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

The Construction of Support Vector Machine Classifier Using the Firefly Algorithm

The setting of parameters in the support vector machines (SVMs) is very important with regard to its accuracy and efficiency. In this paper, we employ the firefly algorithm to train all parameters of the SVM simultaneously, including the penalty parameter, smoothness parameter, and Lagrangian multiplier. The proposed method is called the firefly-based SVM (firefly-SVM). This tool is not considered the feature selection, because the SVM, together with feature selection, is not suitable for the application in a multiclass classification, especially for the one-against-all multiclass SVM. In experiments, binary and multiclass classifications are explored. In the experiments on binary classification, ten of the benchmark data sets of the University of California, Irvine (UCI), machine learning repository are used; additionally the firefly-SVM is applied to the multiclass diagnosis of ultrasonic supraspinatus images. The classification performance of firefly-SVM is also compared to the original LIBSVM method associated with the grid search method and the particle swarm optimization based SVM (PSO-SVM). The experimental results advocate the use of firefly-SVM to classify pattern classifications for maximum accuracy

Training Support Vector Machines Using Frank-Wolfe Optimization Methods

Training a Support Vector Machine (SVM) requires the solution of a quadratic programming problem (QP) whose computational complexity becomes prohibitively expensive for large scale datasets. Traditional optimization methods cannot be directly applied in these cases, mainly due to memory restrictions. By adopting a slightly different objective function and under mild conditions on the kernel used within the model, efficient algorithms to train SVMs have been devised under the name of Core Vector Machines (CVMs). This framework exploits the equivalence of the resulting learning problem with the task of building a Minimal Enclosing Ball (MEB) problem in a feature space, where data is implicitly embedded by a kernel function. In this paper, we improve on the CVM approach by proposing two novel methods to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast method to approximate the solution of a MEB problem. In contrast to CVMs, our algorithms do not require to compute the solutions of a sequence of increasingly complex QPs and are defined by using only analytic optimization steps. Experiments on a large collection of datasets show that our methods scale better than CVMs in most cases, sometimes at the price of a slightly lower accuracy. As CVMs, the proposed methods can be easily extended to machine learning problems other than binary classification. However, effective classifiers are also obtained using kernels which do not satisfy the condition required by CVMs and can thus be used for a wider set of problems

Performance and optimization of support vector machines in high-energy physics classification problems

In this paper we promote the use of Support Vector Machines (SVM) as a machine learning tool for searches in high-energy physics. As an example for a new- physics search we discuss the popular case of Supersymmetry at the Large Hadron Collider. We demonstrate that the SVM is a valuable tool and show that an automated discovery- significance based optimization of the SVM hyper-parameters is a highly efficient way to prepare an SVM for such applications. A new C++ LIBSVM interface called SVM-HINT is developed and available on Github.Comment: 20 pages, 6 figure