Handling Imbalanced Classification Problems With Support Vector Machines via Evolutionary Bilevel Optimization

Support vector machines (SVMs) are popular learning algorithms to deal with binary classification problems. They traditionally assume equal misclassification costs for each class; however, real-world problems may have an uneven class distribution. This article introduces EBCS-SVM: evolutionary bilevel cost-sensitive SVMs. EBCS-SVM handles imbalanced classification problems by simultaneously learning the support vectors and optimizing the SVM hyperparameters, which comprise the kernel parameter and misclassification costs. The resulting optimization problem is a bilevel problem, where the lower level determines the support vectors and the upper level the hyperparameters. This optimization problem is solved using an evolutionary algorithm (EA) at the upper level and sequential minimal optimization (SMO) at the lower level. These two methods work in a nested fashion, that is, the optimal support vectors help guide the search of the hyperparameters, and the lower level is initialized based on previous successful solutions. The proposed method is assessed using 70 datasets of imbalanced classification and compared with several state-of-the-art methods. The experimental results, supported by a Bayesian test, provided evidence of the effectiveness of EBCS-SVM when working with highly imbalanced datasets.Comment: Copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Soft Methodology for Cost-and-error Sensitive Classification

Many real-world data mining applications need varying cost for different types of classification errors and thus call for cost-sensitive classification algorithms. Existing algorithms for cost-sensitive classification are successful in terms of minimizing the cost, but can result in a high error rate as the trade-off. The high error rate holds back the practical use of those algorithms. In this paper, we propose a novel cost-sensitive classification methodology that takes both the cost and the error rate into account. The methodology, called soft cost-sensitive classification, is established from a multicriteria optimization problem of the cost and the error rate, and can be viewed as regularizing cost-sensitive classification with the error rate. The simple methodology allows immediate improvements of existing cost-sensitive classification algorithms. Experiments on the benchmark and the real-world data sets show that our proposed methodology indeed achieves lower test error rates and similar (sometimes lower) test costs than existing cost-sensitive classification algorithms. We also demonstrate that the methodology can be extended for considering the weighted error rate instead of the original error rate. This extension is useful for tackling unbalanced classification problems.Comment: A shorter version appeared in KDD '1