Large scale fuzzy least squares twin SVMs for class imbalance learning

Abstract

Twin support vector machines (TSVMs) have been successfully employed for binary classification problems. With the advent of machine learning algorithms, the data has proliferated and there is a need to handle or process large scale data. TSVMs are not successful in handling large scale data as: i) The optimization problem solved in TSVM needs to calculate large matrix inverses, which makes it an ineffective choice for large scale problems. ii) Empirical risk minimization principle is employed in TSVM and hence may suffer due to overfitting. iii) Wolfe dual of TSVM formulation involves positive semi-definite matrices and hence singularity issues need to be resolved manually. Keeping in view the aforementioned shortcomings, we propose a novel large scale fuzzy least squares TSVM for class imbalance learning (LS-FLSTSVM-CIL). We formulate the LS-FLSTSVM-CIL such that the proposed optimization problem ensures that: i) No matrix inversion is involved in the proposed LS-FLSTSVM-CIL formulation, which makes it an efficient choice for large scale problems. ii) Structural risk minimization principle is implemented which avoids the issues of overfitting and results in better performance. iii) Wolfe dual formulation of the proposed LS-FLSTSVM-CIL model involves positive definite matrices. Also, to resolve the issues of class imbalance, we assigned fuzzy weights in proposed LS-FLSTSVM-CIL to avoid the bias in dominating samples of class imbalance problems. To make it more feasible for large scale problems, we used iterative procedure known as sequential minimization principle to solve the objective function of the proposed LS-FLSTSVM-CIL model. From the experimental results, one can see that the proposed LS-FLSTSVM-CIL demonstrated superior performance in comparison to baseline classifiers. To demonstrate the feasibility of the proposed LS-FLSTSVM-CIL on large scale classification problems, we evaluated the classification models on large scale NDC data. To demonstrate the practical applications of proposed LS-FLSTSVM-CIL model, we evaluated it for the diagnosis of the Alzheimer's disease and Breast cancer disease. Evaluation on NDC datasets show that proposed LS-FLSTSVM-CIL has feasibility in large scale problems as it is fast in comparison with the baseline classifiers. IEEE