Class Probability and Generalized Bell Fuzzy Twin SVM for Imbalanced Data

The data mining community has a major challenge in classifying datasets with noise, outliers and imbalanced classes. Twin support vector machine (TSVM) is a well-known plane-based learning technique for classification, however, it has poor performance on aforementioned datasets. To address the issue, in this paper, we propose a novel class probability and generalized bell fuzzy twin SVM for imbalanced data (CGFTSVM-ID). The proposed CGFTSVM-ID assigns membership value to the data points by a new membership function called class probability and generalized bell (CPGB) function. The membership function for majority class is a combination of generalized bell (gbell) function, class probability and imbalance ratio. The gbell function suppress the negative impact of outliers in the training data by assigning them less value. The less class probability of the majority class data points denotes their higher possibility to be noise. The imbalance ratio of the classes considered in the membership function tackles the imbalancing issue of the datasets. In order to ensure the importance of minority class samples in model learning, relatively high memberships are assigned to them. Thus, the proposed CPGB function handles the class imbalance learning problem having noise, and outliers. We employ successive overrelaxation technique to solve the proposed optimization problem. The extensive numerical experiments and statistical analysis carried out over imbalanced real-world UCI and KEEL datasets clearly reveal that the proposed CGFTSVM-ID has superior generalization performance in comparison to baseline models. Moreover, the experiments are also conducted on the publicly available ADNI dataset for Alzheimer's disease classification and results demonstrate the superiority of the proposed CGFTSVM-ID. The code for the proposed CGFTSVM-ID can be found on https://github.com/mtanveer1/CGFTSVM-ID .