Neighborhood Rough Set Research Articles

Variable radius neighborhood rough sets and attribute reduction

Neighborhood rough sets provide important insights into dealing with numerical data. Neighborhood radius, a key factor that affects data uncertainty, is uniformly given in most of the existing neighborhood rough sets. Although it is concise and convenient to construct a granular structure, the same radius is not appropriate for the unique circumstance of each element in the universe. Therefore, taking the different environment of each object and label distribution into consideration, in this paper, we propose two novel neighborhood rough set models, namely, variable radius neighborhood rough sets (VRNRs) and neighborhood rough sets based on α-covering (α-CNRSs). They customize the neighborhood radius for each object or local region of the universe by surrounding functions. Based on an investigation of the basic properties of VRNRs and α-CNRSs, we present two attribute reduction algorithms. Moreover, three comparative experiments are designed in terms of the running time, model stability, and classification accuracy. Theoretical analyses and experimental results show that the two new neighborhood rough set models have good robustness and validity in attribute reduction and classification performance.

Dam safety assessment through data-level anomaly detection and information fusion

The anomaly detection and safety assessment of dams have attracted increasing attentions. To assess the safety of dams, a novel dam safety assessment model is proposed. The safety assessment model consists of data-level anomaly detection and information fusion. In the anomaly detection, a novel model based on the generative adversarial network and variational autoencoder is proposed. Through the stepwise training, the anomaly scores with reconstruction and discrimination losses can be obtained. Considering the multi-source and complexity of information system, a two-step fusion model is proposed. In the multi-source and multi-attribute fusion, the neighborhood rough set model is employed to construct the neighborhood granular structure. Through the idea of granular computing, the uncertainty of these sources and attributes is measured. Then the Sup-Inf fusion functions and fusion weights are employed to integrate the information. Finally, the anomaly scores with interval form are obtained. For verification, an arch dam is taken as an example. Through the analysis of detection and fusion results, the proposed model can detect the abnormal signals accurately and have the comprehensive assessment of the dam.

Neighborhood rough set based multi‐label feature selection with label correlation

SummaryNeighborhood rough set (NRS) is considered as an effective tool for feature selection and has been widely used in processing high‐dimensional data. However, most of the existing methods are difficult to deal with multi‐label data and are lack of considering label correlation (LC), which is an important issue in multi‐label learning. Therefore, in this article, we introduce a new NRS model with considering LC. First, we explore LC by calculating the similarity relation between labels and divide the related labels into several label subsets. Then, a new neighborhood relation is proposed, which can solve the problem of neighborhood granularity selection by using the nearest neighbor information distribution of instances under the related labels. On this basis, the NRS model is reconstructed by embedding LC information, and the related properties of the model are discussed. Moreover, we design a new feature significance function to evaluate the quality of features, which can well capture the specific relationship between features and labels. Finally, a greedy forward feature selection algorithm is designed. Extensive experiments which are conducted on different types of datasets verify the effectiveness of the proposed algorithm.

Multigranulation Relative Entropy-Based Mixed Attribute Outlier Detection in Neighborhood Systems

Outlier detection is widely used in many fields, such as intrusion detection, credit card fraud detection, medical diagnosis, and so on. Existing outlier detection algorithms are mostly designed for dealing with numeric or categorical attributes. However, data usually exist in the form of mixed attributes in real-world applications. In this article, we propose a novel mixed attribute outlier detection method based on multigranulation relative entropy by employing the neighborhood rough set. First, the neighborhood system is constructed by optimizing the mixed distance metric and the radius of the statistical value. Second, the neighborhood entropy is introduced as an uncertainty measure of data. Furthermore, the three kinds of multigranulation relative entropy-based matrices are defined by three kinds of attribute sequences, and the multigranulation relative entropy-based outlier factor is integrated to indicate the outlier degree of every object. Based on the proposed outlier detection model, the corresponding algorithm is designed. Finally, the proposed algorithm is compared with other nine algorithms through experiments on public data. The experimental results show that the proposed technique is adaptive and effective.

Self-adaptive weighted interaction feature selection based on robust fuzzy dominance rough sets for monotonic classification

Feature selection is an effective dimensionality reduction technique for classification tasks. Monotonic classification task (MCT) is a special classification task in which features and decision obey a monotonic constraint, which is widely used in various application fields. Most of the existing feature selection methods for MCTs are based on some dominance rough set models. However, these methods only consider the correlation between features and decisions, and ignore the interaction between features. Moreover, these dominance rough set models are not robust to noisy information. Thus, to make up for these two deficiencies, we propose a novel feature selection approach based on an improved robust fuzzy dominance rough set for MCTs. First, a β−precision fuzzy dominance neighborhood rough set (β−PFDNRS) with robustness is proposed. Second, a feature evaluation index is presented, which not only considers the correlation between features and decision, but also considers the interaction between features. Finally, a β−PFDNRS based self-adaptive weighted interaction feature selection (β−SWIFS) algorithm is designed to select a feature sequence. Extensive experiments are conducted on fifteen public datasets, and the results show that the β−PFDNRS model has good robustness and the proposed feature selection algorithm has an excellent classification performance.

Multi-granularity visual explanations for CNN

The interpretability of convolutional neural networks (CNNs) is attracting increasing attention. Class activation maps (CAM) intuitively explain the classification mechanisms of CNNs by highlighting important areas. However, as coarse-grained explanations, classical CAM methods are incapable of explaining the classification mechanism in detail. Inspired by the concept of granular computing theory, we propose a new CAM method to divide the highlighted areas into commonality saliency maps and specificity saliency maps for multi-granularity visualization. This method consists of three components. First, the universe is simplified to contain only a category pair. Then, neighborhood rough sets are used to divide the universe into three disjointed regions containing the commonality and specificity of category pairs by adaptive thresholds of optimal granularity. Finally, these three regions are used to generate multi-granularity saliency maps. This method well visualizes the multi-granularity classification mechanism of the CNN and further explains the misclassification. We compare this method to five representative CAM methods using two newly proposed fine-grained evaluation metrics and subjective observations. First, experiments demonstrate that the multi-granularity visualization method provides a more extensive and detailed explanation. Second, the adaptive thresholds can be adapted to different situations to obtain a reliable visualization explanation. Finally, in explaining of the adversarial attack, it visualizes the details that caused misclassification.

FNC: A fast neighborhood calculation framework

Efficiency has always been a key issue in neighborhood calculations. This study analyzes the low efficiency of traditional neighborhood calculation and concludes that the root cause lies in the large number of repetitive and unnecessary calculations because of the large neighborhood search range. To solve the problem, this study proposes a fast neighborhood calculation framework (FNC), including a neighborhood acceleration method with respect to a single attribute and a neighborhood acceleration method with respect to joint attributes. After avoiding many repetitive and unnecessary calculations, the efficiency of the neighborhood calculation can be significantly improved, and its time complexity is reduced from O(n2) to O(nlogn). This study also proves that the proposed framework is valid for different distance functions. Also, the proposed framework is applied to the popular research on neighborhood rough set attribute reduction. L∞-norm and L2-norm are used to verify the proposed framework is valid for different distance functions in the experiments. Multiple detailed experiments have been carried out on seventeen datasets. The experimental results demonstrate that, with the reduction results unchanged, the efficiency of the accelerated algorithms by FNC is greatly improved compared to the original algorithms. The effectiveness and efficiency of the proposed framework have been well verified. All codes have been released in the open source library at http://www.cquptshuyinxia.com/FNC.html.

Hierarchical neighborhood entropy based multi-granularity attribute reduction with application to gene prioritization

As a prominent model of granular computing, neighborhood rough set provides clear granularity organization and expression in terms of inherent parameter (neighborhood radius). Such characteristic is widely captured in a plenitude of attribute reduction procedures, while igniting a tricky issue of tuning parameters. In this study, we therefore propose a parameter-free multi-granularity attribute reduction scheme. Fundamentally, our scheme applies three-way decision as thinking in threes. First, data-aware multi-granularity structure is automatically induced from self-contained distance space instead of manually edited or appointed granularities. Second, a novel multi-granularity feature evaluation criterion named hierarchical neighborhood entropy is defined to measure the feature significance. Finally, a sequential forward searching algorithm is designed to find the optimal reduct. With application to gene prioritization, our method performed on microarray data is experimentally demonstrated to be more effective and efficient in differentially expressed genes discovery as compared with other well-established attribute reduction algorithms.

A fast neighborhood classifier based on hash bucket with application to medical diagnosis

In the medical diagnosis, expensive costs will increase significantly with the increment of medical information, and they can be reduced by data mining methods. The neighborhood classifier, as one of the extensions of the neighborhood rough set, has become an intuitive and effective classification method in data mining. However, there are still some defects which limit its performance. On the one hand, most existing neighborhood classifiers suffer from high computation complexity to obtain the neighborhood of samples; on the other hand, the difference between samples in the neighborhood is ignored when classifying samples, which diminishes the classification ability of the model. Therefore, in this paper, hash buckets and distance voting rule are introduced to solve the above problems, and a fast neighborhood classifier based on hash bucket (FNC-HB) is proposed. First, all samples are mapped to corresponding buckets through the hash function. Next, for any test sample, a bucket-based adaptive neighborhood classification radius is defined, in which the artificial parameter has been eliminated. Then, to avoid the indiscernibility of traditional voting rule when predicting labels of the test sample, a new rule called distance voting rule is defined. Finally, experimental results show that FNC-HB has better classification performance and computation efficiency, which is feasible and effective.

Incremental Feature Selection Using a Conditional Entropy Based on Fuzzy Dominance Neighborhood Rough Sets

Incremental feature selection approaches can improve the efficiency of feature selection used for dynamic datasets, which has attracted increasing research attention. Nevertheless, there is currently no work on incremental feature selection approaches for dynamic ordered data. Moreover, the monotonic classification effect of ordered data is easily affected by noise, so a robust feature evaluation metric is needed for feature selection algorithm. Motivated by these two issues, we investigate incremental feature selection approaches using a new conditional entropy with robustness for dynamic ordered data in this study. First, we propose a new rough set model, i.e., fuzzy dominance neighborhood rough sets (FDNRS). Second, a conditional entropy with robustness is defined based on FDNRS model, which is used as evaluation metric for features and combined with a heuristic feature selection algorithm. Finally, two incremental feature selection algorithms are designed on the basis of the above researches. Experiments are performed on ten public datasets to evaluate the robustness of the proposed metric and the performance of the incremental algorithms. Experimental results verify that the proposed metric is robust and our incremental algorithms are effective and efficient for updating reducts in dynamic ordered data.

The Water, Energy, Food, and Sustainability Nexus Decision Environment: A Multistakeholder Transdisciplinary Approach

The water, energy, and food (WEF) nexus has gained particular attention in the sustainable development community. Making effective decisions in this environment is difficult. Entwinement from multiple sustainability dimensions and various stakeholder perspectives contribute to this difficulty. Stakeholders have differing goals, interests, and preferences for potential technological and developmental solutions that address WEF nexus concerns. A holistic sustainable management approach with supporting decision support can address these concerns. This article introduces such a holistic framework to address WEF-sustainability (WEFS) concerns. Using a joint neighborhood rough set, interval-valued hesitant fuzzy set, and regret theory technique, this article introduces a multistakeholder transdisciplinary method to support WEFS nexus decisions. An illustrative example integrates the multiple stakeholder and WEFS nexus factors. The illustrative example provides insights into the modeling effort and data requirements. Research, practical implications, along with limitations of the study—which are all discussed—provide a foundation for future research directions in this socio-environmentally important field.

Research on the Intrusion Detection Model of Underwater Sensor Networks

The characteristics of underwater nodes, the harshness of the underwater environment, and the openness of the deployment area make underwater sensor networks vulnerable to various network attacks; in order to defend against potential threats and attacks, intrusion detection, as an active defense technology, can detect different attacks before they occur; currently, the technology is less used in underwater sensor networks and has a low detection rate for some types of attacks and cannot effectively detect the problem of multiple attack types. To address this problem, this paper proposes an intrusion detection model for underwater sensor networks for multiple types of attacks. Firstly, cluster head nodes use neighborhood rough sets for feature extraction, and the reduced dimensional data is transmitted to sink nodes to reduce the node computation. Further, the synthetic minority oversampling technique (SMOTE) is used to balance the data set, increase the number of minority class samples, and improve the detection rate of minority class attacks. Finally, determine whether a node is trusted according to the trust value of the cluster head node, and train the classifier using the random forest algorithm to detect the type of attack; it suffers to achieve intrusion detection of multiple types of attacks. Simulation results show that the model can not only improve the performance of intrusion detection of multitype attacks but also achieve an accuracy of over 99% for the detection of imbalance classes.

Statistical-mean double-quantitative K-nearest neighbor classification learning based on neighborhood distance measurement

Neighborhood granulation underlies neighborhood rough sets, and it also induces the basic classifier of K-nearest neighbor (KNN). Based on neighborhood granulation and its distance measurement, a relative-quantitative classifier (KNGR) and an absolute-quantitative classifier (KNGA) already promote the KNN classifier, and a double-quantitative classifier (KNGD) makes a further improvement but still has advancement space. This paper devotes to developing more general and robust double-quantitative classifiers via statistical integration, so two statistical-average double-quantitative distances are systematically constructed to establish arithmetic-mean and geometric-mean double-quantitative classifiers (KNGD-AM and KNGD-GM). Aiming at neighborhood distance measurement, the single-quantitative preference and double-quantitative compromise are first analyzed, and their statistical averages imply the better systematic semantics, simplified mechanism, general adaptability, compromised proportion for information fusion. Then, arithmetic-mean and geometric-mean double-quantitative distances are proposed, and they acquire the essence formula, optimization algorithm, squeeze positioning, metric axiom, and granulation non-monotonicity. Furthermore, the two new neighborhood distances motivate two corresponding classifiers, i.e., KNGD-AM and KNGD-GM. Finally, both the distance property and classifier effectiveness are verified by data experiments with 16 datasets. As shown by experimental results, classifiers KNGD-AM and KNGD-GM generally improve and outperform KNGD as well as KNGR, KNGA, KNN, and they achieve the better applicability and performance of classification learning.

General assembly framework for online streaming feature selection via Rough Set models

We may not know the entire feature space in advance for real-world applications, and features can exist in a stream mode, called streaming features. Online streaming feature selection aims to select optimal streaming features on the fly and can be summarized into three main components: irrelevant feature discarding, relevant feature selecting, and redundant feature removing. Therefore, the core issue of the streaming feature selection framework is the calculation of the relationship between features. This paper applies Rough Set models to discover the feature relationships for the most crucial advantages: they do not require any domain knowledge and can measure the selected features as integral. After the formal definitions of feature relevance, irrelevance, and redundancy from the Rough Set perspective, we analyze and abstract the feature relationship calculation from three levels: Rough Set model, positive region, and consistency calculation. Then we design a novel general assembly Rough Set based Streaming Feature Selection Framework, named RS-SFSF, which could assemble new algorithms for different problems step by step. Researchers in different areas can quickly build the algorithms they need based on our new framework. To demonstrate the effectiveness of RS-SFSF, we derived four new algorithms based on RS-SFSF by using the classical Rough Set model, neighborhood Rough Set model, and fuzzy Rough Set model, respectively. Extensive experiments conducted on twelve real-world datasets indicate the efficiency of our new framework.

Online group streaming feature selection using entropy-based uncertainty measures for fuzzy neighborhood rough sets

Online group streaming feature selection, as an essential online processing method, can deal with dynamic feature selection tasks by considering the original group structure information of the features. Due to the fuzziness and uncertainty of the feature stream, some existing methods are unstable and yield low predictive accuracy. To address these issues, this paper presents a novel online group streaming feature selection method (FNE-OGSFS) using fuzzy neighborhood entropy-based uncertainty measures. First, a separability measure integrating the dependency degree with the coincidence degree is proposed and introduced into the fuzzy neighborhood rough sets model to define a new fuzzy neighborhood entropy. Second, inspired by both algebra and information views, some fuzzy neighborhood entropy-based uncertainty measures are investigated and some properties are derived. Furthermore, the optimal features in the group are selected to flow into the feature space according to the significance of features, and the features with interactions are left. Then, all selected features are re-evaluated by the Lasso model to discard the redundant features. Finally, an online group streaming feature selection algorithm is designed. Experimental results compared with eight representative methods on thirteen datasets show that FNE-OGSFS can achieve better comprehensive performance.

ASFS: A novel streaming feature selection for multi-label data based on neighborhood rough set

ASFS: A novel streaming feature selection for multi-label data based on neighborhood rough set

Online multi-label stream feature selection based on neighborhood rough set with missing labels

Online multi-label stream feature selection based on neighborhood rough set with missing labels

Lithology identification of logging data based on improved neighborhood rough set and AdaBoost

Lithology identification of logging data based on improved neighborhood rough set and AdaBoost

Accelerated multi-granularity reduction based on neighborhood rough sets

Accelerated multi-granularity reduction based on neighborhood rough sets

Mixed measure-based feature selection using the Fisher score and neighborhood rough sets

Mixed measure-based feature selection using the Fisher score and neighborhood rough sets