With the successful application of granular computing in anomaly detection, a variety of tools including fuzzy information entropy can achieve superior detection results. However, fuzzy information entropy calculates fuzzy similarity through a global strategy, ignoring the local information in the data. To address this deficiency, this paper constructs a fuzzy$k$NN entropy theory and applies it to identify anomalies. Firstly, fuzzy$k$-similarity and fuzzy$k$NN are defined, and$k$NN entropy theory and the related information-theoretic metrics are proposed. Then, the relevant definitions and propositions of fuzzy$k$NN entropy, fuzzy$k$-joint entropy, fuzzy$k$-conditional information entropy, as well as fuzzy$k$-mutual information are elaborated. Based on the proposed theory, an anomaly detection model is constructed. At first, the fuzzy$k$-similarity relation matrix is constructed based on the fuzzy$k$-similarity in the proposed theory, and the relative fuzzy$k$NN entropy is calculated. Based on the relative fuzzy$k$NN entropy, the fuzzy$k$-relation anomaly degree is defined to characterize the anomaly intensity of fuzzy$k$NN information granules. Then, the anomaly factor based on fuzzy$k$NN entropy is built to represent the anomaly degree of data objects. Finally, the corresponding Fuzzy$k$NN Entropy-based Anomaly Detection algorithm (F$k$EAD) is designed. Comparative experiments are conducted with 11 state-of-the-art anomaly detection methods on thirty public datasets. The results reveal that the proposed method achieves better performance.

Unsupervised feature selection aims to enhance the quality of unlabeled data, thereby improving the performance of subsequent unsupervised learning models. However, most of the existing unsupervised feature selection methods rely on single-granularity modeling, which reduces the expressive capability of data to some extent. In addition, the existing studies are generally based on a forward greedy feature selection strategy, which tends to fall into a local optimum. To address these issues, this paper proposes a novel unsupervised feature selection method for handling hybrid data, called unsupervised feature selection method using fuzzy graph momentum random walk in bi-level granular-ball knowledge space. Specifically, a Bi-level Granular-ball Knowledge Space (BGKS) is first constructed by combining fine granularity and coarse granularity representations through a hybrid Gaussian kernel function. Then, a multi-granularity fuzzy graph is built on the BGKS using upper and lower fuzzy approximation operators. Based on this graph, a Momentum Random Walk (MRW) mechanism is introduced to design the Fuzzy Graph Momentum Random Walk (FGMRW) model. Finally, an iterative unsupervised feature selection algorithm is developed. Extensive experiments on 20 public datasets demonstrate that, compared with existing algorithms, the proposed method is able to maintain or even improve clustering performance while selecting fewer features, thus achieving superior overall performance. The source code of this work is publicly available athttps://github.com/HongtaoGao-code/FGMRW-UFS.

In information systems lacking decision-making information, effectively leveraging fuzzy rough sets for outlier detection in complex data is challenging, especially in capturing inherent uncertainty and multi-granularity characteristics to construct discriminative outlier scores. However, existing fuzzy rough sets-based outlier detection methods often suffer from three key limitations: (1) Local data distributions are often ignored when calculating fuzzy relation matrices, resulting in inaccurate fuzzy similarity representations; (2) Use of all objects in fuzzy upper and lower approximations can weaken noise resistance and increase computational complexity; (3) Single-granularity data processing reduces efficiency and may fail to capture the multi-granularity nature of data, thereby limiting the adaptability of these methods in complex data environments. To address these issues, we propose to fusesNatural neighbor fuzzy approximations withGranular-ball representation forOutlierDetection (NGOD), which integrates the multi-granularity granular-ball representation and fuzzy rough sets to improve the effectiveness and robustness of unsupervised outlier detection. Specifically, we first define a local distribution-aware fuzzy relation, enabling more discriminative similarity calculations between samples. To improve the effectiveness and robustness of fuzzy upper and lower approximations, we propose a multi-granularity natural neighbor fuzzy approximation model, which effectively utilizes the inherent uncertainty and local abnormal information of data in approximations. Moreover, by introducing natural neighbors, NGOD can adaptively capture local abnormal information in the data without setting neighborhoods manually. Finally, the outlier factors of each sample are calculated in NGOD to measure their outlier degrees. Extensive experiments on diverse datasets demonstrate that NGOD outperforms state-of-the-art methods, validating its superior performance and adaptability. The NGOD code and associated datasets are publicly available athttps://github.com/Mxeron/NGOD.

Air quality modeling and forecasting has become a key problem in environmental protection. The existing prediction models typically require large‐scale and high‐quality historical data to achieve better performance. However, insufficient data volume and significant differences between data distribution across different regions will definitely reduce the effectiveness of the model reuse. To address the above issues, we propose a novel hybrid recurrent network based on domain adversarial transfer to achieve a stronger generalization ability when training air quality data from multisource domains. The proposed model mainly consists of three fundamental modules, i.e., feature extractor, regression predictor, and domain classifier. One‐dimensional convolutional neural networks (1D‐CNNs) are used to extract temporal feature of data from source and target stations. Bi‐directional gated recurrent unit (bi‐GRU) and bi‐directional long short‐term memory (bi‐LSTM) are utilized to learn temporal dependencies pattern of multivariate time series data. Two adversarial transfer strategies are employed to ensure that our model is capable of finding domain invariant representations automatically. Experiments with different number of source domains are conducted to demonstrate the effectiveness of the proposed domain transfer strategies. The experimental results also show that our composite model has superior performance for forecasting air quality in various regions. As further evidence, the adversarial training method could promote the positive transfer and alleviate the negative effect of irrelevant source data. Besides, our model exhibits preferable generalization capability as more robust prediction results are achieved on both unseen target domains and original source domains.

Outlier Detection (OD) has attracted extensive research due to its application in many fields. The idea of neighborhood computing is one of the widely used methods in outlier analysis. Nevertheless, these methods mainly use certainty strategies to model outlier detection, so they cannot effectively handle the fuzzy information in the dataset. Moreover, they mainly focus on dealing with outlier detection in numerical data and cannot effectively find outliers in mixed-attribute data. Fuzzy information granulation theory is an effective granular computing model that allows objects to belong to a set to a certain extent (i.e., membership degree), which makes it possible to better handle uncertainty problems such as fuzziness. In this work, we propose an outlier detection model based on fuzzy neighborhoods. First, a hybrid fuzzy similarity is constructed to granulate the set of objects to form fuzzy information granules. Second, the fuzzy$k$-nearest neighbor is defined to describe the fuzzy local information. Then, the fuzzy neighborhood density is defined to indicate the degree of aggregation of each object. The smaller the fuzzy neighborhood density of an object, the more likely it is to be an outlier. Based on this idea, the fuzzy neighborhood deviation degree is defined to quantify the degree of outliers of objects. Finally, the fuzzy deviation degree on the set of conditional attributes is constructed to indicate the outlier scores of objects. Experimental comparisons with state-of-the-art methods show that the proposed method has a significant improvement on the AUC index and applies to three types of data.

Feature selection refers to choose an optimal non-redundant feature subset with minimal degradation of learning performance and maximal avoidance of data overfitting. The appearance of large data explosion leads to the sequential execution of algorithms are extremely time-consuming, which necessitates the scalable parallelization of algorithms by efficiently exploiting the distributed computational capabilities. In this paper, we present parallel feature selection algorithms underpinned by a rough hypercuboid approach in order to scale for the growing data volumes. Metrics in terms of rough hypercuboid are highly suitable to parallel distributed processing, and fits well with the Apache Spark cluster computing paradigm. Two data parallelism strategies, namely, vertical partitioning and horizontal partitioning, are implemented respectively to decompose the data into concurrent iterative computing streams. Experimental results on representative datasets show that our algorithms significantly faster than its original sequential counterpart while guaranteeing the quality of the results. Furthermore, the proposed algorithms are perfectly capable of exploiting the distributed-memory clusters to accomplish the computation task that fails on a single node due to the memory constraints. Parallel scalability and extensibility analysis have confirmed that our parallelization extends well to process massive amount of data and can scales well with the increase of computational nodes.

This article aims to develop a new and robust approach to feature representation. Motivated by the success of Auto-Encoders, we first theoretically analyze and summarize the general properties of all algorithms that are based on traditional Auto-Encoders: (1) The reconstruction error of the input cannot be lower than a lower bound, which can be viewed as a guiding principle for reconstructing the input. Additionally, when the input is corrupted with noises, the reconstruction error of the corrupted input also cannot be lower than a lower bound. (2) The reconstruction of a hidden representation achieving its ideal situation is the necessary condition for the reconstruction of the input to reach the ideal state. (3) Minimizing the Frobenius norm of the Jacobian matrix of the hidden representation has a deficiency and may result in a much worse local optimum value. We believe that minimizing the reconstruction error of the hidden representation is more robust than minimizing the Frobenius norm of the Jacobian matrix of the hidden representation. Based on the above analysis, we propose a new model termedDouble Denoising Auto-Encoders(DDAEs), which uses corruption and reconstruction on both the input and the hidden representation. We demonstrate that the proposed model is highly flexible and extensible and has a potentially better capability to learn invariant and robust feature representations. We also show that our model is more robust than Denoising Auto-Encoders (DAEs) for dealing with noises or inessential features. Furthermore, we detail how to train DDAEs with two different pretraining methods by optimizing the objective function in a combined and separate manner, respectively. Comparative experiments illustrate that the proposed model is significantly better for representation learning than the state-of-the-art models.

Attribute reduction based on rough set theory has attracted much attention recently. In real-life applications, many decision tables may vary dynamically with time, e.g., the variation of attributes, objects, and attribute values. The reduction of decision tables may change on the alteration of attribute values. The paper focuses on dynamic maintenance of attribute reduction when varying data values of multiple objects. Incremental mechanisms for knowledge granularity are proposed first, which aims to update attribute reduction effectively. Then, a group incremental reduction algorithm with varying data values is developed. When attribute values of multiple objects have been replaced by new ones in decision table, the proposed incremental algorithm can find the new reduct in a much shorter time. The time complexity analysis and experiments on different data sets from UCI have validated that the proposed incremental algorithms are efficient and effective to update the reduction with the variation of attribute values.

The rough set model over dual universes (RSMDU) as a generalized model of classical rough set theory (RST) on the two universes has been well studied with the objective to establishment of model and discussion of its corresponding properties. Approximations of a concept in RSMDU, which may further be applied to knowledge discovery or related work, need to be updated effectively under a dynamic environment. Despite recent advances in using the incremental method to speed up updating approximations of RST, there has been little effort toward incorporating the incremental method into computing approximations under RSMDU. This paper proposes an incremental learning approach for updating approximations in RSMDU when the objects of two universes vary with time. An illustration is employed to show the proposed method. Extensive experimental results on various real and synthetic data sets verify the effectiveness of the proposed incremental updating method while comparing with the nonincremental method.

Rule induction method based on rough set theory (RST) has received much attention recently since it may generate a minimal set of rules from the decision system for real-life applications by using of attribute reduction and approximations. The decision system may vary with time, e.g., the variation of objects, attributes and attribute values. The reduction and approximations of the decision system may alter on Attribute Values' Coarsening and Refining (AVCR), a kind of variation of attribute values, which results in the alteration of decision rules simultaneously. This paper aims for dynamic maintenance of decision rules w.r.t. AVCR. The definition of minimal discernibility attribute set is proposed firstly, which aims to improve the efficiency of attribute reduction in RST. Then, principles of updating decision rules in case of AVCR are discussed. Furthermore, the rough set-based methods for updating decision rules in the inconsistent decision system are proposed. The complexity analysis and extensive experiments on UCI data sets have verified the effectiveness and efficiency of the proposed methods.

Approximations of a concept by a variable precision rough-set model (VPRS) usually vary under a dynamic information system environment. It is thus effective to carry out incremental updating approximations by utilizing previous data structures. This paper focuses on a new incremental method for updating approximations of VPRS while objects in the information system dynamically alter. It discusses properties of information granulation and approximations under the dynamic environment while objects in the universe evolve over time. The variation of an attribute's domain is also considered to perform incremental updating for approximations under VPRS. Finally, an extensive experimental evaluation validates the efficiency of the proposed method for dynamic maintenance of VPRS approximations.

In rough set theory, upper and lower approximations for a concept will change dynamically as the information system changes over time. How to update approximations based on the original information is an important task that can help improve the efficiency of knowledge discovery. This paper focuses on the approach of dynamically updating approximations when attribute values are coarsened or refined. The main contributions include: (1) defining coarsening and refining attribute values in information systems and introducing the properties and the principles of coarsening and refining attribute values; (2) analyzing the properties for dynamic maintenance in terms of upper and lower approximations with coarsening and refining attribute values; (3) proposing an incremental algorithm for updating the approximations of a concept as coarsening or refining attributes values; and finally (4) validating the efficiency of the proposed approach to handle the dynamic maintenance of the approximations for a given concept. © 2010 Wiley Periodicals, Inc.