Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.Comment: 13 page

Attribute Equilibrium Dominance Reduction Accelerator (DCCAEDR) Based on Distributed Coevolutionary Cloud and Its Application in Medical Records

© 2013 IEEE. Aimed at the tremendous challenge of attribute reduction for big data mining and knowledge discovery, we propose a new attribute equilibrium dominance reduction accelerator (DCCAEDR) based on the distributed coevolutionary cloud model. First, the framework of N-populations distributed coevolutionary MapReduce model is designed to divide the entire population into N subpopulations, sharing the reward of different subpopulations' solutions under a MapReduce cloud mechanism. Because the adaptive balancing between exploration and exploitation can be achieved in a better way, the reduction performance is guaranteed to be the same as those using the whole independent data set. Second, a novel Nash equilibrium dominance strategy of elitists under the N bounded rationality regions is adopted to assist the subpopulations necessary to attain the stable status of Nash equilibrium dominance. This further enhances the accelerator's robustness against complex noise on big data. Third, the approximation parallelism mechanism based on MapReduce is constructed to implement rule reduction by accelerating the computation of attribute equivalence classes. Consequently, the entire attribute reduction set with the equilibrium dominance solution can be achieved. Extensive simulation results have been used to illustrate the effectiveness and robustness of the proposed DCCAEDR accelerator for attribute reduction on big data. Furthermore, the DCCAEDR is applied to solve attribute reduction for traditional Chinese medical records and to segment cortical surfaces of the neonatal brain 3-D-MRI records, and the DCCAEDR shows the superior competitive results, when compared with the representative algorithms

Enhancing Big Data Feature Selection Using a Hybrid Correlation-Based Feature Selection

This study proposes an alternate data extraction method that combines three well-known feature selection methods for handling large and problematic datasets: the correlation-based feature selection (CFS), best first search (BFS), and dominance-based rough set approach (DRSA) methods. This study aims to enhance the classifier’s performance in decision analysis by eliminating uncorrelated and inconsistent data values. The proposed method, named CFS-DRSA, comprises several phases executed in sequence, with the main phases incorporating two crucial feature extraction tasks. Data reduction is first, which implements a CFS method with a BFS algorithm. Secondly, a data selection process applies a DRSA to generate the optimized dataset. Therefore, this study aims to solve the computational time complexity and increase the classification accuracy. Several datasets with various characteristics and volumes were used in the experimental process to evaluate the proposed method’s credibility. The method’s performance was validated using standard evaluation measures and benchmarked with other established methods such as deep learning (DL). Overall, the proposed work proved that it could assist the classifier in returning a significant result, with an accuracy rate of 82.1% for the neural network (NN) classifier, compared to the support vector machine (SVM), which returned 66.5% and 49.96% for DL. The one-way analysis of variance (ANOVA) statistical result indicates that the proposed method is an alternative extraction tool for those with difficulties acquiring expensive big data analysis tools and those who are new to the data analysis field.Ministry of Higher Education under the Fundamental Research Grant Scheme (FRGS/1/2018/ICT04/UTM/01/1)Universiti Teknologi Malaysia (UTM) under Research University Grant Vot-20H04, Malaysia Research University Network (MRUN) Vot 4L876SPEV project, University of Hradec Kralove, Faculty of Informatics and Management, Czech Republic (ID: 2102–2021), “Smart Solutions in Ubiquitous Computing Environments

Shared Nearest-Neighbor Quantum Game-Based Attribute Reduction with Hierarchical Coevolutionary Spark and Its Application in Consistent Segmentation of Neonatal Cerebral Cortical Surfaces

© 2012 IEEE. The unprecedented increase in data volume has become a severe challenge for conventional patterns of data mining and learning systems tasked with handling big data. The recently introduced Spark platform is a new processing method for big data analysis and related learning systems, which has attracted increasing attention from both the scientific community and industry. In this paper, we propose a shared nearest-neighbor quantum game-based attribute reduction (SNNQGAR) algorithm that incorporates the hierarchical coevolutionary Spark model. We first present a shared coevolutionary nearest-neighbor hierarchy with self-evolving compensation that considers the features of nearest-neighborhood attribute subsets and calculates the similarity between attribute subsets according to the shared neighbor information of attribute sample points. We then present a novel attribute weight tensor model to generate ranking vectors of attributes and apply them to balance the relative contributions of different neighborhood attribute subsets. To optimize the model, we propose an embedded quantum equilibrium game paradigm (QEGP) to ensure that noisy attributes do not degrade the big data reduction results. A combination of the hierarchical coevolutionary Spark model and an improved MapReduce framework is then constructed that it can better parallelize the SNNQGAR to efficiently determine the preferred reduction solutions of the distributed attribute subsets. The experimental comparisons demonstrate the superior performance of the SNNQGAR, which outperforms most of the state-of-the-art attribute reduction algorithms. Moreover, the results indicate that the SNNQGAR can be successfully applied to segment overlapping and interdependent fuzzy cerebral tissues, and it exhibits a stable and consistent segmentation performance for neonatal cerebral cortical surfaces