTP, when subjected to randomly changing speeds. Moreover, it has higher positioning precision than HMTP due to its capability of self-adjustment.

The study of definable sets in various generalized rough set models would provide better understanding to these models. Some algebraic structures of all definable sets have been investigated, and the relationships among the definable sets, the inner definable sets and the outer definable sets have been presented. In this paper, we further study the definable sets in three types of covering-based rough sets and present several necessary and sufficient conditions of definable sets. These three types of covering-based rough sets are based on three kinds of neighborhoods: the neighborhood, the complementary neighborhood and the indiscernible neighborhood, respectively. Some necessary and sufficient conditions of definable sets are presented through these three types of neighborhoods, and the relationships among the definable sets are investigated. Moreover, we study the relationships among these three types of neighborhoods, and present certain conditions that the union of the neighborhood and the complementary neighborhood is equal to the indiscernible neighborhood.

Covering is an important form of data, and covering-based rough sets provide an effective tool to deal with this data. In this paper, we use bipartite graphs to study covering-based rough sets. Firstly, a bipartite graph is constructed through a covering, named bipartite graph associated with a covering. According to a bipartite graph associated with a covering, two equivalent representations of a pair of covering approximation operators are presented. Then, some properties of this pair of covering approximation operators and reducible elements in a covering are investigated through the constructed bipartite graph. In a word, these results show an interesting view of graphs to investigate covering-based rough sets.

Rough sets are efficient to extract rules from information systems. Matroids generalize the linear independency in vector spaces and the cycle in graphs. Specifically, matroids provide well-established platforms for greedy algorithms, while most existing algorithms for many rough set problems including attribute reduction are greedy ones. Therefore, the combination between rough sets and matroids may bring new efficient solutions to those important and difficult problems. In this paper, 2-circuit matroids, abstracted from matroidal characteristics of rough sets, are studied and axiomatized. A matroid is induced by an equivalence relation, and its characteristics including the independent set and duality are represented with rough sets. Based on these rough set representations, this special type of matroid is defined as 2-circuit matroids. Conversely, an equivalence relation is induced by a matroid, and its relationship with the above induction is further investigated. Finally, a number of axioms of the 2-circuit matroid are obtained through rough sets. These interesting and diverse axioms demonstrate the potential for the connection between rough sets and matroids.

With the deep penetration of the Internet, uncontrolled flood of information has become one of the most serious problems to Internet users. Harmful contents about pornography, violence and other illegal messages, etc have posed serious influence to the whole society, especially to the young people. In this paper, a novel Web text filter based on rough set and Bayesian theory is proposed to analysis text content of Web pages to filter harmful pages. Some of current feature selection methods such as inverse document frequency (IDF) does not take the classification information into account. To avoid this shortcoming rough set is used to reduce original feature terms. Meanwhile, a novel coefficient weighted method based on rough set is proposed and introduced into Bayesian formula, which will greatly improve filtering performance. In the final experiment, this paper compared the novel method with other weighted methods applied in Bayesian formula, such as Tf, IDF and TFIDF. The results demonstrate that this novel filter works efficiently.

Rough set theory is a useful tool for data mining. It is based on equivalence relations and has been extended to covering-based generalized rough set. This paper studies three kinds of covering generalized rough sets for dealing with the vagueness and granularity in information systems. First, we examine the properties of approximation operations generated by a covering in comparison with those of the Pawlak's rough sets. Then, we propose concepts and conditions for two coverings to generate an identical lower approximation operation and an identical upper approximation operation. After the discussion on the interdependency of covering lower and upper approximation operations, we address the axiomization issue of covering lower and upper approximation operations. In addition, we study the relationships between the covering lower approximation and the interior operator and also the relationships between the covering upper approximation and the closure operator. Finally, this paper explores the relationships among these three types of covering rough sets.