Abstract
Traditional Belief-Rule-Based (BRB) ensemble learning methods integrate all of the trained sub-BRB systems to obtain better results than a single belief-rule-based system. However, as the number of BRB systems participating in ensemble learning increases, a large amount of redundant sub-BRB systems are generated because of the diminishing difference between subsystems. This drastically decreases the prediction speed and increases the storage requirements for BRB systems. In order to solve these problems, this paper proposes BRBCS-PAES: a selective ensemble learning approach for BRB Classification Systems (BRBCS) based on Pareto-Archived Evolutionary Strategy (PAES) multi-objective optimization. This system employs the improved Bagging algorithm to train the base classifier. For the purpose of increasing the degree of difference in the integration of the base classifier, the training set is constructed by the repeated sampling of data. In the base classifier selection stage, the trained base classifier is binary coded, and the number of base classifiers participating in integration and generalization error of the base classifier is used as the objective function for multi-objective optimization. Finally, the elite retention strategy and the adaptive mesh algorithm are adopted to produce the PAES optimal solution set. Three experimental studies on classification problems are performed to verify the effectiveness of the proposed method. The comparison results demonstrate that the proposed method can effectively reduce the number of base classifiers participating in the integration and improve the accuracy of BRBCS.
Highlights
In 2006, for the modelling of data characterized by incompleteness, fuzzy uncertainty, probability uncertainty, and non-linearity, Yang et al.[1] extendedPresent research on BRB systems is mainly focused on the use of a single BRB system
The rest of the paper is organized as follows: Section 2 briefly reviews the basics of BRB, multi-objective optimization, and selective ensemble learning, and reviews some related works; Section 3 introduces the belief rule-base classification system of selective ensemble learning; Section 4 discusses three case studies to demonstrate the efficiency of the proposed method; and Section 5 concludes the paper
We proposed BRB Classification Systems (BRBCS)-ParetoArchived Evolutionary Strategy (PAES): using selective ensemble learning methods for BRBCS based on PAES
Summary
In 2006, for the modelling of data characterized by incompleteness, fuzzy uncertainty, probability uncertainty, and non-linearity, Yang et al.[1] extended. In 2016, Wu et al.[5] introduced the Bagging and AdaBoost algorithms Their approach uses the accelerated gradient method[6] to train the parameters of a single BRB system, and integrates multiple sub-BRB systems with ensemble learning methods to improve the reasoning ability. As the number of individuals participating in ensemble learning increases, the subBRB system begins to produce a large number of redundant base learning machines because of the decrease in individual differences This results in a noticeable decrease in prediction speed and a dramatic increase in storage overhead, reducing the effective generalization ability of the system. In response to these deficiencies, this paper proposes BRBCS-PAES, using selective ensemble learning methods for Belief-Rule-Base Classification Systems (BRBCS) based on the Pareto-Archiving Evolution Strategy (PAES). The rest of the paper is organized as follows: Section 2 briefly reviews the basics of BRB, multi-objective optimization, and selective ensemble learning, and reviews some related works; Section 3 introduces the belief rule-base classification system of selective ensemble learning; Section 4 discusses three case studies to demonstrate the efficiency of the proposed method; and Section 5 concludes the paper
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