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Multi-granulation decision-theoretic rough set effectively combines Bayesian decision approaches with multi-granulation rough set theory, and provides an important theoretical framework for studying rough set. In this paper, we explore several extensional models of multi-granulation decision-theoretic rough sets under the normal distribution of the decision loss function. Using the 3σ rule of normal distribution, we transform the decision loss of the multi-granulation decision-theoretic rough set into a set of interval values. We construct the upper and lower approximations from the optimistic, weakly optimistic, pessimistic, weakly pessimistic, optimistic-pessimistic, weakly optimistic-pessimistic, pessimistic-optimistic, and weakly pessimistic-optimistic viewpoints, and provide the decision rules of the proposed rough set models. The work in this paper brings the decision behavior based on a multi-granulation decision-theoretic rough set closer to the actual situation.

Abundant data with limited labeling are a widespread bottleneck in multilabel learning. Active learning (AL) is an effective solution to gradually enhance model robustness, however how to effectively extend instance selection criteria to multilabel case remains challenging. Considering the label specificity and label correlation, a granular batch mode-based ranking active model for the multilabel (GBRAML) is proposed. Taking a bottom-up view, three granulation operators are successively constructed to formulate three granular structures. In low-level granulation operator, auxiliary label is introduced to enhance the informativeness and representativeness of each label. The contribution of labels to the usefulness of instances is incorporated with pair-wise label correlation, and is considered in the middle-level granulation operator. The labeling priority is determined by ranking the scorings coming from high-level granulation operator. To alleviate the impact of skewed label correlation, we take a three-way strategy on fitness of representative label correlation, thus a three-way GBRAML model (TGBRAML) is devised. Extensive experiments on six multilabel benchmark demonstrate GBRAML gains 5.4% and 210.1% improvement on MicroF1 and Average Precision over state-of-the-art batch mode multilabel active learning. The effectiveness of three-way decisions in multilabel AL is also verified.

Person search aims to locate and retrieve specific pedestrians in scene images, including two subtasks, pedestrian detection and person re-identification. Recently, triplet loss has been widely used in person re-identification, which effectively improves the pedestrian features embedding and achieves superior performance. However, forming triplet in the person search is not an easy task. Most of the existing end-to-end person search methods are based on Faster R-CNN. The training process of person re-identification part is affected by the detector. It is difficult to form pedestrian triplets within a limited batch size. Also, there are many pedestrian identities in the person search dataset, but each pedestrian identity only has a few samples. It is difficult to learn a robust pedestrian feature representation for person search. To resolve the problem discussed above, a novel Feature Compactness (FC) Loss for the person search is designed, which efficiently improves the inter-class discrimination and intra-class compactness of pedestrian features embedding without the need for positive or negative pairs. Besides, we propose a pedestrian attention module (PAM) to help the network focuses more on pedestrian information and suppresses irrelevant background information. Our method achieves comparable performance on two benchmarks, CUHK-SYSU and PRW, and achieves 91.96% of mAP and 93.34% of rank1 accuracy on CUHK-SYSU.

Attribute reduction is attracting considerable attention in the theory of rough sets, and thus many rough-set-based attribute reduction methods have been presented. However, most of them are specifically designed for either labeled or unlabeled data, whereas many real-world applications involve partial supervision. In this paper, we propose a rough-set-based semi-supervised attribute reduction method for partially labeled data. Specifically, using prior class-distribution information, we first develop a simple yet effective strategy to produce proxy labels for unlabeled data. Then, the concept of information granularity is integrated into an information-theoretic measure, based on which, a novel granular conditional entropy measure is proposed, and its monotonicity is theoretically proved. Furthermore, a fast heuristic algorithm is provided to generate the optimal reduct of partially labeled data, which could accelerate the process of attribute reduction by removing irrelevant examples and simultaneously excluding redundant attributes. Extensive experiments conducted on UCI data sets demonstrate that the proposed semi-supervised attribute reduction method is promising and, in terms of classification performance, it even compares favorably with supervised methods on labeled and unlabeled data with true labels (Our code and experimental data are released at Mendeley Data https://doi.org/10.17632/v3byhx2v8s.1).

This paper develops a weak-label-based global and local multi-view multi-label learning with three-way clustering (WL-GLMVML-ATC) to solve multi-view multi-label data sets and exploit more authentic global and local label correlations of both the whole data set and each view simultaneously. Different from the traditional learning methods, WL-GLMVML-ATC pays more attention to the solutions of weak-label cases and uncertain relationships of clusters with the usage of Universum and active three-way clustering. According to Universum notion, even though the size of labeled instances is much more smaller than the unlabeled ones, the useful sample information can still be enhanced. Through the active three-way clustering strategy, the belongingness of instances to a cluster depend on the probabilities of uncertain instances belonging to core regions. This strategy brings a more authentic local label correlation since many traditional methods suppose that instances and the corresponding clusters always exhibit certain relationships such as belong-to definitely and not belong-to definitely. This hypothesis is not ubiquitous in real-world applications. According to the experiments, we can see WL-GLMVML-ATC (1) achieves a better performance, be superior to the classical multi-view learning methods and multi-label learning methods in statistical, advances the development of these learning methods in final; (2) won’t add too much running time; (3) has a good convergence and ability to process multi-view multi-label data sets.

Person search aims to locate and recognize a specified person from a gallery of uncropped scene images, which combines pedestrian detection and person re-identification (re-ID). Existing methods based on Faster R-CNN have been widely used to tackle the two sub-tasks jointly, but they ignore the feature misalignment problem, i.e., re-ID feature localization is not fully aligned with the detected bounding boxes (BBoxes). Due to the fine-grained property of re-ID, it is crucial to extract accurate appearance features. In addition, the granularity of BBoxes detected from gallery images is quite different, and it is defective to treat gallery boxes with different granularity as equal in estimating their similarities with the query. Three-way decision methods are fields of research on human-inspired computation. Inspired by them, we propose a three-way-based feature alignment framework (3W-AlignNet) to optimize the re-ID feature localization. The framework is implemented by iteratively generating new BBoxes and features from previous BBoxes. The three-way decision theory is applied to avoid the mismatch problem caused by increasing Intersection over Union (IoU). We further propose a Granularity Weighted Similarity (GWS) algorithm to relieve the granularity mismatch problem. Extensive experiments show that our method outperforms all other state-of-the-art end-to-end methods on two widely used person search datasets, CUHK-SYSU and PRW.

Attribute reduction of rough set theory underlies knowledge acquisition and has two hierarchical types (classification-based and class-specific attribute reducts) and two perspectives from algebra and information theory; thus, there are four combined modes in total. Informational class-specific reducts are fundamental but lacking and are thus investigated by correspondingly constructing class-specific information measures. First, three types of information measures (i.e., information entropy, conditional entropy, and mutual information) are novelly established at the class level by hierarchical decomposition to acquire their hierarchical connection, systematical relationship, uncertainty semantics, and granulation monotonicity. Second, three types of informational class-specific reducts are correspondingly proposed to acquire their internal relationship, basic properties, and heuristic algorithm. Third, the informational class-specific reducts achieve their transverse connections, including the strength feature and consistency degeneration, with the algebraic class-specific reducts and their hierarchical connections, including the hierarchical strength and balance, with the informational classification-based reducts. Finally, relevant information measures and attribute reducts are effectively verified by decision tables and data experiments. Class-specific information measures deepen existing classification-based information measures by a hierarchical isomorphism, while the informational class-specific reducts systematically perfect attribute reduction by level and viewpoint isomorphisms; these results facilitate uncertainty measurement and information processing, especially at the class level.

The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information, and the limited tolerance relation is developed to overcome the problem that objects leniently satisfy the tolerance relation. However, the classification based on the limited tolerance relationship cannot reflect the matching degree of uncertain information of objects. In this article, we explore the influence of null values in an incomplete system, and propose the constrained tolerance relation based on the matching degree of uncertain information of objects. The proposed rough set based on the constrained tolerance relation can provide a more detailed structure of an object class through threshold. Proofs and example analyses further show the rationality and superiority of the proposed model.

The notion of fuzzy concept is proposed to deal with object-attribute data with L-values (where L is a truth-value structure). One disadvantage of fuzzy concept is that a fuzzy context contains a considerable number of fuzzy concepts. This makes it very time-consuming to generate a fuzzy concept lattice, and it is very difficult to find important concepts. In addition, the fuzzy concept shows great strictness when applying to crisp sets. To overcome these problems, we propose several new kinds of variable-precision concepts within L-contexts in this paper. First, we present two kinds of variable-precision two-way (VP2W) concepts: α-positive concept and β-negative concept. The family of each kind of VP2W concept forms a complete lattice. Next, considering both the positive and negative parts, we investigate two kinds of variable-precision three-way (VP3W) concepts: ( α , β ) -object-induced three-way concept and ( α , β ) -attribute-induced three-way concept. The family of each kind of VP3W concept forms a complete lattice. Then, we study the relationships between VP2W concepts and VP3W concepts. The results show that VP3W concept lattices can be directly generated by VP2W concept lattices. Finally, the experiments are preformed to verify the effectiveness of our model.

Machine reading comprehension is a very challenging task, which aims to determine the answer span based on the given context and question. The newly developed pre-training language model has achieved a series of successes in various natural language understanding tasks with its powerful contextual representation ability. However, these pre-training language models generally lack the downstream processing structure for specific tasks, which limits further performance improvement. In order to solve this problem and deepen the model’s understanding of the question and context, this paper proposes S&I Reader. On the basis of the pre-training model, skimming, intensive reading, and gated mechanism modules are added to simulate the behavior of humans reading text and filtering information. Based on the idea of granular computing, a multi-granularity module for computing context granularity and sequence granularity is added to the model to simulate the behavior of human beings to understand the text from words to sentences, from parts to the whole. Compared with the previous machine reading comprehension model, our model structure is novel. The skimming module and multi-granularity module proposed in this paper are used to solve the problem that the previous model ignores the key information of the text and cannot understand the text with multi granularity. Experiments show that the model proposed in this paper is effective for both Chinese and English datasets. It can better understand the question and context and give a more accurate answer. The performance has made new progress on the basis of the baseline model.

The theory of three-way decision plays an important role in decision making and knowledge reasoning. However, little attention has been paid to the problem of learning from partially labeled data with three-way decision. In this paper, we propose a three-way co-decision model for partially labeled data. More specifically, the problem of attribute reduction for partially labeled data is first investigated, and two semi-supervised attribute reduction algorithms based on novel confidence discernibility matrix are proposed. Then, a three-way co-decision model is introduced to classify unlabeled data into useful, useless, and uncertain data, and the model is iteratively retrained on the carefully selected useful data to improve its performance. Moreover, we theoretically analyze the effectiveness of the proposed model. The experimental results conducted on UCI data sets demonstrate that the proposed model is promising, and even compares favourably with the single supervised classifier trained on all training data with true labels.

Person re-identification (Re-ID) is a challenging task in the field of computer vision and focuses on matching people across images from different cameras. The extraction of robust feature representations from pedestrian images through CNNs with a single deterministic pooling operation is problematic as the features in real pedestrian images are complex and diverse. To address this problem, we propose a novel center-triplet (CT) model that combines the learning of robust feature representation and the optimization of metric loss function. Firstly, we design a fusion feature learning network (FFLN) with a novel fusion strategy consisting of max pooling and average pooling. Instead of adopting a single deterministic pooling operation, the FFLN combines two pooling operations that can learn high response values, bright features, and low response values, discriminative features simultaneously. Our model obtains more discriminative fusion features by adaptively learning the weights of the features learned by the corresponding pooling operations. In addition, we design a hard mining center-triplet loss (HCTL), a novel improved triplet loss, which effectively optimizes the intra/inter-class distance and reduces the cost of computing and mining hard training samples simultaneously, thereby enhancing the learning of robust feature representation. Finally, we proved our method can learn robust and discriminative feature representations for complex pedestrian images in real scenes. The experimental results also illustrate that our method achieves an 81.8% mAP and a 93.8% rank-1 accuracy on Market1501, a 68.2% mAP and an 83.3% rank-1 accuracy on DukeMTMC-ReID, and a 43.6% mAP and a 74.3% rank-1 accuracy on MSMT17, outperforming most state-of-the-art methods and achieving better performance for person re-identification.

The regression is one of classical models in machine learning. Traditional regression algorithms involve operations of real values, which are difficult to handle the discrete or set data in information systems. Granules are structural objects on which agents perform complex computations. The structural objects are forms of sets that can measure the uncertainty of data. In order to deal with uncertain and vague data in the real world, we propose a set-based regression model: granular regression. Granules are constructed by introducing a distance metric on single-atom features. Meanwhile, we establish conditional granular vectors, weight granular vectors and decision granules. The operations among them induce a granular regression model. Furthermore, we propose a gradient descent method for the granular regression model, and the optimal solution of granular regression is achieved. We prove the convergence of granular regression and design a gradient descent algorithm. Finally, several UCI data sets are used to test and verify the granular regression model. We compare our proposed model with popular regression models from three aspects of convergence, fitting and prediction. The results show that the granular regression model is valid and effective.

Attribute reduction is a critical issue in rough sets theory. In recent years, there are many kinds of attribute reduction proposed, such as positive region preservation reduction, generalized decision preservation reduction, distribution preservation reduction, maximum distribution preservation reduction, and relative discernibility relation preservation reduction. General reduction approaches to obtaining various types of reducts also have been explored, but they are computationally time-consuming in the condition of large-scale data processing. In this study, we focus on the efficient general reduction algorithm to obtain five typical reducts mentioned above. At first, we introduce a concept called granularity space to establish a unified representation of five typical reducts. Based on the unified representation, we construct two quick general reduction algorithms by extending the positive region approximation to the granularity space. Then, we conduct a series of comparisons with existing reduction algorithms in aspects of theoretical analysis and experiments to evaluate the performance of the proposed algorithms. The results of analysis and experiments indicate that the proposed algorithms are effective and efficient.

By reformulating and extending the properties of three-way operators, this paper investigates the relationship between different kinds of three-way concept lattices. Three-way operators are defined through eight kinds of two-way operators which are connected by the complement operation. To examine the interrelations systematically, we study (a) the relationship between two-way operators, (b) the relationship between two-way concepts, (c) the relationship between three-way operators, and (d) the relationship between three-way concepts. The results show that the four kinds of object-induced three-way concept lattices are order isomorphic to each other and the four kinds of attribute-induced three-way concept lattices are also order isomorphic to each other.

Minimal and maximal descriptions of concepts are two important notions in covering-based rough sets. Many issues in covering-based rough sets (e.g., reducts, approximations, etc.) are related to them. It is well known that, it is time-consuming and error-prone when set representations are used to compute minimal and maximal descriptions in a large scale covering approximation space. To address this problem, matrix-based methods have been proposed in which calculations can be conveniently implemented by computers. In this paper, motivated by the need for knowledge discovery from large scale covering information systems and inspired by the previous research work, we present two novel matrix-based approaches to compute minimal and maximal descriptions in covering-based rough sets, which can reduce the computational complexity of traditional methods. First, by introducing the operation “sum” into the calculation of matrix instead of the operation “ ⊕ ”, we propose a new matrix-based approach, called approach-1, to compute minimal and maximal descriptions, which does not need to compare the elements in two matrices. Second, by using the binary relation of inclusion between elements in a covering, we propose another approach to compute minimal and maximal descriptions. Finally, we present experimental comparisons showing the computational efficiency of the proposed approaches on six UCI datasets. Experimental results show that the proposed approaches are promising and comparable with other tested methods.

Hierarchical classification (HC) is effective when categories are organized hierarchically. However, the blocking problem makes the effect of hierarchical classification greatly reduced. Blocking means that samples are easily getting misclassified in high-level classifiers so that the samples are blocked at the high-level of the hierarchy. This issue is caused by the inconsistency between the artificially defined hierarchy and the actual hierarchy of the raw data. Another issue is that it is flippant to strictly process data following the hierarchy. Therefore, special treatment is required for some uncertain data. To address the first issue, we learn category relationships and modify the hierarchy. To address the second issue, we introduce three-way decisions (3WD) to targetedly deal with the ambiguous data. We extend original studies and propose two HC models based on 3WD, collectively referred to as TriHC, for carefully modifying the hierarchy to alleviate the blocking problem. The proposed TriHC model learns new category hierarchies by the following three steps: (1) mining category relations; (2) modifying category hierarchies according to the latent category relations; and (3) using 3WD to divide observed objects into three regions: positive region, boundary region, and negative region, and making decisions based on different strategies. Specifically, based on different category relation mining methods, there are two versions of TriHC, cross-level blocking priori knowledge based TriHC (CLPK-TriHC) and expert classifier based TriHC (EC-TriHC). The CLPK-TriHC model defines a cross-level blocking distribution matrix to mine the category relations between the higher and lower levels. To better exploit category hierarchical relations, the EC-TriHC model builds expert classifiers using topic model to learn latent category topics. Experimental results validate that the proposed methods can simultaneously reduce the blocking and improve the classification accuracy.

Rough set theory is an essential tool for measuring uncertainty, which has been widely applied in attribute reduction algorithms. Most of the related researches focus on how to update the lower and the upper approximation operator to match data characteristics or how to improve the efficiency of the attribute reduction algorithm. However, in the nominal data environment, existing rough set models that use the Hamming metric and its variants to evaluate the relations between nominal objects can not capture the inherent ordered relationships and statistic information from nominal values due to the complexity of data. The missing information will affect the accuracy and validity of the data representation, thereby reducing the reliability of rough set models. To overcome this challenge, we propose a novel object dissimilarity measure, i.e., relative object dissimilarity metric(RODM) that learned from nominal data to replace the Hamming metric and then construct a ψ-neighborhood rough set model. It extends the classical rough set model to a robust, representative, and effective model which is close to the characteristics of nominal data. Based on the ψ-neighborhood rough set model, we propose a heuristic two-stage attribute reduction algorithm(HTSAR) to perform the feature selection task. Experiments show that the ψ-neighborhood rough set model can take advantage of more potential knowledge in nominal data and achieve better performance for attribute reduction than the existing rough set model.

In some real-world situations, Pythagorean fuzzy sets are more powerful and effective than intuitionistic fuzzy sets to describe vague and uncertain information, and there are many Pythagorean fuzzy information systems for conflicts in which attitudes of agents on issues are depicted by Pythagorean fuzzy numbers. In this paper, we first provide the concepts of positive, neutral, and negative alliances with two thresholds and employ examples to illustrate how to compute positive, neutral, and negative alliances in Pythagorean fuzzy information systems for conflicts. Then, we focus on three-way conflict analysis based on the Bayesian minimum risk theory and explore examples to show how to compute the positive, neutral, and negative alliances with a Pythagorean fuzzy loss function given by an expert. Finally, we study how to calculate positive, neutral, and negative alliances with group decision theory and take examples to demonstrate how to construct the positive, neutral, and negative alliances with a group of Pythagorean fuzzy loss functions given by more experts.

Person Re-identification (ReID) aims to retrieve the pedestrian with the same identity across different views. Existing studies mainly focus on improving accuracy, while ignoring their efficiency. Recently, several hash based methods have been proposed. Despite their improvement in efficiency, there still exists an unacceptable gap in accuracy between these methods and real-valued ones. Besides, few attempts have been made to simultaneously explicitly reduce redundancy and improve discrimination of hash codes, especially for short ones. Integrating Mutual learning may be a possible solution to reach this goal. However, it fails to utilize the complementary effect of teacher and student models. Additionally, it will degrade the performance of teacher models by treating two models equally. To address these issues, we propose a salience-guided iterative asymmetric mutual hashing (SIAMH) to achieve high-quality hash code generation and fast feature extraction. Specifically, a salience-guided self-distillation branch (SSB) is proposed to enable SIAMH to generate hash codes based on salience regions, thus explicitly reducing the redundancy between codes. Moreover, a novel iterative asymmetric mutual training strategy (IAMT) is proposed to alleviate drawbacks of common mutual learning, which can continuously refine the discriminative regions for SSB and extract regularized dark knowledge for two models as well. Extensive experiment results on five widely used datasets demonstrate the superiority of the proposed method in efficiency and accuracy when compared with existing state-of-the-art hashing and real-valued approaches. The code is released at https://github.com/Vill-Lab/SIAMH .

Neighborhood Covering (NC) is the union of homogeneous neighborhoods and provides a set-level approximation of data distribution. Because of the nonparametric property and the robustness to complex data, neighborhood covering has been widely used for data classification . Most existing methods directly classify data samples according to the nearest neighborhoods. However, the certain classification methods strictly classify the uncertain data and may lead to serious classification mistakes. To tackle this problem, we extend traditional neighborhood coverings to fuzzy ones and thereby propose a Three-Way Classification method with Fuzzy Neighborhood Covering (3WC-FNC). Fuzzy neighborhood covering consists of membership functions and forms an approximate distribution of neighborhood belongingness. Based on the soft partition induced by the memberships of fuzzy neighborhood coverings of different classes, data samples are classified into Positive (certainly belonging to a class), Negative (certainly beyond classes) and Uncertain cases. Experiments verify that the proposed three-way classification method is effective to handle the uncertain data and in the meantime reduce the classification risk.

In order to process multi-view multi-label data sets, we propose global and local multi-view multi-label learning (GLMVML). This method can exploit global and local label correlations of both the whole data set and each view simultaneously. What’s more, GLMVML introduces a consensus multi-view representation which encodes the complementary information from different views. Related experiments on three multi-view data sets, fourteen multi-label data sets, and one multi-view multi-label data set have validated that (1) GLMVML has a better average AUC and precision and it is superior to the classical multi-view learning methods and multi-label learning methods in statistical; (2) the running time of GLMVML won’t add too much; (3) GLMVML has a good convergence and ability to process multi-view multi-label data sets; (4) since the model of GLMVML consists of both the global label correlations and local label correlations, so parameter values should be moderate rather than too large or too small.

Three-way decisions provide a trisecting-and-acting framework for complex problem solving. For a cost-sensitive decision-making problem under multiple levels of granularity, sequential three-way decisions have come into being. Within this framework, how to act upon the three pair-wise disjoint regions is the most important issue. To this end, we propose a generalized model of sequential three-way decisions via multi-granularity in this paper. Subsequently, we adopt the typical aggregation strategies to implement the following five kinds of multigranulation sequential three-way decisions—the weighted arithmetic mean multigranulation sequential three-way decisions, the optimistic multigranulation sequential three-way decisions, the pessimistic multigranulation sequential three-way decisions, the pessimistic-optimistic multigranulation sequential three-way decisions and the optimistic-pessimistic multigranulation sequential three-way decisions. Furthermore, we discuss the rightness and rationality of the five kinds of multigranulation sequential three-way decisions and also analyze the relationships and differences between them. Finally, the experimental results demonstrate that the first four different multigranulation sequential three-way decisions are effective. These models will accelerate and enrich the development of multigranulation three-way decisions.

Three-way decisions (3WD) is an important methodology in solving problems with uncertainty. A systematic analysis on three-way based uncertainty measures is conducive to the promotion of three-way decisions. Meanwhile, confusion matrix, with multifaceted views, serves as a fundamental role in evaluating classification performance. In this paper, confusion matrix is endowed with semantics of three-way decisions. A collection of measures are thus deduced and summarized into seven measure modes. We further investigate the formulation of three-way regions from a measure driven view. To satisfy the preferences of stakeholder, two different objective functions are formulated, and each of them can include different combinations of measures. To demonstrate the effectiveness, we generate probabilistic three-way decisions for a wealth of datasets. Compared with Gini coefficient based and Shannon entropy based objective functions, our model can deduce more satisfying three-way regions.

Semi-supervised multi-view learning machine is developed to process the corresponding semi-supervised multi-view data sets which consist of labeled and unlabeled instances. But in real-world applications, for a multi-view data set, only few instances are labeled with the limitation of manpower and cost. As a result, few prior knowledge which is necessary for the designing of a learning machine is provided. Moreover, in practice, different views and features play diverse discriminant roles while traditional learning machines treat these roles equally and assign the same weight just for convenience. In order to solve these problems, we introduce Universum learning to obtain more prior knowledge and assign different weights for views and features to reflect their diverse discriminant roles. The proposed learning machine is named as weight-and-Universum-based semi-supervised multi-view learning machine (WUSM). In WUSM, we first obtain weights of views and features. Then, we construct Universum set to obtain more prior knowledge on the basis of these weights. Different from traditional construction ways, the used construction way makes full use of the information of all labeled and unlabeled instances rather than only a pair of positive and negative training instances. Finally, we design the machine with the usage of the Universum set along with original data set. Our contributions are given as follows. (1) With the usage of all (labeled, unlabeled) instances of the data set, the Universum set provides more useful prior knowledge. (2) WUSM considers the diversities of views and features. (3) WUSM advances the development of semi-supervised multi-view learning machines. Experiments on bipartite ranking, feature selection, dimensionality reduction, classification, clustering, etc. validate the advantages of WUSM and draw a conclusion that with the introduction of Universum learning, view weights, and feature weights, the performance of a semi-supervised multi-view learning machine is boosted.

Data and rules power expert systems and intelligent systems. Rules, as a form of knowledge representation, can be acquired by experts or learned from data. The accuracy and precision of knowledge largely determines the success of the systems, which awakens the concern for causality. The ability to elicit cause–effect rules directly from data is key and difficult to any expert systems and intelligent systems. Rough set theory has succeeded in automatically transforming data into knowledge, where data are often presented as an attribute-value table. However, the existing tools in this theory are currently incapable of interpreting counterfactuals and interventions involved in causal analysis. This paper offers an attempt to characterize the cause–effect relationships between attributes in attribute-value tables with intent to overcome existing limitations. First, we establish the main conditions that attributes need to satisfy in order to estimate the causal effects between them, by employing the back-door criterion and the adjustment formula for a directed acyclic graph. In particular, based on the notion of lower approximation, we extend the back-door criterion to an original data table without any graphical structures. We then identify the effects of the interventions and the counterfactual interpretation of causation between attributes in such tables. Through illustrative studies completed for some attribute-value tables, we show the procedure for identifying the causation between attributes and examine whether the dependency of the attributes can describe causality between them.

Classical radial basis function network (RBFN) is widely used to process the non-linear separable data sets with the introduction of activation functions. However, the setting of parameters for activation functions is random and the distribution of patterns is not taken into account. To process this issue, some scholars introduce the kernel clustering into the RBFN so that the clustering results are related to the parameters about activation functions. On the base of the original kernel clustering, this study further discusses the influence of kernel clustering on an RBFN when the setting of kernel clustering is changing. The changing involves different kernel-clustering ways [bubble sort (BS) and escape nearest outlier (ENO)], multiple kernel-clustering criteria (static and dynamic) etc. Experimental results validate that with the consideration of distribution of patterns and the changes of setting of kernel clustering, the performance of an RBFN is improved and is more feasible for corresponding data sets. Moreover, though BS always costs more time than ENO, it still brings more feasible clustering results. Furthermore, dynamic criterion always cost much more time than static one, but kernel number derived from dynamic criterion is fewer than the one from static.

In some information system with order features, when users consider “greater than” or “less than” relations to a certain degree rather than in the full sense, using traditional methods may face great limitations. In light of natural connections among concept lattice, inclusion degree, order relations, and the feasibility of mutual integration among the three (concept lattice is essentially a type of data analysis tool using binary relations as research objects, while inclusion degree is a type of powerful tool for measuring uncertain order relations), the paper attempts to analyze uncertain order relations quantitatively within the framework of integration theory of concept lattice and inclusion degree. By which, the research scope of order relations undergoes an expansion-to-contraction process. Namely, certain order relations are first expanded to fuzzy or uncertain relations, and then the fuzzy or uncertain relations are allowed to contract to a degree of certainty by setting threshold parameters. Clearly, by properly widening the research scope of order relations, the model not only has good robustness and generalization ability, but also can meet actual needs flexibly. On this basis, solutions for algebraic structure, reduction, core, dependency, et al. are further studied deeply in ordered information systems. In short, the paper, as a meaningful try and exploration, is conducive to the integration of theories, and may offer some new and feasible ways for the study of order relations and ordered information systems.

Three-way approximations of fuzzy sets aim at abstracting fuzzy sets into three pair-wise disjoint categories which facilitate semantic-oriented interpretations and reduce computing burden. Shadowed sets are a schema of three-way approximations of fuzzy sets which are formed based on a specific optimization mechanism. Among different principles guiding the construction of shadowed sets, the criterion of minimum distance offers a new insight within the framework of three-way decision theory. In this paper, the essential mathematical properties of the objective function used as a criterion to construct three-way approximations of fuzzy sets based on the principle of minimal distance, as well the characteristics of the optimal solutions, are analyzed. It is demonstrated that this optimization objective function is continuous but nonconvex with respect to the optimized variables. The nonconvex property makes the solution difficult and different approximate region partitions are obtainable even under the same optimization model. Therefore, further criteria are required to select final partition thresholds and make the construction process well-defined. To address this limitation, the notion of constrained three-way approximations of fuzzy sets is proposed from the perspective of minimal distance. Moreover, a constructive algorithm is provided to obtain the proposed constrained three-way approximations rather than using a direct enumeration method, and its performance is illustrated by considering some typical fuzzy sets along with some data from UCI repository.

Image retrieval algorithms based on the whole image exhibit high complexity due to background interference, low-level description abilities and large storage requirements, while image retrieval algorithms based on the saliency detection have been found to have low accuracy owing to the lack of important information in extracted salient regions caused by the uncertainty of the salient regions of the image. In this paper, we propose a shadowed-set-based image retrieval algorithm, and develop techniques of an automatic selection of two threshold parameters by combining saliency detection and edge detection, which automatically determine shadowed regions. The developed algorithm uses shadowed set theory to divide the image into salient regions, non-salient regions and shadowed regions, in order to extract the useful information of the image and ignore irrelevant one. As a consequence, this leads to the salient regions and the shadowed regions to be jointly involved in the retrieval process. The experimental results reported for several datasets show that the proposed algorithm can effectively improve the retrieval accuracy compared with the existing state-of-the-art algorithms.

Flow graphs in rough set theory exhibit intuitive and explicit formalization , straightforward computation, parallel processing and Markov property . This paper focuses on the extraction of flow graphs directly from data in the form of attribute-value tables as well as the identification of the causation between variables in such tables. Using the equivalence classes and the partitions derived directly from data tables, the variables having Markov property can be founded to form the structures that can be integrated into flow graphs. Then based on these structures, the causation hidden in data tables can be identified via the front-door criterion proposed by Pearl, also sometimes via the back-door criterion. The relation between the existence of the causation and the flow graph among variables has been established. According to the illustrations, the identification of the causation also relates to the selection of data sample, besides these flow graphs which are similar to the structures hidden in front-door criterion and part in back-door criterion.

Traditional supervised multi-view learning machines aim to process multi-view data sets which consist of labeled instances from multiple views. While they cannot deal with semi-supervised data sets whose training instances consist of both labeled and unlabeled ones. Moreover, with the limitation of storage and process ability, some learning machines cannot process large-scale data sets. Furthermore, some instances maybe have missing features or views and traditional multi-view learning machines have no ability to process the data sets with variable features and views. Thus, this paper develops a semi-supervised one-pass multi-view learning with variable features and views (SOMVFV) so as to process the large-scale semi-supervised data sets with variable features and views. Related experiments on some supervised, semi-supervised, large-scale, and small-scale data sets validate the effectiveness of our proposed SOMVFV and we can get the following conclusions, (1) SOMVFV can process multiple kinds of special data sets; (2) compared with most learning machines used in our experiments, the better performance of SOMVFV is significant; (3) compared with missing views, missing features has a greater influence on the classification accuracy.

Deep neural network models have achieved remarkable results in sentiment classification. Traditional feature-based methods perform slightly worse than deep learning methods in terms of classification accuracy , but they have their own advantages in interpretability and time complexity. To the best of our knowledge, few works study the ensemble of deep learning methods and traditional feature-based methods. Inspired by the methodology of three-way decisions, we proposed a three-way enhanced convolutional neural network model named 3W-CNN. 3W-CNN can be seen as an ensemble method which uses the enhance model to optimize convolutional neural networks (CNN). The enhance model is selected according to the classification accuracy and the difference in classification results compared to CNN. Support vector machine with naive bayes features (NB-SVM) is selected as the enhance model after comparing with several baseline models . However, the performance of NB-SVM is worse than CNN on most of benchmark datasets. To address this issue, we construct a component named confidence divider and design a confidence function to distinguish the classification quality of CNN. NB-SVM is further utilized to reclassify the predictions with weak confidence. The experimental results validated the effectiveness of 3W-CNN and showed three-way decisions could further improve the accuracy of sentiment classification.

Multi-view clustering aims to group multi-view samples into different clusters based on the similarity. Since side information can describe the relation between samples, for example, must-links and cannot-links, thus multi-view clustering with the consideration about side information along with samples can get more feasible clustering results. As a recent developed multi-view clustering approach, multi-view matrix completion (MVMC) constructs similarity matrix for each view and casts clustering into a matrix completion problem. Different from traditional multi-view clustering approaches, MVMC enforces the consistency of clustering results on different views as constraints for alternative optimization and the global optimal solution can be obtained. Although related experiments show that MVMC exhibits impressive performance, it still neglects the possibility of a sample belonging to a cluster. In this paper, we consider the possibility on the base of entropy and develop an entropy-based multi-view matrix completion for clustering with side information (EMVMC). Experiments on multi-view datasets Course, Citeseer, Cora, WebKB, NewsGroup, and Reuters validate the effectiveness of EMVMC.

Uncertainty is a fundamental and unavoidable feature in daily life, which is the same for a single classifier. Thus, combining the predictions of many different classifiers is a very successful way to reduce the uncertainty. In this paper, we present a Correcting Reliability Level (CRL) supervised three-way decision (3WD) cascade model to implement image classification tasks. Our model simulates the human decision process by using 3WD to judge “certainty” or “uncertainty” of the classification result. When judged as “uncertainty”, CRL will supervise the 3WD and learn more information to make the final prediction. In addition, we introduce two Class Grouping methods to mining the relation between labels, which help us to train several expert ConvNets for different types of images. Experimental results show that our model can effectively reduce the classification error rate compared with the base classifier.

Person re-identification (Re-ID) is a typical computer vision problem which matches pedestrians from different cameras. It remains challenging to cope with the variation in light, the change of human pose and view point difference. Many existing person re-identification methods may have difficulty in matching pedestrians when their pictures are similar in appearance or there is object occlusion in pictures. The main problem with these existing methods is that the detail and global features of the images are not well combined. In this paper, we improved the performance of deep CNN network with the proposed Multilevel feature extraction strategy and built a novel Multilevel triplet deep learning model corresponding to our method. The Multilevel feature extraction strategy focuses on combining fine, shallow layer information with coarse, deeper layer information by extracting fusion feature maps from different layers for a better representation of pedestrians. The Multilevel triplet deep learning model (MT-net) provides an end-to-end training and testing plain for our feature extraction strategy. The experiment on the benchmark datasets validated that our multilevel triplet deep learning model had better performance comparing with many state-of-the-art person re-identification methods.

Label ambiguity and data complexity are widely recognized as major challenges in multi-label classification. Existing studies strive to find approximate representations concerning label semantics, however, most of them are predefined, neglecting the personality of instance-label pair. To circumvent this drawback, this paper proposes a three-way selective ensemble (TSEN) model. In this model, three-way decisions is responsible for minimizing uncertainty, whereas ensemble learning is in charge of optimizing label associations. Both label ambiguity and data complexity are firstly reduced, which is realized by a modified probabilistic rough set. For reductions with shared attributes, we further promote the prediction performance by an ensemble strategy. The components in base classifiers are label-specific, and the voting results of instance-based level are utilized for tri-partition. Positive and negative decisions are determined directly, whereas the deferment region is determined by label-specific reduction. Empirical studies on a collection of benchmarks demonstrate that TSEN achieves competitive performance against state-of-the-art multi-label classification algorithms.

Ridge regression (RR) and its extended versions are widely used as an effective feature extraction method in pattern recognition. However, the RR-based methods are sensitive to the variations of data and can learn only limited number of projections for feature extraction and recognition. To address these problems, we propose a new method called robust discriminant regression (RDR) for feature extraction. In order to enhance the robustness, the ${L_{2,1}}$ -norm is used as the basic metric in the proposed RDR. The designed robust objective function in regression form can be solved by an iterative algorithm containing an eigenfunction, through which the optimal orthogonal projections of RDR can be obtained by eigen decomposition. The convergence analysis and computational complexity are presented. In addition, we also explore the intrinsic connections and differences between the RDR and some previous methods. Experiments on some well-known databases show that RDR is superior to the classical and very recent proposed methods reported in the literature, no matter the ${L_{2}}$ -norm or the ${L_{2,1}} $ -norm-based regression methods. The code of this paper can be downloaded from http://www.scholat.com/laizhihui .

This paper proposes a novel descriptor called Maximal Granularity Structure Descriptor (MGSD) for feature representation and an effective metric learning method called Generalized Multi-view Discriminant Analysis based on representation consistency (GMDA-RC) for person re-identification (Re-ID). The proposed descriptor of MGSD captures rich local structural information from overlapping macro-pixels in an image, analyzes the horizontal occurrence of multi-granularity and maximizes the occurrence to extract a robust representation for viewpoint changes. As a result, the proposed descriptor of MGSD can obtain rich person appearance whilst being robust against different condition changes. Besides, considering multi-view information, we present a new GMDA-RC for different views, inspired by the observation that different views share similar data structures. The proposed metric learning method of GMDA-RC seeks multiple discriminant common spaces for multiple views by jointly learning multiple view-specific linear transforms. Finally, we evaluate the proposed method of (MGSD+GMDA-RC) on three publicly available person Re-ID datasets: VIPeR, CUHK-01 and Wide Area Re-ID dataset (WARD). For the VIPeR and CUHK-01, the experimental results show that our method significantly outperforms the state-of-the-art methods, achieving the rank-1 matching rates of 67.09%, 70.61%, and the improvements of 17.41%, 5.34%, respectively. For the WARD, we consider different pairwise camera views (camera 1–2, camera 1–3, camera 2–3) and our method can achieve the rank-1 matching rates of 64.33%, 59.42%, 70.32%, increasing of 5.68%, 11.04%, 9.06% compared with the state-of-the-art methods, respectively.