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This paper investigates the resilient leader-following consensus problem for a class of high-order multi-agent systems subject to unmatched lower triangular uncertainty dynamics and sensor–actuator attacks. Compared with previous work, the sensor and actuator attacks are modeled to be both time-varying and state-dependent, which makes the resilient consensus control more challenging. To deal with the unmatched uncertainties and sensor–actuator attacks, a new compensator with two online tuned dynamic gains is proposed relying only on the relative output measurements of neighboring agents. Then, using only the local compensation information, a fully distributed output feedback resilient protocol is designed to guarantee the leader-following consensus. Sufficient conditions in terms of matrix inequalities are derived to determine control gains and compensator parameters and simulation studies are presented to demonstrate the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Commonsense question answering (CQA) generally means that the machine uses its mastered commonsense to answer questions without relevant background material, which is a challenging task in natural language processing. Existing methods focus on retrieving relevant subgraphs from knowledge graphs based on key entities and designing complex graph neural networks to perform reasoning over the subgraphs. However, they have the following problems: i) the nested entities in key entities lead to the introduction of irrelevant knowledge; ii) the QA context is not well integrated with the subgraphs; and iii) insufficient context knowledge hinders subgraph nodes understanding. In this paper, we present a heterogeneous-graph reasoning with context paraphrase method (HCP), which introduces the paraphrase knowledge from the dictionary into key entity recognition and subgraphs construction, and effectively fuses QA context and subgraphs during the encoding phase of the pre-trained language model (PTLM). Specifically, HCP filters the nested entities through the dictionary's vocabulary and constructs the Heterogeneous Path-Paraphrase (HPP) graph by connecting the paraphrase descriptions11The paraphrase descriptions are English explanations of words or phrases in WordNet and Wiktionary. with the key entity nodes in the subgraphs. Then, by constructing the visible matrices in the PTLM encoding phase, we fuse the QA context representation into the HPP graph. Finally, to get the answer, we perform reasoning on the HPP graph by Mask Self-Attention. Experimental results on CommonsenseQA and OpenBookQA show that fusing QA context with HPP graph in the encoding stage and enhancing the HPP graph representation by using context paraphrase can improve the machine's commonsense reasoning ability.

Electronic health records (EHRs) contain vast medical information like diagnosis, medication, and procedures, enabling personalized drug recommendations and treatment adjustments. However, current drug recommendation methods only model patients’ health conditions from EHR data, neglecting the rich relationships within the data. This paper seeks to utilize a heterogeneous information network (HIN) to represent EHR and develop a graph representation learning method for medication recommendation. However, three critical issues need to be investigated: (1) co-occurrence of diagnosis and drug for the same patient does not imply their relevance; (2) patients’ directly associated information may not be sufficient to reflect their health conditions; and (3) the cold start problem exists when patients have no historical EHRs. To tackle these challenges, we develop a bi-channel heterogeneous local structural encoder to decouple and extract the diverse information in HIN. Additionally, a global information capture and fusion module, aggregating meta-paths to form a global representation, is introduced to fill the information gaps in records. A longitudinal model using rich structural information available in EHR data is proposed for drug recommendations to new patients. Experimental results on real-world EHR data demonstrate significant improvements over existing approaches.

Improving the generalization performance of classifiers from data pre-processing perspective has recently received considerable attention in the machine learning community. Although many methods have been proposed in the past decades, most of them lack theoretical foundations and cannot guarantee better generalization performance of classifiers on processed datasets. To overcome this flaw, in this paper, we propose a method, which is supported by Bayesian decision theory and percolation theory, to improve generalization performance by removing Bayesian confusing samples (abbr. BCS). Specifically, for a training set, we define the samples that misclassified by the Bayesian optimal classifier as BCS and prove that a classifier trained on the training set after removing BCS can obtain better generalization performance. To find out BCS, we indicate that BCS can be identified according to the size of global homogeneous cluster, a set of samples with the same labels, based on percolation theory. Based on these analysis, we propose a method to construct global homogeneous clusters and remove BCS from the training set. Extensive experiments show that the proposed method is effective for a number of classical and state-of-the-art classifiers.

Graph convolutional neural networks can effectively process geometric data and thus have been successfully used in point cloud data representation. However, existing graph-based methods usually adopt the K-nearest neighbor (KNN) algorithm to construct graphs, which may not be optimal for point cloud analysis tasks, owning to the solution of KNN is independent of network training. In this paper, we propose a novel graph structure learning convolutional neural network (GSLCN) for multiple point cloud analysis tasks. The fundamental concept is to propose a general graph structure learning architecture (GSL) that builds long-range and short-range dependency graphs. To learn optimal graphs that best serve to extract local features and investigate global contextual information, respectively, we integrated the GSL with the designed graph convolution operator under a unified framework. Furthermore, we design the graph structure losses with some prior knowledge to guide graph learning during network training. The main benefit is that given labels and prior knowledge are taken into account in GSLCN, providing useful supervised information to build graphs and thus facilitating the graph convolution operation for the point cloud. Experimental results on challenging benchmarks demonstrate that the proposed framework achieves excellent performance for point cloud classification, part segmentation, and semantic segmentation.

Graph matching endeavors to find corresponding nodes across two or more graphs, which plays a fundamental role in many vision and pattern matching tasks. However, existing graph matching algorithms often meet abnormal graphs with missing node features and suffer from numerous cluttered outliers in practical applications. To address these, we propose a novel deep graph matching method called Random Deep Graph Matching (RDGM). Different from the deterministic affinity inference in existing deep graph matching methods, RDGM performs message passing in a random manner during model training through randomly masking some available node features in the source or target graph, so that the affinity inference between nodes is insensitive to specific neighborhoods. In addition, a hierarchical attention graph neural network framework is devised in the node embedding process of RDGM, which can obtain more sufficient high-order structural information to reduce the impact of latent noise on affinity learning. Extensive experiments suggest that the proposed RDGM outperforms state-of-the-art graph matching methods, and demonstrates strong robustness and generalization performance.

We consider the problem of distinguishing direct causes from direct effects of a target variable of interest from multiple manipulated datasets with unknown manipulated variables and nonidentical data distributions. Recent studies have shown that datasets attained from manipulated experiments (i.e., manipulated data) contain richer causal information than observational data for causal structure learning. Thus, in this article, we propose a new algorithm, which makes full use of the interventional properties of a causal model to discover the direct causes and direct effects of a target variable from multiple datasets with different manipulations. It is more suited to real-world cases and is also a challenge to be addressed in this article. First, we apply the backward framework to learn parents and children (PC) of a given target from multiple manipulated datasets. Second, we orient some edges connected to the target in advance through the assumption that the target variable is not manipulated and then orient the remaining undirected edges by finding invariant V-structures from multiple datasets. Third, we analyze the correctness of the proposed algorithm. To the best of our knowledge, the proposed algorithm is the first that can identify the local causal structure of a given target from multiple manipulated datasets with unknown manipulated variables. Experimental results on standard Bayesian networks validate the effectiveness of our algorithm.

The pure accuracy measure is used to eliminate random consistency from the accuracy measure. Biases to both majority and minority classes in the pure accuracy are lower than that in the accuracy measure. In this paper, we demonstrate that compared with the accuracy measure and F-measure, the pure accuracy measure is class distribution insensitive and discriminative for good classifiers. The advantages make the pure accuracy measure suitable for traditional classification. Further, we mainly focus on two points: exploring a tighter generalization bound on pure accuracy based learning paradigm and designing a learning algorithm based on the pure accuracy measure. Particularly, with the self-bounding property, we build an algorithm-independent generalization bound on the pure accuracy measure, which is tighter than the existing bound of an order $O(1/\sqrt{N})$O(1/N) (N is the number of instances). The proposed bound is free from making a smoothness or convex assumption on the hypothesis functions. In addition, we design a learning algorithm optimizing the pure accuracy measure and use it in the selective ensemble learning setting. The experiments on sixteen benchmark data sets and four image data sets demonstrate that the proposed method statistically performs better than the other eight representative benchmark algorithms.

As a leading graph clustering technique, spectral clustering is one of the most widely used clustering methods to capture complex clusters in data. Some additional prior information can help it to further reduce the difference between its clustering results and users’ expectations. However, it is hard to get the prior information under unsupervised scene to guide the clustering process. To solve this problem, we propose a self-constrained spectral clustering algorithm. In this algorithm, we extend the objective function of spectral clustering by adding pairwise and label self-constrained terms to it. We provide the theoretical analysis to show the roles of the self-constrained terms and the extensibility of the proposed algorithm. Based on the new objective function, we build an optimization model for self-constrained spectral clustering so that we can simultaneously learn the clustering results and constraints. Furthermore, we propose an iterative method to solve the new optimization problem. Compared to other existing versions of spectral clustering algorithms, the new algorithm can discover a high-quality cluster structure of a data set without prior information. Extensive experiments on benchmark data sets illustrate the effectiveness of the proposed algorithm.

The majority of the classical dimensionality reduction methods can be unified into a graph-embedding-based framework. A fixed graph constructed in a high-dimensional space has been extensively employed in the graph-embedding-based dimensionality reduction methods. However, a fixed graph often cannot characterize the structure of high-dimensional data owing to the curse of dimensionality. To solve this problem, we combine graph construction and dimensionality reduction into a coherent framework. Thus, the constructed graph can be updated dynamically in dimensionality reduction. In the existing methods based on the coherent framework, graphs are usually constructed by a type of neighborhood relationship and single clustering result. This study proposes an unsupervised dimensionality reduction method guided by fusing multiple clustering results. In the proposed method, multiple clustering results are first obtained by the k-means algorithm, and then a graph is constructed using a weighted co-association matrix of fusing the clustering results to capture data distribution information. Based on the graph, we present an objective function of combining graph construction and dimensionality reduction to implement mutual guidance between them. Numerical experiments on real data sets illustrate that the proposed method achieves significant improvement over some representative and state-of-the-art unsupervised dimensionality reduction methods.

Uncovering the underlying community structure of a social network is an important task in social network analysis. To solve this problem, many community detection algorithms for the full topology of an original social network have been proposed. However, these algorithms are not very effective at analyzing large-scale social networks. To overcome this deficiency, this paper proposes a community detection algorithm based on graph compression. Specifically, a compressed graph is first obtained by iteratively merging vertices with a degree of 1 or 2 into their neighbors with a higher degree. Then, two indices, i.e., the density and quality of vertices, are defined to evaluate the probability of vertices as community seeds. By considering these two measures together, in a compressed social network, the number of communities and the corresponding initial community seeds are determined simultaneously. After obtaining the community structure of the compressed social network via seed expansion, the community results are propagated to the original social network. Extensive experiments conducted on various social networks have demonstrated the superiority of our proposal compared to several existing state-of-the-art community detection algorithms. [ABSTRACT FROM AUTHOR]

Collaborative filtering is a fundamental technique in recommender systems, for which memory-based and matrix-factorization-based collaborative filtering are the two types of widely used methods. However, the performance of these two types of methods is limited in the case of sparse data, particularly with extremely sparse data. To improve the effectiveness of the methods in a sparse scenario, this paper proposes a multi-factor similarity measure that captures linear and nonlinear correlations between users resulting from extreme behavior. Subsequently, a fusion method that simultaneously considers the multi-factor similarity and the global rating information in a probability matrix factorization framework is proposed. In our framework, users' local relations are integrated into the global ratings optimization process, so that prediction accuracy and robustness are improved in sparse data, particularly in extremely sparse data. To verify the performance of the proposed methods, we conduct experiments on four public datasets. The experimental results show that the fusion method is superior to the typical matrix factorization models used in collaborative filtering and significantly improves both the prediction results and robustness in sparse data. [ABSTRACT FROM AUTHOR]

Score functions play an important role in ranking hesitant fuzzy elements (HFEs) and hesitant fuzzy sets (HFSs). Currently, various kinds of HFE and HFS score functions have been investigated in the literature. However, the essential characteristic and generation mechanism of these score functions have not been systematically studied. To address these issues, this paper introduces an axiomatic definition of deviation degree measure and proposes a general form of dual HFE and HFS deviation score functions, from which a family of existing HFE and HFS score functions can be derived. Besides, we develop two ranking methods based on a pair of dual deviation score functions for distinguishing HFEs and HFSs that are indiscernible by a single score function. Moreover, the mathematical and behavioral properties of HFS deviation score functions are analyzed for applying them in practice. Finally, the proposed ranking method for HFSs is applied to the multi-criteria decision-making problems with hesitant fuzzy information.

Detecting protein complexes from available protein–protein interaction (PPI) networks is an important task, and several related algorithms have been proposed. These algorithms usually consider a single topological metric and ignore the rich topological characteristics and inherent organization information of protein complexes. However, the effective use of such information is crucial to protein complex detection. To overcome this deficiency, this study presents a heuristic clustering algorithm to identify protein complexes by fully exploiting the topological information of PPI networks. By considering the clustering coefficient and the node degree, a new nodal metric is proposed to quantify the importance of each node within a local subgraph. An iterative paradigm is used to incrementally identify seed proteins and expand each seed to a cluster. First, among the unclustered nodes, the node with the highest nodal metric is selected as a new seed. Then, the seed is expanded to a cluster by adding candidate nodes recursively from its neighbors according to both the density of the cluster and the connection between a candidate node and the cluster. The experimental results demonstrate that the proposed algorithm outperforms other competing algorithms in terms of F -measure and accuracy. [ABSTRACT FROM AUTHOR]

In the era of big data, the fusion of uncertain information from different data sources is a crucial issue in various applications. In this paper, a sign fusion method of multiple qualitative probabilistic networks (QPNs) with the same structure from different data sources is proposed. Specifically, firstly, the definition of parallel path in multiple QPNs is given and the problem of fusion ambiguity is described. Secondly, the fusion operator (⊕f-operator) theorem is introduced in detail, including its proof and algebraic properties. Further, an efficient sign fusion algorithm is proposed. Finally, experimental results demonstrate that our fusion algorithm is feasible and efficient.

The functional k -means clustering algorithm is a widely used method for clustering functional data. However, with this algorithm, the derivative information is not further considered in calculating the similarity between two functional samples. In fact, the derivative information is very important for catching the trend characteristic differences among functional data. In this paper, we define a novel distance used to measure the similarity among functional samples by adding their derivative information. Furthermore, in theory, we construct cluster centroids that can minimize the objective function of the functional k -means clustering algorithm based on the proposed distance. After preprocessing functional data using three types of common basis representation techniques, we compare the clustering performance of the functional k -means clustering algorithms based on four different similarity metrics. The experiments on six data sets with class labels show the effectiveness and robustness of the functional k -means clustering algorithm with the defined distance statistically. In addition, the experimental results on three real-life data sets verify the convergence and practicability of the functional k -means clustering algorithm with the defined distance. [ABSTRACT FROM AUTHOR]

In data mining, objects are often represented by a set of features, where each feature of an object has only one value. However, in reality, some features can take on multiple values, for instance, a person with several job titles, hobbies, and email addresses. These features can be referred to as set-valued features and are often treated with dummy features when using existing data mining algorithms to analyze data with set-valued features. In this paper, we propose an SV- $k$ -modes algorithm that clusters categorical data with set-valued features. In this algorithm, a distance function is defined between two objects with set-valued features, and a set-valued mode representation of cluster centers is proposed. We develop a heuristic method to update cluster centers in the iterative clustering process and an initialization algorithm to select the initial cluster centers. The convergence and complexity of the SV- $k$ -modes algorithm are analyzed. Experiments are conducted on both synthetic data and real data from five different applications. The experimental results have shown that the SV- $k$ -modes algorithm performs better when clustering real data than do three other categorical clustering algorithms and that the algorithm is scalable to large data.

Zero-shot learning (ZSL) methods mainly associate global or region features to semantic vectors within a single image, for transferring semantic knowledge from the seen classes to unseen ones. However, the interactive region learning among a group of images from different categories, which can enhance the discrimination of region features and thus lead to a desirable knowledge transfer between seen and unseen classes, is seldom considered. To remedy the above challenge, we propose a group-wise interactive region learning (GIRL) model to guarantee a comprehensive and explicit region interaction. Specifically, GIRL consists of an attentive region interaction (ARI) module and a holistic semantic embedding (HSE) module. ARI utilizes the semantic commonalities and differences of group regions to produce refined region features. HSE holistically maps these region features to the semantic space for a more stable semantic transfer. We also present a semantic consistency loss and a relation alignment loss that can distill the refined/original region features and introduce unseen class semantic vectors for training, respectively. Extensive experiments demonstrate the effectiveness of GIRL over other methods, achieving 68.9%, 42.9%, 75.5%, and 47.8% the Generalized ZSL (GZSL) H scores on CUB, SUN, AWA2, and APY. The code is publicly available at https://github.com/TingML/GIRL. • Group-wise interactive region learning (GIRL) model is proposed. • Attentive region interaction (ARI) refines the region features. • Holistic semantic embedding (HSE) maps region features to semantic space. • Show the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Ensemble clustering has recently emerged a powerful clustering analysis technology for multi-view data. From the existing work, these techniques held great promise, but most of them are inefficient for large data. Some researchers have also proposed efficient ensemble clustering algorithms, but these algorithms devote to data objects with the same feature spaces, which are not satisfied for multi-view data. To overcome these deficiencies, an efficient ensemble clustering algorithm for multi-view mixed data is developed from the cluster-level perspective. Firstly, a set of clustering solutions are produced with the K-prototypes clustering algorithm on each view multiple times, respectively. Then, a cluster-cluster similarity matrix is constructed by considering all the clustering solutions. Next, the METIS algorithm is conduct meta-clustering based on the similarity matrix. After that, the final clustering results are obtained by applying majority voting to assign the objects to their corresponding clusters based on the meta-clustering. The corresponding time complexity of the proposed algorithm is analysed as well. Experimental results on several multi-view datasets demonstrated the superiority of our proposed algorithm.

Learning from categorical data plays a fundamental role in such areas as pattern recognition, machine learning, data mining, and knowledge discovery. To effectively discover the group structure inherent in a set of categorical objects, many categorical clustering algorithms have been developed in the literature, among which $k$ -modes-type algorithms are very representative because of their good performance. Nevertheless, there is still much room for improving their clustering performance in comparison with the clustering algorithms for the numeric data. This may arise from the fact that the categorical data lack a clear space structure as that of the numeric data. To address this issue, we propose, in this paper, a novel data-representation scheme for the categorical data, which maps a set of categorical objects into a Euclidean space. Based on the data-representation scheme, a general framework for space structure based categorical clustering algorithms (SBC) is designed. This framework together with the applications of two kinds of dissimilarities leads two versions of the SBC-type algorithms. To verify the performance of the SBC-type algorithms, we employ as references four representative algorithms of the $k$ -modes-type algorithms. Experiments show that the proposed SBC-type algorithms significantly outperform the $k$ -modes-type algorithms.

Multigranulation rough set (MGRS) theory provides two kinds of qualitative combination rules that are generated by optimistic and pessimistic multigranulation fusion functions. They are used to aggregate multiple granular structures from a set theoretic standpoint. However, the two combination rules seem to lack robustness because one is too relaxed and the other too restrictive to solve some practical problems. Dempster’s combination rule in the evidence theory has been employed to aggregate information coming from multiple sources. However, it fails to deal with conflict evidence. To overcome these limitations, we focus on the combination of granular structures with both reliability and conflict from multiple sources, which has been a challenging task in the field of granular computing. We first address the connection between multigranulation rough set theory and the evidence theory. Then, a two-grade fusion approach involved in the evidence theory and multigranulation rough set theory is proposed, which is based on a well-defined distance function among granulation structures. Finally, an illustrative example is given to show the effectiveness of the proposed fusion method. The results of this study will be useful for pooling the uncertain data from different sources and significant for establishing a new direction of granular computing. [ABSTRACT FROM AUTHOR]

The incompleteness of multi-view data is a phenomenon associated with real-world data mining applications, which brings a huge challenge for multi-view clustering. Although various types of clustering methods, which try to obtain a complete and consensus clustering result from a latent subspace, have been developed to overcome this problem, most methods excessively rely on views-public instances to bridge the connection with view-private instances. When lacking sufficient views-public instances, existing methods fail to transmit the information among incomplete views effectively. To overcome this limitation, we propose an incomplete multi-view clustering algorithm via local and global co-regularization (IMVC-LG). In this algorithm, we define a new objective function that is composed of two terms: local clustering from each view and global clustering from multiple views, which constrain each other to exploit the local clustering information from different incomplete views and determine a global consensus clustering result, respectively. Furthermore, an iterative optimization method is proposed to minimize the objective function. Finally, we compare the proposed algorithm with other state-of-the-art incomplete multi-view clustering methods on several benchmark datasets to illustrate its effectiveness.

Abstract: The fast global k-means (FGKM) clustering algorithm is one of the most effective approaches for resolving the local convergence of the k-means clustering algorithm. Numerical experiments show that it can effectively determine a global or near global minimizer of the cost function. However, the FGKM algorithm needs a large amount of computational time or storage space when handling large data sets. To overcome this deficiency, a more efficient FGKM algorithm, namely FGKM+A, is developed in this paper. In the development, we first apply local geometrical information to describe approximately the set of objects represented by a candidate cluster center. On the basis of the approximate description, we then propose an acceleration mechanism for the production of new cluster centers. As a result of the acceleration, the FGKM+A algorithm not only yields the same clustering results as that of the FGKM algorithm but also requires less computational time and fewer distance calculations than the FGKM algorithm and its existing modifications. The efficiency of the FGKM+A algorithm is further confirmed by experimental studies on several UCI data sets. [Copyright &y& Elsevier]

Abstract: The classical multigranulation rough set (MGRS) theory offers a formal theoretical framework for solving the complex problem under multigranulation environment. However, it is noticeable that MGRS theory cannot be applied in multi-source information systems with a covering environment in the real world. To address this issue, we firstly present in this paper three types of covering based multigranulation rough sets, in which set approximations are defined by different covering approximation operators. Then, by using two different approximation strategies, i.e., seeking common reserving difference and seeking common rejecting difference, two kinds of covering based multigranulation rough set are presented, namely, a covering based optimistic multigranulation rough set and a covering based pessimistic multigranulation rough sets. Finally, we develop some properties and several uncertainty measures of the covering based multigranulation rough sets. These results will enrich the MGRS theory and enlarge its application scope. [Copyright &y& Elsevier]

Abstract: The roughness of a rough set arises from the existence of its boundary region. In such a boundary region, each object has a non-zero rough membership degree. When an object’s rough membership degree is regarded as its fuzzy membership degree, a rough set can induce a fuzzy set. This relationship motivates us to assert that there may exist some inherent relations between the roughness of a rough set and the fuzziness of the fuzzy set induced from the rough set. This assertion leads us to the question: Can the existing fuzzy entropies be used to evaluate the roughness of a rough set? To answer this question, we first analyze how the boundary region varies when the partition of the universe becomes coarser, and then exploit this analysis in the introduction of a more appropriate definition on the roughness of a rough set. To determine whether a fuzzy entropy can be used to evaluate the roughness of a rough set or not, we develop three methods for estimating the ability of a fuzzy entropy to measure the roughness. The experiments show that these methods are very effective and can be applied to select a fuzzy entropy as a measure of the roughness of a rough set. [Copyright &y& Elsevier]

Abstract: Feature selection is a challenging problem in many areas such as pattern recognition, machine learning and data mining. Rough set theory, as a valid soft computing tool to analyze various types of data, has been widely applied to select helpful features (also called attribute reduction). In rough set theory, many feature selection algorithms have been developed in the literatures, however, they are very time-consuming when data sets are in a large scale. To overcome this limitation, we propose in this paper an efficient rough feature selection algorithm for large-scale data sets, which is stimulated from multi-granulation. A sub-table of a data set can be considered as a small granularity. Given a large-scale data set, the algorithm first selects different small granularities and then estimate on each small granularity the reduct of the original data set. Fusing all of the estimates on small granularities together, the algorithm can get an approximate reduct. Because of that the total time spent on computing reducts for sub-tables is much less than that for the original large-scale one, the algorithm yields in a much less amount of time a feature subset (the approximate reduct). According to several decision performance measures, experimental results show that the proposed algorithm is feasible and efficient for large-scale data sets. [Copyright &y& Elsevier]

Abstract: To discover knowledge from hybrid data using rough sets, researchers have developed several fuzzy rough set models and a neighborhood rough set model. These models have been applied to many hybrid data processing applications for a particular purpose, thus neglecting the issue of selecting an appropriate model. To address this issue, this paper mainly concerns the relationships among these rough set models. Investigating fuzzy and neighborhood hybrid granules reveals an important relationship between these two granules. Analyzing the relationships among rough approximations of these models shows that Hu’s fuzzy rough approximations are special cases of neighborhood and Wang’s fuzzy rough approximations, respectively. Furthermore, one-to-one correspondence relationships exist between Wang’s fuzzy and neighborhood rough approximations. This study also finds that Wang’s fuzzy and neighborhood rough approximations are cut sets of Dubois’ fuzzy rough approximations and Radzikowska and Kerre’s fuzzy rough approximations, respectively. [Copyright &y& Elsevier]

Abstract: The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak’s rough set theory are special instances of those of MGRS. Moreover, several important measures, such as accuracy measure , quality of approximation and precision of approximation , are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski–Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (“AND” rules) from Pawlak’s rough set model, the form of decision rules in MGRS is “OR”. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations. [Copyright &y& Elsevier]

Abstract: In rough set theory, accuracy and roughness are used to characterize uncertainty of a set and approximation accuracy is employed to depict accuracy of a rough classification. Although these measures are effective, they have some limitations when the lower/upper approximation of a set under one knowledge is equal to that under another knowledge. To overcome these limitations, we address in this paper the issues of uncertainty of a set in an information system and approximation accuracy of a rough classification in a decision table. An axiomatic definition of knowledge granulation for an information system is given, under which these three measures are modified. Theoretical studies and experimental results show that the modified measures are effective and suitable for evaluating the roughness and accuracy of a set in an information system and the approximation accuracy of a rough classification in a decision table, respectively, and have a much simpler and more comprehensive form than the existing ones. [Copyright &y& Elsevier]

Abstract: One of the strengths of rough set theory is the fact that an unknown target concept can be approximately characterized by existing knowledge structures in a knowledge base. Knowledge structures in knowledge bases have two categories: complete and incomplete. In this paper, through uniformly expressing these two kinds of knowledge structures, we first address four operators on a knowledge base, which are adequate for generating new knowledge structures through using known knowledge structures. Then, an axiom definition of knowledge granulation in knowledge bases is presented, under which some existing knowledge granulations become its special forms. Finally, we introduce the concept of a knowledge distance for calculating the difference between two knowledge structures in the same knowledge base. Noting that the knowledge distance satisfies the three properties of a distance space on all knowledge structures induced by a given universe. These results will be very helpful for knowledge discovery from knowledge bases and significant for establishing a framework of granular computing in knowledge bases. [Copyright &y& Elsevier]

Node order is one of the most important factors in learning the structure of a Bayesian network (BN) for probabilistic reasoning. To improve the BN structure learning, we propose a node order learning algorithm based on the frequently used Bayesian information criterion (BIC) score function. The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective. Specifically, we first find the most dependent node for each individual node, prove analytically that the dependencies are undirected, and then construct undirected subgraphs UG. Secondly, the UGis examined and connected into a single undirected graph UGC. The relation between the subgraph number and the node number is analyzed. Thirdly, we provide the rules of orienting directions for all edges in UGC, which converts it into a directed acyclic graph (DAG). Further, we rank the DAG’s topology order and describe the BIC-based node order learning algorithm. Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples, and in polynomial time with respect to the number of variables. Finally, experimental results demonstrate significant performance improvement by comparing with other methods.

Abstract: As two classical measures, approximation accuracy and consistency degree can be employed to evaluate the decision performance of a decision table. However, these two measures cannot give elaborate depictions of the certainty and consistency of a decision table when their values are equal to zero. To overcome this shortcoming, we first classify decision tables in rough set theory into three types according to their consistency and introduce three new measures for evaluating the decision performance of a decision-rule set extracted from a decision table. We then analyze how each of these three measures depends on the condition granulation and decision granulation of each of the three types of decision tables. Experimental analyses on three practical data sets show that the three new measures appear to be well suited for evaluating the decision performance of a decision-rule set and are much better than the two classical measures. [Copyright &y& Elsevier]

With the progress of deep learning used in unsupervised learning, deep approach based multi-view clustering methods have been increasingly proposed in recent years. However, in most of these methods, deep representation learning is not organically integrated into the multi-view clustering process. They either conduct deep representation learning and clustering in a separate manner, or use the pseudo cluster labels to supervise deep representation learning. In this paper, we propose a centroids-guided deep multi-view k -means clustering method, which organically incorporates deep representation learning into the multi-view k -means objective by using the cluster centroids in multi-view k -means to guide the deep learning of each view. In turn, more k -means-friendly representations are produced to further optimize the multi-view k -means objective. The cluster centroids of each view obtained under a common clustering partition not only represent the semantic information of the clusters but also imply consistency among different views. By reducing the loss between each representation and its assigned cluster centroid with respect to the network parameters of each view, the representations of different views will be more k -means-friendly toward a common partition. Experiments on several datasets demonstrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In multi-label learning, each training instance is associated with multiple class labels. It is typical in reality that relevant labels are partially missing and only a part of labels are valid, resulting in the problem of weak multi-label learning with missing labels. It is still an evident challenge to estimate the ground-truth label matrix and to generate a prediction function, especially on the multi-label data with a large number of missing labels. In this paper, we propose a multi-label learning framework within which feature structure and label manifold are both utilized to recover the incomplete label matrix and to train the classification model simultaneously. To mitigate the imbalanced risks brought by the sparse label issue, a self-adaptive penalty factor is imposed on the deviated predictions of different labels. Moreover, instance granular discrimination is incorporated in the framework to characterize the approximate distribution structure of data. Matrix vectorization, cave-convex programming (CCCP), and block coordinate descent techniques are employed to solve the proposed optimization problem. Extensive experiments illustrate the superiority of the proposed method against some well-established methods. [ABSTRACT FROM AUTHOR]

• A new single IVHF membership degree is constructed. • Four IVHF MG-DTRSs over two universes based on diverse risk appetites are designed. • General IVHF MAGDM methods in consensus processes are studied via MG-3WD frameworks. • Case studies of M&A target selections show the validity of the proposed methods. Multi-attribute group decision making (MAGDM) is a common activity for multi-variable complicated decision making situations by integrating collective wisdom. Aiming at fusing granular computing with three-way decisions (3WD) to study scheme synthesis and analysis of solution space, multi-granularity three-way decisions (MG-3WD) provide multi-dimension problem solving methods for MAGDM problems. By using MG-3WD frameworks, this paper intends to study viable strategies of processing consensus and conflicting opinions provided by different decision makers in the interval-valued hesitant fuzzy (IVHF) MAGDM problem. More specifically, after reviewing the relevant literature, four kinds of IVHF multigranulation decision-theoretic rough sets (MG-DTRSs) over two universes are proposed according to different risk appetites of experts firstly. Then, we explore some fundamental propositions of newly proposed models. Afterwards, solutions to MAGDM problems in the context of mergers and acquisitions (M&A) target selections by using the presented IVHF MG-DTRSs over two universes are constructed. At last, a M&A target selection case study, along with a sensitivity analysis and a comparative analysis, is applied to illustrate the established decision making approaches. [ABSTRACT FROM AUTHOR]

With the increasing complexity of decision-making problems and environment, the integration and fusion of three-way decisions, rough set and multi-attribute group decision-making (MAGDM) have become a major trend in the field of decision analysis. Although many researchers have presented various MAGDM methods under different environments, there are still some imperfections, such as the weight information is not comprehensive or flexible enough, the decision results lack interpretability, and the impact of risk attitude is not fully taken into account. In order to overcome the above shortcomings and improve the scientificity and rationality of decision-making, a novel data-driven MAGDM method under interval-valued intuitionistic uncertain linguistic environment is established based on the idea of multi-granulation and three-way decisions. Our contributions can be identified as follows: (1) The multi-granulation weight mining and fusion methods for experts and attributes are proposed, respectively; (2) The coarse-granulation grading information based on three-way decisions is developed to enhance the interpretability and reference value of decision results; (3) The expected value with risk attitude factor is defined to compare interval-valued intuitionistic uncertain linguistic variables (IVIULVs) and then is used to grade and rank alternatives under different risk attitudes. To illustrate the feasibility and practicality of the proposed method, a case of logistics supplier selection in e-commerce enterprises is demonstrated. Furthermore, the advantages and characteristics of the proposed method are highlighted via detailed comparison and thorough analysis. [ABSTRACT FROM AUTHOR]

The notion of hesitant fuzzy linguistic term sets (HFLTSs), which enables experts to utilize a few possible linguistic terms to evaluate varieties of common qualitative information, plays a significant role in handling situations in cases where these experts are hesitant in offering linguistic expressions. For addressing the challenges of information analysis and information fusion in hesitant fuzzy linguistic (HFL) group decision making, in accordance with the multi-granularity three-way decisions paradigm, the primary purpose of this study is to develop the notion of multigranulation decision-theoretic rough sets (MG-DTRSs) into the HFL background within the two-universe framework. Having revisited the relevant literature, we first propose a hybrid model named adjustable HFL MG-DTRSs over two universes by introducing an adjustable parameter for the expected risk appetite of experts, in which both optimistic and pessimistic versions of HFL MG-DTRSs over two universes are special cases of the adjustable version. Second, some of the fundamental properties of the proposed model are discussed. Then, on the basis of the presented hybrid model, a group decision making approach within the HFL context is further constructed. Finally, a practical example, a comparative analysis, and a validity test concerning person-job fit problems are explored to reveal the rationality and practicability of the constructed decision making rule. [ABSTRACT FROM AUTHOR]

GCN is a widely-used representation learning method for capturing hidden features in graph data. However, traditional GCNs suffer from the over-smoothing problem, hindering their ability to extract high-order information and obtain robust data representation. To overcome this limitation, we propose a novel graph model, the high-order graph attention network. Compared to other existing graph attention networks, our model can adaptively aggregate node features from multi-hop neighbors through an attention mechanism. Moreover, the edges in the original graph may not accurately represent the relationships between nodes. We implement a new approach to update the graph by using the aggregated node representation to adjust the edges with small step sizes. Additionally, we perform a theoretical analysis to demonstrate the relationships between our proposed model and other GCN models. Finally, we evaluate our proposed model against eight variants of GCN models on multiple widely-used benchmark datasets. The experimental results show the superiority of our proposed model over other models. We propose a novel model that integrates low- and high-order information from node neighborhoods. First, we perform feature mapping and propagation to create a feature tensor that stores diverse-order node representations. Then, we use an attention mechanism to aggregate the node features across different orders. Finally, we can update the edges of the original adjacency matrix using obtained with the newly obtained node features. • Propose a high-order graph attention model to alleviate the over-smoothing problem. • Implement a new strategy that incrementally updates the edge weights using a small step size. • Explore relations between the new model and other models. • Show that the new model is very effective in the experiments. [ABSTRACT FROM AUTHOR]

Adaptive distance metric learning based on the characteristics of data can significantly improve the learner's performance. Due to the limitations of single metric learning for heterogeneous data, multiple local metric learning has become an essential representative tool to describe local properties of data. Most existing multiple metric learning algorithms need to perform metric learning on a pre-obtained instance division. However, the number of clusters in the pre-obtained division affects the effectiveness of metric learning. To tackle this problem, we propose a Multiple Metric Learning via Local Metric Fusion (MML-LMF) framework, which unifies local metric learning and fusion of similar local metrics into one metric and adaptively determines the number of local metrics. As an application of the MML-LMF framework to pairwise constraints, we devise a MML-LMF algorithm by constructing a concrete optimization model and acquiring a closed-form solution to the model. The experimental results on several benchmarks, person re-identification, and face verification datasets show that the performance of the proposed algorithm is superior to that of the existing state-of-the-art global and multiple metric learning algorithms. [ABSTRACT FROM AUTHOR]

Efficiently describing and discovering communities in a network is an important research concept for graph clustering. In the paper, we present a community description model that evaluates the local importance of a node in a community and its importance concentration in all communities to reflect its representability to the community. Based on the description model, we propose a new evaluation criterion and an iterative search algorithm for community detection (ISCD). The new algorithm can quickly discover communities in a large-scale network, due to the average linear-time complexity with the number of edges. Furthermore, we provide an initial method of input parameters including the number of communities and the initial partition before algorithm implementation, which can enhance the local-search quality of the iterative algorithm. The proposed algorithm with the initial method is called ISCD+. Finally, we compare the effectiveness and efficiency of the ISCD+ algorithm with six representative algorithms on several real network data sets. The experimental results illustrate that the proposed algorithm is suitable to address large-scale networks. [ABSTRACT FROM AUTHOR]

Rough set theory is one of important tools of soft computing, and rough approximations are the essential elements in rough set models. However, the existing fuzzy rough set model for set-valued data, which is directly constructed based on a kind of similarity relation, fail to explicitly define fuzzy rough approximations. To solve this issue, in this paper, we propose two types of fuzzy rough approximations, and define two corresponding relative positive region reducts. Furthermore, two discernibility matrices and two discernibility functions are introduced to acquire these new proposed reducts, and the relationships among the new reducts and the existing reducts are also be provided. Theoretical analyses demonstrate that the new types of reducts have less redundancy and are more diverse (no lower number of reducts) than those obtained by means of the existing matrices, and experimental results illustrate the new reducts found by our methods outperform those obtained by existing method. [ABSTRACT FROM AUTHOR]

In Value-based and Actor-Critic reinforcement learning (RL) methods, both inaccuracy and instability of value estimation will detrimentally affect their performance. Some typical RL methods, such as Maxmin Q-learning and QMD3, are plagued by the underestimation problem while failing to trade off the estimation bias and variance jointly. We propose the Reinforced Operation (RO) to address these shortcomings, which selects the closest median among multiple Q-function. RO is applicable to any model-free RL method. Theoretically, we introduce the Mean Square Error (MSE) to jointly analyze the estimation bias and variance of value estimation methods. We also demonstrate the superiority of RO in MSE reduction and give an upper bound for the estimation bias of value estimation methods with arbitrary distribution to guide the calculation of the estimation bias of value estimation methods. Based on RO, we propose the variants of Q-learning and TD3, Reinforced Q-learning (RQ) and Reinforced Delayed Deep Deterministic policy gradient (RD3), respectively, to tackle different tasks. We empirically demonstrate that our method can reduce estimation error and achieve superior performance on discrete and continuous benchmark tasks. • A more accurate state-action value estimation method is proposed. • Two algorithms are developed: Reinforced Q-learning and Reinforced Delayed Deep Deterministic policy gradient. • Innovative use of Mean Square Error to analyze bias and variance in different methods. • Theoretically analyze the effectiveness of the proposed method and explore the upper bound. • Experimental results on multiple benchmarks indicate that our methods can achieve state-of-the-art performance. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new method to trend analysis of categorical data streams. A data stream is partitioned into a sequence of time windows and the records in each window are assumed to carry a number of concepts represented as clusters. A data labeling algorithm is proposed to identify the concepts or clusters of a window from the concepts of the preceding window. The expression of a concept is presented and the distance between two concepts in two consecutive windows is defined to analyze the change of concepts in consecutive windows. Finally, a trend analysis algorithm is proposed to compute the trend of concept change in a data stream over the sequence of consecutive time windows. The methods for measuring the significance of an attribute that causes the concept change and the outlier degrees of objects are presented to reveal the causes of concept change. Experiments on real data sets are presented to demonstrate the benefits of the trend analysis method. [Copyright &y& Elsevier]

Abstract: Multigranulation rough sets (MGRS) is one of desirable directions in rough set theory, in which lower/upper approximations are approximated by granular structures induced by multiple binary relations. It provides a new perspective for decision making analysis based on rough set theory. In decision making analysis, people often adopt the decision strategy “Seeking common ground while eliminating differences” (SCED). This strategy implies that one reserves common decisions while deleting inconsistent decisions. From this point of view, the objective of this study is to develop a new multigranulation rough set based decision model based on SCED strategy, called pessimistic multigranulation rough sets. We study this model from three aspects, which are lower/upper approximation and their properties, decision rules and attribute reduction, in this paper. [Copyright &y& Elsevier]

Abstract: Set-valued ordered information systems can be classified into two categories: disjunctive and conjunctive systems. Through introducing two new dominance relations to set-valued information systems, we first introduce the conjunctive/disjunctive set-valued ordered information systems, and develop an approach to queuing problems for objects in presence of multiple attributes and criteria. Then, we present a dominance-based rough set approach for these two types of set-valued ordered information systems, which is mainly based on substitution of the indiscernibility relation by a dominance relation. Through the lower/upper approximation of a decision, some certain/possible decision rules from a so-called set-valued ordered decision table can be extracted. Finally, we present attribute reduction (also called criteria reduction in ordered information systems) approaches to these two types of ordered information systems and ordered decision tables, which can be used to simplify a set-valued ordered information system and find decision rules directly from a set-valued ordered decision table. These criteria reduction approaches can eliminate those criteria that are not essential from the viewpoint of the ordering of objects or decision rules. [Copyright &y& Elsevier]

• We propose a novel end-to-end model for graph-based semi-supervised learning. • The high-order connectivity among nodes can be obtained by GCN learners. • Unlabeled nodes are utilized to augment the diversity among the GCN learners. • Show the effectiveness of the proposed model. Recently, graph convolutional networks (GCN) have made substantial progress in semi-supervised learning (SSL). However, established GCN-based methods have two major limitations. First, GCN-based methods are restricted by the oversmoothing issue that limits their ability to extract knowledge from distant but informative nodes. Second, most available GCN-based methods exploit only the feature information of unlabeled nodes, and the pseudo-labels of unlabeled nodes, which contain important information about the data distribution, are not fully utilized. To address these issues, we propose a novel end-to-end ensemble framework, which is named mixed-order graph convolutional networks (MOGCN). MOGCN consists of two modules. (1) It constructs multiple simple GCN learners with multi-order adjacency matrices, which can directly capture the high-order connectivity among the nodes to alleviate the problem of oversmoothing. (2) To efficiently combine the results from multiple GCN learners, MOGCN employs a novel ensemble module, in which the pseudo-labels of unlabeled nodes from various GCN learners are used to augment the diversity among the learners. We conduct experiments on three public benchmark datasets to evaluate the performance of MOGCN on semi-supervised node classification tasks. The experimental results demonstrate that MOGCN consistently outperforms state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Recently, correlation filter has been widely applied in unmanned aerial vehicle (UAV) tracking due to its high frame rates, robustness and low calculation resources. However, it is fragile because of two inherent defects, i.e., boundary effect and filter corruption. To handle them, in this work, we propose a novel ℓ 1 regularization correlation filter with adaptive contextual learning and keyfilter selection for UAV tracking. Firstly, we adaptively detect the positions of effective contextual distractors by the aid of the distribution of local maximum values on the response map of current frame which is generated by using the previous correlation filter model. Next, we eliminate inconsistent labels for the tracked target by removing one on each distractor and develop a new score scheme for each distractor. Then, we can select the keyfilter from the filters pool by finding the maximal similarity between the target at the current frame and the target template corresponding to each filter in the filters pool. Finally, quantitative and qualitative experiments on three authoritative UAV datasets show that the proposed method is superior to the state-of-the-art tracking methods based on correlation filter framework. [ABSTRACT FROM AUTHOR]