With the improvement of data collection capabilities and the increase in data volume, multiview multilabel feature selection has gained widespread attention. In multiview multilabel feature selection, it is inevitable to consider both the consistency and complementarity information between views. However, many existing methods tend to independently extract consensus and complementary information, and this fragmented approach often leads to ambiguity in the information partitioning, which in turn generates noise. Furthermore, existing methods do not consider the correlation between views and labels when estimating the effectiveness of different views, which can affect the accuracy of view weights. To address these issues, we propose a multiview multilabel feature selection method that integrates a noise-resistant strategy with fuzzy mutual information for jointly learning commonality and individuality label structures. Specifically, first, we learn the commonality label matrix using nonnegative matrix factorization to explore the consistency between views. This matrix not only captures shared patterns across views but also helps the model better fit the ground-truth labels. Second, we learn individuality label matrices to capture the complementary information of each view, and introduce view noise label matrices to mitigate the impact of inherent noise in the true labels and noise labels generated by partitioning. Third, we incorporate view weights based on fuzzy mutual information, which can accurately reflect the correlation between views and labels to enhance important views while reducing the contribution of noise. Finally, we design a sparse model-based multiview multilabel feature selection method and provide theoretical proof of its convergence. Extensive experiments on multiple benchmark datasets are conducted to demonstrate the effectiveness of our approach.

Partial multi-label feature selection (PMFS) effectively addresses the high-dimensionality challenge in partial multi-label data, where each sample is associated with a candidate label set containing both ground-truth and false positive labels. Most existing methods that perform only a single disambiguation step tend to be insufficient. Moreover, they undervalue rare labels, resulting in the neglect of critical but infrequent information. Furthermore, they overlook the overlapping information within each label pair, resulting in redundant counting of shared information. In addition, they explore the relationship between a candidate feature and selected features under labels solely from the redundancy perspective, which is insufficient. To tackle these challenges, we propose a novel PMFS method, called PMFS-F2Deur. First, we propose fuzzy two-stage disambiguation method to sufficiently minimize the disturbance caused by false positive labels. Second, we propose label weight to measure the importance of each label. Third, we define two relationships between a label pair and a candidate feature, and then propose weighted pure relevance to reduce biased relevance estimation. Fourth, we define weighted feature individual contribution ratio from the perspective of individual contribution. Finally, we propose a PMFS method considering weighted pure relevance, weighted feature individual contribution ratio and redundancy information. Experimental results on artificial and practical partial multi-label datasets confirm that PMFS-F2Deur outperforms other representative methods.

Granular computing, which simulates human cognition by partitioning objects into multiple granules, serves as a valuable approach for handling data with uncertainty and has been widely applied to multilabel feature selection. However, existing methods based on granular computing typically assume equal importance across all labels, which limits their ability to capture the relative recognition of features within the label space. In this article, we address this limitation by analyzing label space dependencies through the lens of rough set theory. In addition, a novel method for multilabel feature selection is introduced, which incorporates relative uncertainty information. First, we propose an object grid-based acceleration method to speed up the computation of relationships in the process of constructing neighborhood granularity, and provide a new definition of neighborhood granularity on this basis. Second, based on the constructed neighborhood granularity, we define uncertainty measures under multilabel data and analyze their corresponding theoretical properties. Finally, by analyzing the dependencies within the label space, we derive an importance matrix for the labels and, by combining it with the defined uncertainty measure, develop a multilabel feature selection method that incorporates relative uncertainty. The experimental results validate the effectiveness of the proposed method.

Multi-label feature selection (MFS) has received much attention because it can effectively mitigate the impact of ‘dimensionality curse’. Ambiguity and unavoidable label noise in real life pose significant challenges to MFS. So far, there are relatively few studies on MFS considering label noise. Existing few studies do not consider that label sets of different samples are affected by noise to different degrees, and ignoring differences between samples may reduce robustness of MFS. Moreover, they explore the fuzzy relationship between samples and labels from a local perspective, which is not comprehensive. In addition, they lack a monotonic metric for measuring attribute importance, leading to the unreasonable selected feature subset. To solve these issues, we propose a noise-tolerant MFS method by monotonic noise-tolerant fuzzy confidence conditional entropy with sample reliability degree and fuzzy association confidence called SRDAC. Firstly, sample reliability degree is defined from the perspective of consistency to distinguish samples affected by different levels of label noise. Secondly, the idea of global similarity and the fuzzy association confidence between samples and labels are proposed, and corresponding noise-tolerant label enhancement for different types of samples is carried out to better explore the relationship between samples and labels. Thirdly, based on noise-tolerant label space, the noise-tolerant fuzzy confidence conditional entropy is proposed to more reasonably measure the relationship between attributes. Finally, a robust MFS method based on monotonic noise-tolerant fuzzy confidence conditional entropy is proposed. Extensive experiments show that the effectiveness and robustness of SRDAC is better than other representative methods.

In recent years, multilabel feature selection (MFS) has gained considerable attention as a key technique in the field of data mining. Embedded methods have been widely adopted due to their simplicity and efficiency. However, most embedded MFS methods assume that all labels share the same feature space. Although previous works have noted this issue and proposed solutions, they still suffer from the inability to accurately identify a specific subset of features for each label. Furthermore, most embedded MFS methods often only consider feature similarity through manifold learning concepts, neglecting the impact of feature redundancy, leading to suboptimal performance. In addition, their weight matrix is usually derived from a single perspective of the loss function. To address these limitations, we propose a novel embedded label-specific MFS method based on fuzzy implication granularity information called LSFSFI. This method uses the partial fuzzy mutual implication granularity information to capture the relationships between labels and features, and introduces an auxiliary matrix to achieve label-specific feature selection, which provides a new perspective for the calculation of the weight matrix. In addition, the normalized fuzzy mutual implication granularity information is used to describe the redundancy between features, and a new redundancy constraint regularization term is proposed to ensure a more reasonable assignment of feature weights. Experimental results on several multilabel datasets show that LSFSFI outperforms existing methods in terms of both performance and practicality.

Multi-label feature selection (MFS) plays a vital role in enhancing model performance by identifying the most relevant features. However, most existing methods assume complete feature information and overlook the potential issue of missing features in real-world applications. Furthermore, existing methods mainly focus on feature redundancy while paying insufficient attention to the potential positive interaction among features, which adversely affects the effectiveness of feature selection. To overcome these limitations, this paper proposes a novel incomplete MFS method based on dynamic dual-graph optimization and fuzzy feature interaction (D2GOFI). The method addresses two core challenges systematically: feature-missing processing and feature interaction modeling. Specifically, D2GOFI introduces a fuzzy tolerance relation to mitigate information loss caused by missing features, and proposes fuzzy tolerance implication granularity information to reveal the data's intrinsic structure and guide the feature selection process effectively. To address the potential issue of over-inclusivity introduced by the fuzzy tolerance relation, a non-negative adjustment matrix has been designed to improve the stability and reliability of feature selection. Meanwhile, D2GOFI explicitly models positive fuzzy interaction between features to enhance the expressiveness of feature relevance evaluation. Finally, a dynamic dual-graph optimization strategy is employed to preserve local manifold structures at the feature and label levels simultaneously, ensuring the feature selection process aligns with the data's inherent patterns. Experimental results demonstrate that D2GOFI achieves superior accuracy and robustness across multiple datasets.

Online streaming feature selection has garnered widespread attention due to its efficiency and adaptability in dynamic data environments. However, existing methods primarily focus on the correlation and redundancy among features, often overlooking the complementarity between candidate and selected features. In this paper, we address this gap by introducing three key innovations. First, we construct a novel metric, fuzzy Gini entropy (FGE), to measure feature uncertainty within datasets. Unlike traditional information entropy, fuzzy Gini entropy inherits the advantages of the Gini index, effectively measuring the impurity of datasets, while also being capable of handling common fuzzy environments. Accordingly, related metrics such as fuzzy joint Gini entropy, fuzzy conditional Gini entropy, and fuzzy mutual Gini information are developed. Second, we innovatively propose the concept of the bidirectional complementarity ratio (BCR), which captures the relationship between candidate features and previously selected features in online streaming feature selection. This mitigates the unfairness associated with the late arrival of features, ensuring that candidate features with a bidirectional complementary effect that outweighs their redundancy effect with the selected features are chosen. Third, we design an online streaming feature selection method named FGE-OSFS. The method evaluates streaming features through three steps: online relevance analysis, online bidirectional complementarity analysis, and online redundancy analysis. Finally, we compare the proposed method with five state-of-the-art online streaming feature selection methods, demonstrating the effectiveness of our new approach.

Online streaming feature selection is an effective approach for handling large-scale streaming data in real-world applications. However, many existing online streaming feature selection studies do not effectively leverage the correlation and hidden information in the label space. The measures used in streaming feature selection often face challenges such as computational complexity and insufficient information exploitation. To address these issues, we propose an online streaming feature selection method based on label enhancement and fuzzy synergistic discrimination information. First, we define a novel label enhancement method based on label correlation, which does not require any prior knowledge of feature space. Second, we propose a new measure to evaluate the discriminative ability of multiple feature subsets for labels in fuzzy environment, called fuzzy synergistic discrimination information. It is bounded and has many interesting properties. The fuzzy synergistic discrimination information is computed directly based on fuzzy similarity relations, so the calculation is relatively simple. Third, based on label enhancement and proposed fuzzy synergistic discrimination information, we construct a three-stage online multilabel streaming feature selection method, including online significance analysis, online relevance analysis, and online redundancy analysis. Finally, comparative experiments on 12 datasets demonstrate the effectiveness and superiority of the proposed method. The influences of different feature sequences and these components on the algorithm's performance are further analyzed.

In recent years, multi-view unsupervised feature selection has gained significant interest for its ability to efficiently handle multi-view datasets while offering better interpretability. Existing multi-view unsupervised feature selection methods construct graphs based on the relationship between samples. In fact, in feature selection, it is more important to focus on the relationships between features. However, constructing a complete graph to capture the relationship between features would incur a space and time complexity of $O(d^{2})$ or even higher. Therefore, we introduce an anchor-based strategy and build a feature bipartite graph to reduce complexity. In addition, since existing methods cannot directly extract feature importance from a feature bipartite graph, we design an effective and low-complexity method to directly obtain feature scores from a feature bipartite graph. Compared with the feature importance extraction method based on the complete graph, our proposed method reduces the time complexity from $O(d^{3})$ to $O(d)$ . To the best of our knowledge, our proposed method is the first multi-view unsupervised feature selection algorithm that achieves $O(nd)$ space and time complexity without data segmentation. Specifically, this method adaptively learns feature-level anchor graph structures through self-expressive multi-view subspace learning, which can effectively capture the structural information between features and anchors. Meanwhile, the proposed method projects low-dimensional anchors to common dimensions and aligns them with consensus anchors to capture the consistency and complementary information between different views. The superiority of the proposed algorithm is demonstrated by comparing it with seven state-of-the-art algorithms on five public image and two biological information multi-view datasets. The code of the proposed method is publicly available at https://github.com/getupLiu/AFRC.

Multi-label feature selection can effectively solve the curse of dimensionality problem in multi-label learning. Existing multi-label feature selection methods mostly handle multi-label data without missing features. However, in practical applications, multi-label data with missing features exist widely, and most existing multi-label feature selection methods are not directly applicable. Therefore, we propose a feature selection method for multi-label data with missing features. First, we propose a method to extract implicit label information from the feature space to replenish the binary label information. Second, we learn the positive correlation between features to construct a feature correlation recovery matrix to recover missing features. Finally, we design a sparse model-based multi-label feature selection method for processing multi-label data with missing features and prove the convergence of this method. Comparative experiments with existing feature selection methods demonstrate the effectiveness of our method.

Multi-label feature selection is an effective approach to mitigate the high-dimensional feature problem in multi-label learning. Most existing multi-label feature selection methods either assume that the data is complete, or that either the features or the labels are incomplete. So far, there are few studies on multi-label data with missing features and labels. In many cases, missing features in instances of multi-label data often lead to missing labels, which is ignored by existing studies. We define this type of data as instance-dependent incomplete multi-label data. In this paper, we propose a feature selection method for instance-dependent incomplete multi-label data. Firstly, we use the positive correlations between features to reconstruct the feature space, thereby recovering missing values and enhancing non-missing values. Secondly, we use fuzzy tolerance relation to guide label recovery, and utilize fuzzy mutual implication granularity to impose structural constraint on the projection matrix. Thirdly, we achieve feature selection by eliminating the impact of incomplete instances and imposing sparse regularization on the projection matrix. Finally, we provide a convergent solution for the proposed feature selection framework. Comparative experiments with existing multi-label feature selection methods show that our method can perform effective feature selection on instance-dependent incomplete multi-label data.

In recent years, multi-view unsupervised feature selection has gained significant interest for its ability to efficiently handle multi-view datasets while offering better interpretability. However, most existing methods face the following challenges: First, the presence of noisy features in the data significantly impacts the process of learning accurate feature importance. Second, the selected features contain redundant information due to ignored redundancy between them. Third, graph structure learning is performed on all samples, resulting in large computational and space overheads, which is not conducive to expansion to large-scale data. To address these challenges, we propose a multi-view unsupervised feature selection method based on latent semantics and anchor graph learning. Specifically, this method designs a feature-weighted orthogonal regression and subspace learning framework to suppress noise interference in the consensus latent semantics discovery and anchor graph construction process, enhance the robustness of multi-view representation learning and reduce the computation of graph construction. Meanwhile, the proposed method employs explicit redundancy mitigation mechanisms that penalize discriminative weight allocation to highly correlated features. Furthermore, the proposed method unifies feature weighting, consensus latent semantics discovery, and adaptive graph learning within a multi-layer learning framework, enabling comprehensive feature importance evaluation through interactive learning between multiple layers. Finally, an efficient iterative algorithm is designed to solve the proposed model. The superiority of the proposed algorithm is demonstrated by comparing it with seven state-of-the-art algorithms on seven public multi-view datasets.

Feature selection, as an important step of data analysis, is widely used in the fields of data mining, machine learning, and artificial intelligence. It can not only effectively alleviate the curse of dimensionality and improve model performance but also enhance model interpretability. In the real world, data is usually complex such as different feature types, the presence of missing values, and so on. However, most existing feature selection approaches are only capable of handling data with a single feature type. To address the issue of feature selection under the environment of complex data, this article proposes a unified feature selection (UFS) approach for complex data based on fuzzy $\beta $ -covering reduction via information granulation. To begin with, several monotonic uncertainty measures for fuzzy $\beta $ -covering are constructed from the viewpoints of algebra and information theory. Based on the proposed measures, two forward heuristic algorithms are designed for fuzzy $\beta $ -covering reduction. Meanwhile, the complex data with multiple features is represented by fuzzy $\beta $ -covering via information granulation. On this basis, a UFS approach is put forward for complex data. Finally, the effectiveness and superiority of the proposed approach are verified through a series of experiments compared with 12 state-of-the-art feature selection approaches.

Representing data in different spaces becomes more powerful and suitable for solving downstream learning tasks. The membership degrees obtained through fuzzy C-means (FCM) clustering cannot capture data structures sufficiently, as they represent samples from a single Euclidean geometrical perspective. To address this issue, we propose a novel fuzzy clustering model guided by spectral rotation and scaling (FCSR). In FCSR, both spectral embeddings and membership degrees are considered as new representations of data. They can complement each other from different perspectives which enables the model to engage more structural properties of the data. The process of solving the problem of membership degrees not only inherits the merits of traditional FCM but also preserves data neighborhood structures revealed by the spectral decomposition based on an affinity matrix. Furthermore, to improve the adaptability and extensibility of FCSR, the projected and kernel versions of FCSR (FCSR-P and FCSR-K) are formed. We demonstrate that FCSR-P is suitable for high-dimensional scenarios and FCSR-K can improve the linear separability among data. Extensive experiments conducted on various well-known data sets illustrate the validity of the proposed ideas.

Recently, the three-way decision models based on prospect theory have attracted much attention, because they can well consider the risk attitude of decision-makers when decisions involve gains and losses. However, in terms of reference point selection for prospect theory, these models adopt a unified strat-egy for all alternatives without considering the characteristics of the alternatives themselves. To solve this problem, a reference point selection method based on fuzzy information granules is proposed in this paper. Furthermore, a prospect theory-based generalized intuitionistic fuzzy three-way decision model is established. Specifically, firstly, a reference point selection method based on fuzzy information granules is constructed for the evaluation values of alternatives. Secondly, based on the value function of prospect theory, an intuitionistic fuzzy scoring function is proposed. Meanwhile, based on the difference between the two intuitionistic fuzzy scoring values, a PROMETHEE-based trisecting method is designed. In addition, utilizing the priority relationship existing in three divisions, a generalized ranking strategy using recursive trisecting is established for obtaining the ranking result of alternatives. Finally, based on the priority relationship of the classification attribute, an effectiveness index is proposed to evaluate the effectiveness of the decision-making method in decision-making cases. On this basis, the proposed model is used to process different decision-making cases, verifying its effectiveness, superiority, and feasibility.

With the increase of high-dimensional multilabel data, multilabel feature selection (MFS) has received more and more widespread attention. Embedded feature selection methods have been widely studied due to their high efficiency and low computational cost. Fuzzy mutual information, as an effective tool for processing continuous features, is widely used in filter feature selection, which results in many repeated entropy calculations. Most of the existing multilabel embedded feature selection methods are based on least squares regression, which loses a lot of statistical and structural information. To solve the above-mentioned problems, we established an optimization framework based on fuzzy mutual information that considers global correlation to obtain the weight of each feature. Under this framework, many repeated entropy operations are avoided. Then, the weight of each feature is introduced into the orthogonal regression optimization framework as prior knowledge. Finally, two optimization frameworks are comprehensively considered for MFS. Furthermore, considering the characteristics of multilabel data, we extend the proposed method to feature-specific MFS. We conducted sufficient experiments to demonstrate the efficiency of our proposed method.

Attribute reduction, also called feature selection, serves as a widely adopted approach to reduce data processing complexity by eliminating irrelevant and redundant attributes. It plays a crucial role in addressing the challenges associated with high-dimensional data, optimizing computational resources, and enhancing learning performance. A well-designed attribute reduction method can effectively streamline data analysis processes and improve the overall efficiency and effectiveness of machine learning algorithms. To some extent, the quantity of information contained in an information system can be regarded as the number of distinguishable sample pairs it contains. In this article, the fuzzy distinguishable pair metric is proposed to measure the uncertainty. This metric measures uncertainty by comprehensively considering the number of fuzzy distinguishable pairs and the cardinality of fuzzy similarity relation. Correspondingly, variants of the fuzzy distinguishable pair metric such as joint distinguishable pair metric, conditional distinguishable pair metric, and mutual distinguishable pair metric are constructed. Moreover, the concepts of selected features redundancy upper bound and selected features redundancy lower bound are proposed. These two terms can be flexibly applied to the importance measure to alleviate the problem of over- or under-consideration redundancy. Considering the upper and lower bounds of the selected feature redundancy respectively, two new importance measures are proposed. Based on the previously proposed theory, two attribute reduction algorithms are designed. Finally, comparing the proposed two methods with six effective attribute reduction methods on eighteen datasets with four classifiers, our method achieves good results.

Fuzzy rough set model is a powerful tool for handling attribute reduction tasks for complex data. While the fuzzy rough set model commonly employs fuzzy information entropy to measure attribute uncertainty, utilizing fuzzy conditional information entropy for measuring attribute relationships presents a drawback due to its lack of monotonicity, impacting attribute reduction results. Furthermore, entropy computations involve numerous logarithmic function computations, resulting in a significant computational burden. Moreover, the results obtained from logarithmic functions are unbounded. To address these problems, this paper presents the concept of Fuzzy Implication Granularity Information (FIGI) for measuring attribute information. Additionally, we introduce several related generalizations, such as fuzzy conditional implication granularity information, fuzzy mutual implication granularity information, and fuzzy joint implication granularity information, aiming to measure the relationships between attributes. Notably, the introduced fuzzy conditional implication granularity information to measure the relationship between attributes demonstrates the desirable property of monotonicity. Crucially, all the metrics proposed in this paper are bounded, ensuring that computed values within the range of 0 to 1. Finally, we propose a forward greedy attribute reduction algorithm based on the monotonic fuzzy conditional implication granularity information (MFIGI), and the performance of our MFIGI algorithm was compared against six different attribute reduction algorithms using three classifiers across 15 different datasets, the experimental results demonstrate the excellence of our MFIGI algorithm.

Considering the extensive research on zeroing neurodynamic (ZN), a self-adaptive and enhanced fixed-time convergent zeroing neurodynamic (SEFC-ZN) method for addressing time-variant problems is presented in this paper based on a discrete fuzzy matrix (DFM) design parameter and a novel advanced sign-bi-power activation function (NASbpAf). Due to the distinctive design of the DFM design parameter and NASbpAf, the proposed SEFC-ZN method possesses prominent self-adaptivity and enhanced fixed-time convergence. Specifically, the DFM design parameter is actually a matrix with all elements generated from a discrete fuzzy control system, so it can self-adaptively adjust the convergence rate of every error in the SEFC-ZN method resulting in the self-adaptivity. This feature is greatly different from the conventional scalar design parameters whose values are usually fixed or increase indefinitely and different errors in the ZN method can only be adjusted by the same design parameter. By summarizing the characteristic of the activation functions designed previously according to the SbpAf, it is found that keeping two terms of the SbpAf and adding extra terms can improve the performance of the ZN method. Thereout, built on the SbpAf, the NASbpAf is presented which can make the SEFC-ZN method realize the enhanced fixed-time convergence. Three theoretical analyses and proofs, together with relative corollaries, conclude the properties of the SEFC-ZN method and the advantages of the DFM design parameter and NASbpAf. A numerical experiment about solving time-variant nonlinear equations by the SEFC-ZN method and an application to the linear-quadratic optimal control strongly verify the proposed theory and method.

Taking advantage of the burgeoning zeroing neural network (ZNN) and the widely used fuzzy logic system (FLS), a novel double integral noise-tolerant fuzzy ZNN (DINTFZNN) model for solving the time-varying Sylvester matrix equation (TVSME) is proposed in this article. The special feature of the DINTFZNN model lies in the adoption of a double integral design formula, which makes the DINTFZNN model has superb robustness, that is, it can effectively suppress not only linear noise but also quadratic noise. In addition, the DINTFZNN model utilizes a fuzzy parameter generated by FLS as the design parameter, which can adaptively adjust the convergence rate and enhance the robustness and adaptability of the DINTFZNN model. Theories have rigorously demonstrated the convergence and robustness of the DINTFZNN model. By the comparison experiments with the single integral noise-tolerant ZNN model, the superiority of the DINTFZNN model is further confirmed. In the end, the design method of the DINTFZNN model is applied to the synchronization of Chua's circuit chaotic systems, which epitomizes its excellent applicability.

Some unsupervised approaches have been proposed recently for the person re-identification (ReID) problem since annotations of samples across cameras are time-consuming. However, most of these methods focus on the appearance content of the sample itself, and thus seldom take the structure relations among samples into account when learning the feature representation, which would provide a valuable guide for learning the representations of the samples. Thus hard samples may not be well solved due to the limited or even misleading information of the sample itself. To address this issue, in this article, we propose a Relation-Preserving Feature Embedding (RPE) model that leverages structure relations among samples to boost the performance of the unsupervised person ReID methods without requiring any sample annotations. RPE aims at integrating the sample content and the neighborhood structure relations among samples into the learning of feature embeddings by combining the advantages of the autoencoder and graph autoencoder. Specifically, a relation and content information fusion (RCIF) module is proposed to dynamically merge the information from both perspectives of content and relation levels for feature embedding learning. Also, due to the lack of the identity labels of samples, we adopt an adaptive optimization strategy to update the affinity relations among samples instead of the reconstruction of the whole affinity matrix for optimizing the RPE model, which is more suitable for the unsupervised ReID task. Rigorous experiments on three widely-used large-scale benchmarks for person ReID demonstrate the superiority of the proposed method over current state-of-the-art unsupervised methods.

Quadratic programming with equality constraint (QPEC) problems have extensive applicability in many industries as a versatile nonlinear programming modeling tool. However, noise interference is inevitable when solving QPEC problems in complex environments, so research on noise interference suppression or elimination methods is of great interest. This article proposes a modified noise-immune fuzzy neural network (MNIFNN) model and use it to solve QPEC problems. Compared with the traditional gradient recurrent neural network (TGRNN) and traditional zeroing recurrent neural network (TZRNN) models, the MNIFNN model has the advantage of inherent noise tolerance ability and stronger robustness, which is achieved by combining proportional, integral, and differential elements. Furthermore, the design parameters of the MNIFNN model adopt two disparate fuzzy parameters generated by two fuzzy logic systems (FLSs) related to the residual and residual integral term, which can improve the adaptability of the MNIFNN model. Numerical simulations demonstrate the effectiveness of the MNIFNN model in noise tolerance.

In this article, a novel distributed gradient neural network (DGNN) with predefined-time convergence (PTC) is proposed to solve consensus problems widely existing in multiagent systems (MASs). Compared with previous gradient neural networks (GNNs) for optimization and computation, the proposed DGNN model works in a nonfully connected way, in which each neuron only needs the information of neighbor neurons to converge to the equilibrium point. The convergence and asymptotic stability of the DGNN model are proved according to the Lyapunov theory. In addition, based on a relatively loose condition, three novel nonlinear activation functions are designed to speedup the DGNN model to PTC, which is proved by rigorous theory. Computer numerical results further verify the effectiveness, especially the PTC, of the proposed nonlinearly activated DGNN model to solve various consensus problems of MASs. Finally, a practical case of the directional consensus is presented to show the feasibility of the DGNN model and a corresponding connectivity-testing example is given to verify the influence on the convergence speed.

In this article, a low-order zeroing neural network (LZNN), a high-order ZNN (HZNN), and a variable-parameter ZNN (VZNN) are designed and applied to the time-changing Cholesky decomposition of any positive-definite matrix, where the LZNN and HZNN models are generated based on the traditional and high-order evolutionary formulas, respectively. In addition, a new activation function (N-Acf) is applied to the LZNN, HZNN, and VZNN models to improve the convergence and robustness. Importantly, the LZNN and HZNN models activated by the N-Acf have faster predefined-time convergence velocity when solving the time-changing Cholesky decomposition problem of any positive-definite matrix, which is demonstrated via theoretical analysis and numerical experiments. Finally, in light of empirical and theoretical evidence, it can be established that the solution model of the VZNN model is able to undergo convergence to the theoretical solution of Cholesky decomposition despite the presence of interposing noise.

Computer vision has always been a hot field of research by contemporary scholars due to its wide range of applications. As an important branch of this field, the visual monitoring technology has shown superior vitality in the actual monitoring environment of the Internet of Things (IoT). However, when the monitoring environment is complex, once the target monitoring fails, the important information related to the target also disappears. At this time, if the existing monitoring method is used, the target cannot be monitored again. Moreover, the current filtering monitoring algorithm also has the problem of poor interpretability. Therefore, this article combines the relevant characteristics of human inertial thinking when dealing with such problems. First, our method screens the movement information of the target and introduces a fuzzy reasoning mechanism to infer the location area of the target through fuzzy thinking. Then, an alternative selection strategy based on the thinking set is applied, which alternates between the location of thinking reasoning and the location of memory to further obtain the effective visual monitoring of the target. The filtering and monitoring algorithm fused with the new mechanism in the OTB-2015 data set, the UVA123 data set, and the TC128 data set all show that the proposed fuzzy inference mechanism has good robustness and universality. Furthermore, our results confirm that it can not only ensure the monitoring speed and overall accuracy but also improve the stability of monitoring in the IoT-assisted monitoring environment, showing its effectiveness compared to state-of-the-art methods. In addition, our results confirm that the integration of the proposed edge learning method with the IoT can be well applied to the construction of smart cities and future generation systems.

Document-level Relation Extraction (DRE) aims to recognize the relations between two entities. The entity may correspond to multiple mentions that span beyond the sentence boundary. Few previous studies have investigated the mention integration, which may be problematic because coreferential mentions do not equally contribute to a specific relation. Moreover, prior efforts mainly focus on reasoning at entity-level rather than capturing the global interactions between the entity pairs. In this paper, we propose two novel techniques,ContextGuidedMentionIntegration andInter-pairReasoning (CGM2IR), to improve DRE. Instead of simply applying average pooling, the contexts are utilized to guide the integration of coreferential mentions in a weighted sum manner. Additionally, inter-pair reasoning executes an iterative algorithm on the entity pair graph, so as to model the interdependency of relations. We evaluate our CGM2IR model on three widely used benchmark datasets, namely DocRED, CDR, and GDA. Experimental results show that our model outperforms previous strong baselines and achieves remarkable effectiveness.

Time-varying matrix inversion (TVMI) is a basic mathematical problem, which is widely involved in many scientific fields. In this article, an event-triggered control fuzzy adaptive zeroing neural network (ETC-FAZNN) model is proposed for solving the TVMI problem, where the fuzzy adaptive convergence parameter (FACP) is got by the redesigned fuzzy logic system, which makes the ETC-FAZNN model adaptive. Meanwhile, the event-triggered control is introduced to control the update of the FACP, which improves the calculation speed of the ETC-FAZNN model. Moreover, a novel activation function called segmented predefined-time activation function is put forward in this article to improve the convergence and robustness of the ETC-FAZNN model. Theoretical analysis and simulation experiments reveal that the ETC-FAZNN model can realize stability, predefined-time convergence, robustness, and adaptability performances in solving the TVMI problem.

Fuzzy$\beta$-covering rough sets, as an effective extension of covering-based rough sets, have been concerned by many researchers. All fuzzy$\beta$-covering rough set models are constructed under a corresponding fuzzy$\beta$-covering approximation space. However, fuzzy$\beta$-covering is difficult to find directly from the real data. Fortunately, fuzzy information granulation provides a reasonable and effective way to obtain fuzzy$\beta$-coverings from the real data. Since fuzzy information granulation is capable of generating multiple fuzzy$\beta$-coverings, we introduce the notion of multifuzzy$\beta$-covering approximation spaces. Fuzzy$\beta$-covering approximation spaces are a special case of multifuzzy$\beta$-covering approximation spaces. Besides, we employ fuzzy$\beta$-neighborhood operators with reflexivity and symmetry to characterize the similarity between samples. In this article, we first present the definition of multifuzzy$\beta$-covering approximation spaces and investigate some useful properties about fuzzy$\beta$-covering. Second, several information measures are explored in the context of multifuzzy$\beta$-covering approximation spaces. On this basis, a novel heuristic fuzzy$\beta$-covering reduction method with the measure of monotone conditional entropy is proposed. Moreover, a general framework of attribute reduction based on fuzzy$\beta$-covering reduction is also designed. Finally, through the comparative and experimental analyses with other four state-of-the-art attribute reduction methods, the effectiveness and superiority of the proposed method are verified.

To overcome the disadvantages of the current zeroing neural network (ZNN) in noise tolerance, this article first proposes an intensive noise-tolerant ZNN (INT-ZNN) by introducing a novel fuzzy control approach (FCA). This FCA is designed dexterously according to the variation of two errors related to the INT-ZNN. Thus, the most feature of the INT-ZNN is that the added fuzzy control can inherently restrain the various noises. Compared with the previous noise-tolerant ZNN derived by the integral design formula, the INT-ZNN with a much simpler structure can tolerate the noise in finite/fixed time. That is, the INT-ZNN activated by nonlinear functions possesses finite/fixed-time convergence while suppressing the noise, which is guaranteed by the presented theorems. Besides, it also theoretically proves that the INT-ZNN has global stability under the interference of noise. In the simulative experiment, the INT-ZNN is used to solve the time-varying Sylvester matrix equation problem and the experimental results verify the excellent noise-tolerance of the INT-ZNN. Meanwhile, the INT-ZNN is successfully applied to image processing.

Two nonlinear zeroing neural network (ZNN) models with prescribed-time convergence for time-dependent matrix LR and QR factorization are proposed in this article. To do so, two algorithms and two error functions are constructed to transform the time-dependent matrix LR and QR factorization problems into time-dependent linear equation systems, respectively. Simultaneously, a new activation function is introduced based on the initial ZNN models for the prescribed-time convergence of models. The excellent performance (robustness and convergence) of the two proposed ZNN models are analyzed theoretically. Furthermore, the prescribed-time convergence and antinoise abilities of the proposed ZNN models are well demonstrated in numerical experiments. Finally, the proposed ZNN model is applied to the moving target location problem, and the results show that the location error is at the millimeter level.

Processing large-scale data sets with limited labels has always been a difficult task in data mining. Facing this difficulty, two local feature selection algorithms, LARD and LRSD, have been proposed based on dependency degree, which can process partially labeled data sets and greatly improve the computational efficiency. However, it is very difficult for these algorithms to calculate large-scale data with millions of samples on a typical personal computer. Although the related family method is a more efficient approach than dependency degree, it cannot be used for partially labeled large-scale data. As a result, a local feature selection method based on related family is proposed to accelerate data processing in the paper. Experiments show that the proposed algorithm can run 405 times faster than LARD on partially labeled data sets and maintain high classification accuracy. In addition, this new algorithm can effectively process partially labeled large-scale data sets with 5,000,000 samples or 20,000 features on a typical personal computer.

In order to solve the time-varying quadratic programming (TVQP) problem more effectively, a new self-adaptive zeroing neural network (ZNN) is designed and analyzed in this article by using the Takagi-Sugeno fuzzy logic system (TSFLS) and thus called the Takagi-Sugeno (T-S) fuzzy ZNN (TSFZNN). Specifically, a multiple-input-single-output TSFLS is designed to generate a self-adaptive convergence factor to construct the TSFZNN model. In order to obtain finite- or predefined-time convergence, four novel activation functions (AFs) [namely, power-bi-sign AF (PBSAF), tanh-bi-sign AF (TBSAF), exp-bi-sign AF (EBSAF), and sinh-bi-sign AF (SBSAF)] are developed and applied in the TSFZNN model for solving the TVQP problem. Both theoretical proofs and experimental simulations show that the TSFZNN model using PBSAF or TBSAF has the property of converging in a finite time, and the TSFZNN model using EBSAF or SBSAF has the property of converging in a predefined time, which have superior convergence performance compared to the traditional ZNN model.

As a category of the recurrent neural network (RNN), zeroing neural network (ZNN) can effectively handle time-variant optimization issues. Compared with the fixed-parameter ZNN that needs to be adjusted frequently to achieve good performance, the conventional variable-parameter ZNN (VPZNN) does not require frequent adjustment, but its variable parameter will tend to infinity as time grows. Besides, the existing noise-tolerant ZNN model is not good enough to deal with time-varying noise. Therefore, a new-type segmented VPZNN (SVPZNN) for handling the dynamic quadratic minimization issue (DQMI) is presented in this work. Unlike the previous ZNNs, the SVPZNN includes an integral term and a nonlinear activation function, in addition to two specially constructed time-varying piecewise parameters. This structure keeps the time-varying parameters stable and makes the model have strong noise tolerance capability. Besides, theoretical analysis on SVPZNN is proposed to determine the upper bound of convergence time in the absence or presence of noise interference. Numerical simulations verify that SVPZNN has shorter convergence time and better robustness than existing ZNN models when handling DQMI.

Circular RNAs (circRNAs) are a category of novelty discovered competing endogenous non-coding RNAs that have been proved to implicate many human complex diseases. A large number of circRNAs have been confirmed to be involved in cancer progression and are expected to become promising biomarkers for tumor diagnosis and targeted therapy. Deciphering the underlying relationships between circRNAs and diseases may provide new insights for us to understand the pathogenesis of complex diseases and further characterize the biological functions of circRNAs. As traditional experimental methods are usually time-consuming and laborious, computational models have made significant progress in systematically exploring potential circRNA-disease associations, which not only creates new opportunities for investigating pathogenic mechanisms at the level of circRNAs, but also helps to significantly improve the efficiency of clinical trials. In this review, we first summarize the functions and characteristics of circRNAs and introduce some representative circRNAs related to tumorigenesis. Then, we mainly investigate the available databases and tools dedicated to circRNA and disease studies. Next, we present a comprehensive review of computational methods for predicting circRNA-disease associations and classify them into five categories, including network propagating-based, path-based, matrix factorization-based, deep learning-based and other machine learning methods. Finally, we further discuss the challenges and future researches in this field.

On account of the rapid progress of zeroing neural network (ZNN) and the extensive use of fuzzy logic system (FLS), this article proposes an intelligent fuzzy robustness ZNN (IFR-ZNN) model and applies it to solving the time-variant Stein matrix equation (TVSME) problem. Be different from ZNN models before, the IFR-ZNN model uses a fuzzy parameter as the design parameter and adopts a first proposed improved nonlinear piecewise activation function. Particularly, the FLS that generates the fuzzy parameter utilizes an improved membership function of nonuniform distribution which can improve the adaptability and robustness of the IFR-ZNN model. Based on the above two optimizations, the proposed IFR-ZNN model possesses three significant advantages: (1) fixed-time convergence independent of initial states; (2) superior robustness to tolerate two kinds of noises simultaneously; and (3) better adaptiveness based on computational error. Besides, the upper bounds of fixed-time convergence of the IFR-ZNN model under noisy or non-noisy situations are calculated theoretically, and the stability as well as the excellent adaptability are analyzed in detail. Finally, simulation comparison results manifest the availability and meliority of the proposed IFR-ZNN model in solving the TVSME problem.

In accordance with the advantages of zeroing neural network (ZNN) with the parallel processing character and fuzzy logic systems for calculating the uncertainties, two complex-type fuzzy ZNN (CtFZNN) models, which are mainly derived from two different limit forms of the Drazin inverse, are developed for solving the time-dependent complex-value Drazin inversion (TDCVDI) problem in this article. The most significant feature of the CtFZNN models is to use the improved fuzzy evolutionary formula, where the traditional constant or time-dependent factors are replaced by the fuzzy factors. For the non-noise or the noise disturbed CtFZNN models, the applied fuzzy factors are, respectively, generated from the single-input and single-output fuzzy logic system or the double-input and single-output fuzzy logic system. From the analytical discussions, it can conclude that the proposed CtFZNN models not only have finite-time convergence and inherent noise tolerance simultaneously, but also possess faster adaptive convergence rate even in a noisy environment. The presented theorems and the provided numerical simulations demonstrate the effectiveness of the proposed methods for addressing the TDCVDI problem, especially compared to the general ZNN model.

Faced with any decision-making problems with fuzzy multicriteria information, decision-makers generally set a minimum requirement on each criterion for satisfying their own preferences, thereby forming a fuzzy set on the criterion universe, which is called the criterion fuzzy set. From the perspective of realistic decision, the final decision of all alternatives should be determined according to this criterion fuzzy set. In view of this, this article proposes the criterion-oriented three-way ranking and clustering strategies, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets. First, we define a criterion fuzzy set as a criterion-oriented fuzzy concept and propose a criterion-oriented relative risk loss model and discuss related properties accordingly. Meanwhile, we use the generalized fuzzy rough lower (upper) approximation to estimate the absolute (relative) conditional probability between the binary fuzzy class of the alternative and the criterion-oriented fuzzy concept. Then, a criterion-oriented absolute (relative) three-way clustering strategy is proposed, which can perform qualitative analysis on all alternatives. Furthermore, based on the three-way semantics and global cost function, we recommend a criterion-oriented absolute (relative) three-way ranking strategy, which can rank all alternatives. Finally, through numerical example, comparative analysis and sensitivity analysis, we test the feasibility and effectiveness of the proposed criterion-oriented three-way ranking and clustering strategies.

Fuzzy sets and fuzzy rough sets are widely applied in data analysis, data mining, and decision-making. So far, the common method is to use rough approximate operators to induce aggregation functions when fuzzy rough sets are used for multicriteria decision-making (MCDM). However, they are parametric linear and the corresponding weights are additive measures. In this article, we give a novel method for MCDM based on fuzzy covering rough sets by using the nonadditive measure [i.e., fuzzy measure (FM)] and the nonlinear integral [i.e., Choquet integral (ChI)]. First, two nonadditive measures are presented by fuzzy covering lower and upper approximation operators, respectively. Moreover, both of them are FMs which are called$\beta$-neighborhood approximation measures. Second, two types of ChIs with respect to$\beta$-neighborhood approximation measures are constructed. A novel method, which considers the association, is presented to solve the problem of MCDM under the fuzzy covering rough set model. Third, a new approach based on$\beta$-neighborhood approximation measures is proposed for attribute reductions in a fuzzy$\beta$-covering information table. This approach of attribute reductions is used in MCDM. Finally, both new methods above are compared with other methods through some numerical examples and UCI datasets, respectively.

Motivated from the convergence capability achieved by gradient neural network (GNN) and zeroing neural network (ZNN) for matrix inversion, in this article, a novel hybrid GNN-ZNN (H-GNN-ZNN) model is proposed by introducing a fuzzy adaptive control strategy to generate a fuzzy adaptive factor that can change its size adaptively according to the residual error. Due to its fuzzy adaptability, this novel model is called the fuzzy adaptive GNN-ZNN (FA-GNN-ZNN) model for presentation convenience. We prove that the FA-GNN-ZNN model has the better performance than the existing H-GNN-ZNN model under the same conditions. In addition, different activation functions are applied to the FA-GNN-ZNN model to improve its performance further, and the corresponding theoretical analysis is given. Finally, comparative simulation results demonstrate the validity and superiority of the FA-GNN-ZNN model for matrix inversion.

In this article, considering the effectiveness and efficiency in solving time-varying problems, a new zeroing neural network (ZNN) is proposed to solve time-varying linear equations with column full rank coefficient matrix. In addition, two novel nonlinear activation functions are developed to enhance the comprehensive performance of the ZNN model. It is demonstrated through theoretical analysis and numerical experiments that the nonlinear activated ZNN model has better noise immunity, and faster prescribed-time convergence speed. Finally, the ZNN method is successfully applied to 2-D and 3-D dynamic positioning, with lower positioning error than the traditional pseudoinverse method.

In order to improve the effect of the Exp-Sign activation function (ESAF) and the Sinh-Sign activation function (SSAF) on the convergence and robustness of the zeroing neural network (ZNN) model, two fuzzy adaptive activation functions, named FAESAF and FASSAF, are constructed by using a Mamdani fuzzy logic controller (MFLC) in this article. Thus, a novel ZNN with the FAESAF and the FASSAF is proposed to solve the time-varying linear matrix equation. Different from the ESAF and the SSAF, whose parameters are fixed, the newly constructed FAESAF and FASSAF have an adaptive property, which comes from the fact that their parameters are intelligently generated by the MFLC according to the error norm of the ZNN model. In order to highlight the superior predefined time convergence and robustness of the corresponding ZNN model with the FAESAF and the FASSAF, several theorems are provided, and the corresponding proof is given in detail. Furthermore, the ESAF and the SSAF with different values of parameters are used as a comparison in numerical experiments to verify the superior performance of the FAESAF and the FASSAF. From theoretical analysis and numerical results, we can conclude that the ZNN model with the FAESAF and the FASSAF has better predefined time convergence and robustness compared to the ZNN model with the ESAF and the SSAF under the same conditions.

Matrix inversion frequently occurs in the fields of science, engineering, and related fields. Numerous matrix inversion schemes are often based on the premise that the solution procedure is ideal and noise-free. However, external interference is generally ubiquitous and unavoidable in practice. Therefore, an integrated-enhanced zeroing neural network (IEZNN) model has been proposed to handle the time-variant matrix inversion issue interfered with by noise. However, the IEZNN model can only deal with small time-variant noise interference. With slightly larger noise interference, the IEZNN model may not converge to the theoretical solution exactly. Therefore, a variable-parameter noise-tolerant zeroing neural network (VPNTZNN) model is proposed to overcome shortcomings and improve the inadequacy. Moreover, the excellent convergence and robustness of the VPNTZNN model are rigorously analyzed and proven. Finally, compared with the original zeroing neural network (OZNN) model and the IEZNN model for matrix inversion, numerical simulations and a practical application reveal that the proposed VPNTZNN model has the best robust property under the same external noise interference.

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value.

Many studies have evidenced that circular RNAs (circRNAs) are important regulators in various pathological processes and play vital roles in many human diseases, which could serve as promising biomarkers for disease diagnosis, treatment and prognosis. However, the functions of most of circRNAs remain to be unraveled, and it is time-consuming and costly to uncover those relationships between circRNAs and diseases by conventional experimental methods. Thus, identifying candidate circRNAs for human diseases offers new opportunities to understand the functional properties of circRNAs and the pathogenesis of diseases. In this study, we propose a novel network embedding-based adaptive subspace learning method (NSL2CD) for predicting potential circRNA-disease associations and discovering those disease-related circRNA candidates. The proposed method first calculates disease similarities and circRNA similarities by fully utilizing different data sources and learns low-dimensional node representations with network embedding methods. Then, we adopt an adaptive subspace learning model to discover potential associations between circRNAs and diseases. Meanwhile, an integrated weighted graph regularization term is imposed to preserve local geometric structures of data spaces, and L1,2-norm constraint is also incorporated into the model to realize the smoothness and sparsity of projection matrices. The experiment results show that NSL2CD achieves comparable performance under different evaluation metrics, and case studies further confirm its ability to discover potential candidate circRNAs for human diseases.

Accumulating evidence has shown that microRNAs (miRNAs) play crucial roles in different biological processes, and their mutations and dysregulations have been proved to contribute to tumorigenesis. In silico identification of disease-associated miRNAs is a cost-effective strategy to discover those most promising biomarkers for disease diagnosis and treatment. The increasing available omics data sources provide unprecedented opportunities to decipher the underlying relationships between miRNAs and diseases by computational models. However, most existing methods are biased towards a single representation of miRNAs or diseases and are also not capable of discovering unobserved associations for new miRNAs or diseases without association information. In this study, we present a novel computational method with adaptive multi-source multi-view latent feature learning (M2LFL) to infer potential disease-associated miRNAs. First, we adopt multiple data sources to obtain similarity profiles and capture different latent features according to the geometric characteristic of miRNA and disease spaces. Then, the multi-modal latent features are projected to a common subspace to discover unobserved miRNA-disease associations in both miRNA and disease views, and an adaptive joint graph regularization term is developed to preserve the intrinsic manifold structures of multiple similarity profiles. Meanwhile, the Lp,q-norms are imposed into the projection matrices to ensure the sparsity and improve interpretability. The experimental results confirm the superior performance of our proposed method in screening reliable candidate disease miRNAs, which suggests that M2LFL could be an efficient tool to discover diagnostic biomarkers for guiding laborious clinical trials.

On the strength of the abundant development of zeroing neural network (ZNN) and the wide application of fuzzy logic system (FLS), this article presents a fuzzy-power ZNN (FPZNN) model for addressing the time-variant matrix Moore-Penrose inversion problem. Different from the original constant or time-variant parameters, a fuzzy power parameter is generated from the FLS, and is first embedded into the FPZNN model to adjust the convergence rate. For the purpose of highlighting the superior performance of the FPZNN model, the other three classical neural network models are developed for comparison purposes. The convergence and noise-tolerance of the FPZNN model are analyzed to guarantee its excellent performance, where the model-implementation and differential errors are taken into account in a noisy environment. Besides, simulative experiments including two kinds of examples are provided to display the advantages of the FPZNN model under three commonly used activation functions. Both the presented theorems and the simulative experiments verify the superiority of the FPZNN model.

Zeroing neural network (ZNN), as an important class of recurrent neural network, has wide applications in various computation and optimization fields. In this article, based on the traditional-type zeroing neural network (TT-ZNN) model, an adaptive fuzzy-type zeroing neural network (AFT-ZNN) model is proposed to settle time-variant quadratic programming problem via integrating an adaptive fuzzy control strategy. The most prominent feature of the AFT-ZNN model is to use an adaptive fuzzy control value to adaptively adjust its convergence rate according to the value of the computational error. Four different activation functions are injected to analyze the convergence rate of the AFT-ZNN model. In addition, different membership functions and different ranges of the fuzzy control value are discussed to study the character of the AFT-ZNN model. Theoretical analysis and numerical comparison results further show that the AFT-ZNN model has better performance than the TT-ZNN model.

A variety of realistic industrial problems can be constructed into quadratic programming (QP) problems, especially their time-varying versions. A zeroing neural network (ZNN) as a good approach for dynamic problems can solve QP problems subject to equality constraints in the past. In this article, we propose a unified predefined-time convergent and robust ZNN (PTCR-ZNN) model for solving time-varying QP problems subject to equality or inequality constraints. Compared with the normal ZNN model, the PTCR-ZNN model mainly has advantages in the following three aspects: 1) solving QP problems with or without inequality constraints in a unified model; 2) converging to the optimal solution of QP problems within a predefined time that can be determined in advance; and 3) resisting many external noises with tiny and predictable residual error. These improvements have been rigorously proved in theory. By conducting both qualitative and quantitative simulations with comparisons, the superior properties of the PTCR-ZNN model are further validated. Finally, the application of the PTCR-ZNN model to image fusion task illustrates the efficiency together with its applicability.

This article is primarily concerned with finite-time convergence (FTC) and predefined-time convergence (PTC) design for a class of general zeroing neural network (ZNN) by constructing different activation functions (AFs). Based on the limit comparison test for improper integrals, some useful theoretical criteria are proposed to determine whether a nonlinear-activated ZNN model has FTC, PTC, or not. This novel method can avoid the valuation loss of the zoom method and the unsolvable barrier of the direct integration method that are widely used in the previous ZNN design. According to these convergence criteria, some instructive corollaries are derived to design valuable AFs to make ZNN models with FTC or PTC more easily. By taking a matrix-inversion ZNN model, some commonly used AFs are used to verify the usability of the criteria. In addition, some new AFs are constructed to further design some better ZNN models with superior FTC or PTC. Finally, convergence types of the ZNN model based on different AFs are visualized in numerical experiments.

For solving complex-valued linear matrix equations with time-varying coefficients (CV-LME-TVC) in the complex field, this article proposes a parameter-changing and complex-valued zeroing neural network (PC-CVZNN) model through integrating a new parameter-changing function. As compared to previous complex-valued zeroing neural networks (CVZNNs) with fixed parameters and existing parameter-changing functions, the PC-CVZNN model can achieve superior performance due to the accelerated role of the new parameter-changing function. In parts of theoretical analysis, we take advantage of Lyapunov methodology to prove that the proposed PC-CVZNN model can acquire the global and super-exponential convergence when the linear activation function is adopted, and even acquire super finite-time convergence when the new sign-bi-power activation function and its modified one are used. In parts of numerical comparison experiments, it is shown that the PC-CVZNN model possesses faster convergence rate than fixed-parameter CVZNN models and other analogy neural networks with parameter-changing function, when applied to finding the solution of CV-LME-TVC. Importantly, an application of the proposed method to the mobile manipulator control provides the potential practical value of the PC-CVZNN model in the industrial field.

The matrix inversion problem plays a very important role in mathematics as well as practical engineering applications. In this article, unlike the traditional fixed-parameter zeroing neural network (ZNN) model, on the basis of the original varying-parameter ZNN (VPZNN) model, an improved VPZNN (IVPZNN) model is established and researched to solve time-varying matrix inversion (TVMI). Specifically, the value of the proposed novel time-varying parameter in the IVPZNN model can grow rapidly over time, which can better meet the needs of ZNN in hardware implementation. In addition, theoretical analyses of the novel time varying parameter and the proposed IVPZNN model are given to guarantee the global superexponential convergence and finite-time convergence. Numerical calculation results verify the superior property of the established IVPZNN model for addressing the TVMI problem, as compared with the existing fixed-parameter ZNN and VPZNN models.

The zeroing neural network (ZNN) activated by nonlinear activation functions plays an important role in many fields. However, conventional ZNN can only realize finite-time convergence, which greatly limits the application of ZNN in a noisy environment. Generally, finite-time convergence depends on the original state of ZNN, but the original state is often unknown in advance. In addition, when meeting with different noises, the applied nonlinear activation functions cannot tolerate external disturbances. In this article, on the strength of this idea, two prescribed-time and robust ZNN (PTR-ZNN) models activated by two nonlinear activation functions are put forward to address the time-variant Stein matrix equation. The proposed two PTR-ZNN models own two remarkable advantages simultaneously: 1) prescribed-time convergence that does not rely on original states and 2) superior noise-tolerance performance that can tolerate time-variant bounded vanishing and nonvanishing noises. Furthermore, the detailed theoretical analysis is provided to guarantee the prescribed-time convergence and noise-tolerance performance, with the convergence upper bounds of steady-state residual errors calculated. Finally, simulative comparison results indicate the effectiveness and the superiority of the proposed two PTR-ZNN models for the time-variant Stein matrix equation solving.

This article focuses on the research of a general time-varying nonlinear optimization (TVNO) problem solving especially in a noise-disturbance environment. For addressing this problem more efficiently, a new noise-enduring and finite-time convergent design formula is suggested to establish a novel zeroing neural network (NZNN). In contrast to the initial zeroing neural network or the noising-enduring zeroing neural network, which either only achieves finite-time convergence or only suppresses external disturbances, the merit of the proposed NZNN model is able to find an error-free optimal solution in a finite time under various different types of external noises. In addition, the detailed mathematical analyses about finite-time convergence and noise endurance are given to prove the excellent characteristics of the NZNN model. Numerical comparative results are provided to demonstrate the accuracy, efficiency, and advantages of the NZNN model for TVNO under various types of external disturbances. Robotic tracking example further validates the applicability of the NZNN model especially in a noise-disturbance environment.

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation.

Granular structure is a mathematical expression of knowledge in granular computing and a direct determinant of the data processing efficiency. To improve the efficiency of data processing, many scholars have studied the reduction of granular structure. The attribute reduction and the granular reduction are two types of reduction on different layers of a granular structure, with the latter being both an essential step for granular structure reduction and the foundation of the attribute reduction. Yet compared with the attribute reduction, the granular reduction has received less attention from scholars. Therefore, a fuzzy granular reduction theory and a granular matrix based on the fuzzy β-coverings is proposed in this article. The insufficiency of the existing granular reduction theory for fuzzy β-coverings is pointed out, and proper sufficient and necessary conditions for two fuzzy β-coverings generating the same upper and lower approximations are also given in this article. In addition, to reduce and evaluate a fuzzy β-covering, a novel reduction algorithm based on a granular matrix is proposed for the first time. Also, since fuzzy covering reduction is NP-hard, a heuristic greedy algorithm is designed to obtain a reduct. Numerical experiments show that the redundancy rates of neighborhood granule sets induced by some big-scale data sets exceed 99%, which indicates that the existing neighborhood granulation methods need to be urgently improved. Based on this, concise granular structures and much more efficient feature selection algorithms can be proposed in the future.

In this article, two improved finite-time convergent complex-valued zeroing neural network (IFTCVZNN) models are presented and investigated for real-time solution of time-varying reciprocal of complex matrices on account of two equivalent processing ways of complex calculations for nonlinear activation functions. Furthermore, a novel nonlinear activation function is explored to modify the comprehensive performance of such two IFTCVZNN models. Compared with existing complex-valued neural networks converging within the limited time, the proposed IFTCVZNN models with the new activation function have better finite-time convergence and less conservative upper bound. Numerical simulations verify that the maximum of convergence time estimated via Lyapunov stability is theoretically much closer to the actual convergence time.

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need to take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this article, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models.

Zeroing neural network (ZNN) is a powerful tool to address the mathematical and optimization problems broadly arisen in the science and engineering areas. The convergence and robustness are always co-pursued in ZNN. However, there exists no related work on the ZNN for time-dependent nonlinear minimization that achieves simultaneously limited-time convergence and inherently noise suppression. In this article, for the purpose of satisfying such two requirements, a limited-time robust neural network (LTRNN) is devised and presented to solve time-dependent nonlinear minimization under various external disturbances. Different from the previous ZNN model for this problem either with limited-time convergence or with noise suppression, the proposed LTRNN model simultaneously possesses such two characteristics. Besides, rigorous theoretical analyses are given to prove the superior performance of the LTRNN model when adopted to solve time-dependent nonlinear minimization under external disturbances. Comparative results also substantiate the effectiveness and advantages of LTRNN via solving a time-dependent nonlinear minimization problem.

Cyborg insects have attracted great attention as the flight performance they have is incomparable by micro aerial vehicles and play a critical role in supporting extensive applications. Approaches to construct cyborg insects consist of two major issues: 1) the stimulating paradigm and 2) the control policy. At present, most cyborg insects are constructed based on invasive methods, requiring the implantation of electrodes into neural or muscle systems, which would harm the insects. As the control policy is basically manual control, the shortcomings of which lie in the requirement of excessive amount of experiments and focused attention. This paper presents the design and implementation of a noninvasive and much safer cyborg insect system based on visual stimulation. The tethered paradigm is adopted here and we look at controlling the flight behavior of bumblebees, especially the abdominal-waving behavior, in the context of a model-free reinforcement learning problem. The problem is formulated as a finite and deterministic Markov decision process, where the agent is designed to change the abdominal-waving behavior from the initial state to the target state. Sarsa with transformed reward function which can speed up the learning process is employed to learn the optimal control policy. Learned policies are compared to the stochastic one by evaluating the results of ten bumblebees, demonstrating that abdominal-waving state can be modulated to approximate the target state quickly with small deviation.

In the previous work, a finite-time zeroing neural network (ZNN) has been established to find the accurate solution of Lyapunov equation in the presence of no noises. In order to further improve the convergence speed of ZNN and suppress various noises encountered in real applications, in this paper, two robust nonlinear zeroing neural networks (RNZNNs) are designed by adding two novel nonlinear activation functions (AFs) for finding the solution of the Lyapunov equation in the presence of various noises. Unlike the previous ZNN activated by known AFs (e.g., linear activation function, bipolar sigmoid activation function, and power activation function), the proposed two RNZNN models possess predefined-time convergence (instead of finite-time convergence) even in the presence of various noises. The greatest advantage of the predefined-time convergence is independent to initial states of a dynamic system, which is much superior to the finite-time convergence related to initial states, and tremendously modifies the convergence performance. In addition, the predefined-time convergence of the RNZNN models for solving the Lyapunov equation are mathematically proved in detail under various external noises. The simulation comparisons further verify the superiority of the proposed RNZNN models for finding the solution of the Lyapunov equation.

The accumulating evidences regarding circular RNAs (circRNAs) indicate that they play crucial roles in a wide range of biological processes and participate in tumorigenesis and progression. The number of newly discovered circRNAs have increased dramatically in recent years, but the functions of vast majority of circRNAs remain unknown, and little effort has been devoted to discover disease-associated circRNAs on a large scale until now. With the advancement of high-throughput technology, the increasing availability of omics data has provided an unprecedented opportunity for prioritizing candidate circRNAs for diseases by computational models, which will contribute to exploring the pathogenesis of complex diseases at the circRNA level and provide promising applications in disease diagnosis and treatment. Here we propose the assumption that circRNAs with similar functions are normally associated with similar diseases and vice versa, and develop an integrated computational framework called MRLDC to identify disease-associated circRNAs. To our knowledge, little efforts have been developed for uncovering circRNA-disease associations on a large scale. By fully exploiting the experimentally validated associations between diseases and circRNAs, we first compute the Gaussian interaction profile kernel similarity for circRNAs and diseases, and then a heterogeneous circRNA-disease bilayer network is constructed by combining a circRNA similar network, a disease similar network, and known circRNA-disease associations. Subsequently, we develop a weighted low-rank approximation optimization algorithm with dual-manifold regularizations for predicting disease-associated circRNAs. Experimental results indicate that MRLDC can effectively identify disease circRNA candidates with high accuracy. In addition, case studies further demonstrate the ability of our method in discovering potential circRNA-disease associations.

In recent years, skeleton based action recognition is becoming an increasingly attractive alternative to existing video-based approaches, beneficial from its robust and comprehensive 3D information. In this paper, we explore an unsupervised representation learning approach for the first time to capture the long-term global motion dynamics in skeleton sequences. We design a conditional skeleton inpainting architecture for learning a fixed-dimensional representation, guided by additional adversarial training strategies. We quantitatively evaluate the effectiveness of our learning approach on three well-established action recognition datasets. Experimental results show that our learned representation is discriminative for classifying actions and can substantially reduce the sequence inpainting errors.

The matrix completion problem is restoring a given matrix with missing entries when handling incomplete data. In many existing researches, rank minimization plays a central role in matrix completion. In this paper, noticing that the locally linear reconstruction can be used to approximate the missing entries, we view the problem from a new perspective and propose an algorithm called locally linear approximation (LLA). The LLA method tries to keep the local structure of the data space while restoring the missing entries from row angle and column angle simultaneously. The experimental results have demonstrated the effectiveness of the proposed method.

Rough set theory, as one of the most useful soft computing methods dealing with vague and uncertain information, has been successfully applied to many fields, and one of its main applications is to perform attribute reduction. Although many heuristic attribute reduction algorithms have been proposed within the framework of the rough set theory, these methods are still computationally time consuming. In order to overcome this deficit, we propose, in this paper, two quick feature selection algorithms based on the neighbor inconsistent pair, which can reduce the time consumed in finding a reduct. At first, we propose several concepts regarding simplified decision table(U') and neighbor inconsistent pairs. Based on neighbor inconsistent pairs, we constructed two new attribute significance measures. Furthermore, we put forward two new attribute reduction algorithms based on quick neighbor inconsistent pairs. The key characteristic of the presented algorithms is that they only need to calculate U'/R once under the process of selecting the best attribute from attribute sets: C - R, while most existing algorithms need to calculate partition of U' for |C - R| times. In addition, the proposed algorithms need only to deal with the equivalent classes in U'/R that contain at least one neighbor inconsistent pair, while most existing algorithms need to consider all objects in U'. The experimental results show that the proposed algorithms are feasible and efficient.

Attribute reduction is one of the biggest challenges encountered in computational intelligence, data mining, pattern recognition, and machine learning. Effective in feature selection as the rough set theory is, it can only handle symbolic attributes. In order to overcome this drawback, the fuzzy rough set model is proposed, which is an extended model of rough sets and is able to deal with imprecision and uncertainty in both symbolic and numerical attributes. The existing attribute selection algorithms based on the fuzzy rough set model mainly take the angle of “attribute set,” which means they define the object function representing the predictive ability for an attribute subset with regard to the domain of discourse, rather than following the view of an “object pair.” Algorithms from the viewpoint of the object pair can ignore the object pairs that are already discerned by the selected attribute subsets and, thus, need only to deal with part of object pairs instead of the whole object pairs from the discourse, which makes such algorithms more efficient in attribute selection. In this paper, we propose the concept of reduced maximal discernibility pairs, which directly adopts the perspective of the object pair in the framework of the fuzzy rough set model. Then, we develop two attribute selection algorithms, named as reduced maximal discernibility pairs selection and weighted reduced maximal discernibility pair selection, based on the reduced maximal discernibility pairs. Experiment results show that the proposed algorithms are effective and efficient in attribute selection.

Attribute selection is considered as the most characteristic result in rough set theory to distinguish itself to other theories. However, existing attribute selection approaches can not handle partially labeled data. So far, few studies on attribute selection in partially labeled data have been conducted. In this paper, the concept of discernibility pair based on rough set theory is raised to construct a uniform measure for the attributes in both supervised framework and unsupervised framework. Based on discernibility pair, two kinds of semisupervised attribute selection algorithm based on rough set theory are developed to handle partially labeled categorical data. Experiments demonstrate the effectiveness of the proposed attribute selection algorithms.

Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.

Uncertainty measures can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. The uncertainty measurement issue is also a key topic in the rough-set theory. Although there are some measures to evaluate the uncertainty for complete decision systems (also called decision tables), they cannot be trivially transplanted into incomplete decision systems. There are relatively few studies on uncertainty measurement in incomplete decision systems. In this paper, we propose a new form of conditional entropy, which can be used to measure the uncertainty in incomplete decision systems. Some important properties of the conditional entropy are obtained. In particular, two validity theorems guarantee that the proposed conditional entropy can be used as a reasonable uncertainty measure for incomplete decision systems. Experiments on some real-life data sets are conducted to test and verify the validity of the proposed measure. Applications of the proposed uncertainty measure in ranking attributes and feature selection are also studied with experiments.

Brain-computer interface (BCI) is a communication system that can help lock-in patients to interact with the outside environment by translating brain signals into machine commands. The present work provides a design for a virtual reality (VR) based BCI system that allows human participants to control a virtual hand to make gestures by P300 signals, with a positive peak of potential about 300 ms posterior to the onset of target stimulus. In this virtual environment, the participants can obtain a more immersed experience with the BCI system, such as controlling a virtual hand or walking around in the virtual world. Methods of modeling the virtual hand and analyzing the P300 signals are also described in detail. Template matching and support vector machine were used as the P300 classifier and the experiment results showed that both algorithms perform well in the system. After a short time of practice, most participants could learn to control the virtual hand during the online experiment with greater than 70% accuracy.