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

arXiv: https://arxiv.org/abs/2204.10231 · HTML: https://mlsanity.com/paper/2204.10231/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 74 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 9 of 9)

- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [AutoML-Zero: Evolving Machine Learning Algorithms From Scratch](https://mlsanity.com/paper/2003.03384/) (2020)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis](https://mlsanity.com/paper/1606.04316/) (2016)
- [Statistical comparison of classifiers through Bayesian hierarchical modelling](https://mlsanity.com/paper/1609.08905/) (2016)
- [A Cost-Sensitive Deep Belief Network for Imbalanced Classification](https://mlsanity.com/paper/1804.10801/) (2018)
- [Lights and Shadows in Evolutionary Deep Learning: Taxonomy, Critical Methodological Analysis, Cases of Study, Learned Lessons, Recommendations and Challenges](https://mlsanity.com/paper/2008.03620/) (2020)
- [Interpretable Rule Discovery Through Bilevel Optimization of Split-Rules of Nonlinear Decision Trees for Classification Problems](https://mlsanity.com/paper/2008.00410/) (2020)
- [On the Use of Default Parameter Settings in the Empirical Evaluation of Classification Algorithms](https://mlsanity.com/paper/1703.06777/) (2017)

## Built on by (most cited first, 5 of 5)

- [A Bilevel Optimization Framework for Imbalanced Data Classification](https://mlsanity.com/paper/2410.11171/) (2024)
- [Distribution Learning Based on Evolutionary Algorithm Assisted Deep Neural Networks for Imbalanced Image Classification](https://mlsanity.com/paper/2207.12744/) (2022)
- [INGB: Informed Nonlinear Granular Ball Oversampling Framework for Noisy Imbalanced Classification](https://mlsanity.com/paper/2307.01224/) (2023)
- [Multi-Class Imbalanced Learning with Support Vector Machines via Differential Evolution](https://mlsanity.com/paper/2502.14597/) (2025)
- [Sampling Imbalanced Data with Multi-objective Bilevel Optimization](https://mlsanity.com/paper/2506.11315/) (2025)

## Abstract (arXiv)

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.