Bell-shaped fuzzy least square twin SVM with biomedical applications

Abstract

In practical applications, datasets frequently encompass noise, outliers, and imbalanced classes, all of which can markedly affect the generalization performance of the model. Support vector machine (SVM) and its twin variant i.e., twin SVM (TWSVM) tend to be biased towards the majority class samples, leading to misclassification of the minority class samples. TWSVM suffers from this biasness as it generates hyperplanes without considering preceding data information. To address the aforementioned issues and accurately classify the samples, in this paper, we propose bell-shaped fuzzy least square twin support vector machine for imbalance data (BSFLSTSVM-ID). The proposed BSFLSTSVM-ID allocates weight to the majority class samples through a novel membership function, namely, &#x201C

class probability and bell-shaped&#x201D

(CPBS). The CPBS function is amalgamation of class probability, bell-shaped function, and imbalance ratio of the dataset. The value of the bell-shaped function diminishes as data points move farther away from the class center. Consequently, noise or outliers receive lower membership values, leading to their reduced influence in constructing the hyperplanes. To underscore the importance of samples from minority class, a weight of one is assigned to them. Furthermore, the proposed BSFLSTSVM-ID requires solving a system of linear equations that involves matrix inversion. We utilize the conjugate gradient method to handle the challenge of matrix inversion. To demonstrate the effectiveness of the proposed BSFLSTSVMID compared to baseline models, we performed experiments on a comprehensive set of 59 UCI and KEEL datasets, each presenting varying imbalance ratios ranging from 1 to 72.69. Furthermore, we conducted experiments on normally distributed clustered (NDC) datasets to assess the scalability of the proposed model. As an application, we implemented the proposed model for diagnosing breast cancer and Alzheimer&#x0027

s disease using the BreakHis and ADNI datasets, respectively. The results distinctly indicate the supremacy of the proposed BSFLSTSVM-ID over the baseline models, underscoring its potential to effectively tackle classification challenges in the biomedical domain. IEEE