Distance metric learning-based multi-granularity neighborhood rough sets for attribute reduction

Neighborhood margin rough set: Self-tuning neighborhood threshold

A novel approach to attribute reduction based on weighted neighborhood rough sets

A neighborhood rough set model with nominal metric embedding

Neighborhood rough set theory is an important method for dealing with uncertainty, fuzziness and undefined objects, and neighborhood rough set theory based on binary relation is studied by scholars a lot. However, most of the current research is used to deal with equivalent binary relations or other binary relations with stringent condition, which has been unable to meet the rapid development of data. This paper proposes a new multi-granulation rough set that can deal with general binary relations based on the C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</inf> neighborhoods, and verifies its related properties. At the same −time, it has richer meanings through weighted methods. Theoretical analysis and practical examples show that this rough set has better ability to process data. Finally, a weighted attribute reduction algorithm is designed based on the significant function under the general binary relation. The experimental results show that this rough set can handle complex data well. The research in this paper develops the theory of classical rough sets, and provides a theoretical basis for the knowledge acquisition of information systems under the general binary relation.

Mixed feature selection based on granulation and approximation

Neighborhood rough sets are an effective model for handling numerical and categorical data entangled with vagueness, imprecision, or uncertainty. However, existing neighborhood rough set models and their feature selection methods treat each sample equally, whereas different types of samples inherently play different roles in constructing neighborhood granules and evaluating the goodness of features. In this study, the sample weight information is first introduced into neighborhood rough sets, and a novel weighted neighborhood rough set model is consequently constructed. Then, considering the lack of sample weight information in practical data, a margin-based weight optimization function is designed, based on which a gradient descent algorithm is provided to adaptively learn sample weights through maximizing sample margins. Finally, an average granule margin measure is put forward for feature selection, and a forward-adding heuristic algorithm is developed to generate an optimal feature subset. The proposed method constructs the weighted neighborhood rough sets using sample weights for the first time and is able to yield compact feature subsets with a large margin. Extensive experiments and statistical analysis on UCI datasets show that the proposed method achieves highly competitive performance in terms of feature reduction rate and classification accuracy when compared with other state-of-the-art methods.

Incremental feature selection for dynamic hybrid data using neighborhood rough set

For continuous numerical data sets, neighborhood rough sets-based attribute reduction is an important step for improving classification performance. However, most of the traditional reduction algorithms can only handle finite sets, and yield low accuracy and high cardinality. In this paper, a novel attribute reduction method using Lebesgue and entropy measures in neighborhood rough sets is proposed, which has the ability of dealing with continuous numerical data whilst maintaining the original classification information. First, Fisher score method is employed to eliminate irrelevant attributes to significantly reduce computation complexity for high-dimensional data sets. Then, Lebesgue measure is introduced into neighborhood rough sets to investigate uncertainty measure. In order to analyze the uncertainty and noisy of neighborhood decision systems well, based on Lebesgue and entropy measures, some neighborhood entropy-based uncertainty measures are presented, and by combining algebra view with information view in neighborhood rough sets, a neighborhood roughness joint entropy is developed in neighborhood decision systems. Moreover, some of their properties are derived and the relationships are established, which help to understand the essence of knowledge and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is designed to improve the classification performance of large-scale complex data. The experimental results under an instance and several public data sets show that the proposed method is very effective for selecting the most relevant attributes with high classification accuracy.

In real-life applications, partial order may exist in the domain of attributes and different data types often coexist in an decision system. Dominance-based rough set approach has been used widely in multi-attribute and multi-criteria decision by using the dominating relation. Neighborhood rough set aims to deal with hybrid data types. But the preference relation in the context of neighborhood rough set has not been taken into consideration. In this paper, a novel rough set model, Dominance-based Neighborhood Rough Sets (DNRS), is proposed which aims to process a decision system with hybrid data types where the partial order between objects is taken into consideration. The properties of DNRS are studied. Attribute reduction under DNRS is investigated.

Considering the fact that the early fault of the rolling-element bearing is difficult to identify correctly, a neighborhood rough set (NRS) and ensemble empirical mode decomposition (EEMD) fault diagnosis model of rolling-element bearing combination is come up with. First of all, the original signal of the vibration is decomposed by EEMD to obtain a number of IMF components, and extracted time-features from the first 3 IMF components in the time domain to form the original features. Then, NRS is used to reduce the attributes of original features, eliminate the redundant information, and put the sensitive reduced feature attributes into the SVM classifier for fault identification. This model is applied to typical rolling-element bearing fault diagnosis experiments, which shows that the NRS is used to select a large number of features containing abundant fault information from the original features. The method not only reduces the complexity of the classification algorithm, but also enhances the accuracy of the fault identification by 5%, which provides a new approach of analysis model for rolling-element bearing fault diagnosis.

Cost-sensitive feature selection based on adaptive neighborhood granularity with multi-level confidence

An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory

Feature selection is one of the widely used pre-processing techniques to deal with large data sets. In this context, rough set theory has been successfully implemented for feature selection of discrete data set but in case of continuous data set it requires discretization, which may cause information loss. Fuzzy rough set theory approaches have also been used successfully to resolve this issue as it can handle continuous data directly. Moreover, almost all feature selection techniques are used to handle homogeneous data set. In this article, the center of attraction is on heterogeneous feature subset reduction. A novel intuitionistic fuzzy neighborhood models have been proposed by combining intuitionistic fuzzy sets and neighborhood rough set models by taking an appropriate pair of lower and upper approximations and generalize it for feature selection, supported with theory and its validation. An appropriate algorithm along with application to a data set has been added.

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions. The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision‐making problems from multi‐levels and multi‐angles, and the neighbourhood rough set model (NRS) can facilitate the analysis and processing of numerical or mixed type data, and can address the limitation of multigranulation decision‐theoretic rough sets (MG‐DTRS), which is not easy to cope with complex data. Based on the in‐depth study of hybrid‐valued decision systems and MG‐DTRS models, this study analysed neighbourhood MG‐DTRS (NMG‐DTRS) deeply by fusing MG‐DTRS and NRS; a matrix‐based approach for approximation sets of NMG‐DTRS model was proposed on the basis of the matrix representations of concepts; the positive, boundary and negative domains were constructed from the matrix perspective, and the concept of positive decision recognition rate was introduced. Furthermore, the authors explored the related properties of NMG‐DTRS model, and designed and described the corresponding solving algorithms in detail. Finally, some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm, but also showed the relationship between the decision recognition rate and the granularity and threshold.

Attribute reduction is one of the most important research issues in the rough set theory. The purpose of attribute reduction is to find a minimal attribute subset that satisfies some specific criteria, while the minimal attribute subset is called attribute reduct. In this paper, we define a similarity-based attribute reduct based on a clustering perspective. Each decision class is treated as a cluster, and the defined similarity-based attribute reduct can maintain or increase the discriminating ability of different clusters in the case of removing redundant attributes. In view of this, firstly, we define the intra-class similarity for objects in the same decision class and the inter-class similarity for objects between different decision classes. Secondly, we define a similarity-based attribute reduct by maximizing intra-class similarity and minimizing inter-class similarity in the rough set model. Thirdly, by considering the heuristic search strategy, we also design a corresponding reduction method for the proposed attribute reduct. The experimental results indicate that compared with other representative attribute reducts, our proposed attribute reduct can significantly improve the classification performance.