Regularized robust fuzzy least squares twin support vector machine for class imbalance learning

Abstract

Twin support vector machines (TWSVM) have been successfully applied to the classification problems. TWSVM is computationally efficient model of support vector machines (SVM). However, in real world classification problems issues of class imbalance and noise provide great challenges. Due to this, models lead to the inaccurate classification either due to higher tendency towards the majority class or due to the presence of noise. We provide an improved version of robust fuzzy least squares twin support vector machine (RFLSTSVM) known as regularized robust fuzzy least squares twin support vector machine (RRFLSTSVM) to handle the imbalance problem. The advantage of RRFLSTSVM over RFLSTSVM is that the proposed RRFLSTSVM implements the structural risk minimization principle by the introduction of regularization term in the primal formulation of the objective functions. This modification leads to the improved classification as it embodies the marrow of statistical learning theory. The proposed RRFLSTSVM doesn't require any extra assumption as the matrices resulting in the dual are positive definite. However, RFLSTSVM is based on the assumption that the inverse of the matrices resulting in the dual always exist as the matrices are positive semi-definite. To subsidize the effects of class imbalance and noise, the data samples are assigned weights via fuzzy membership function. The fuzzy membership function incorporates the imbalance ratio knowledge and assigns appropriate weights to the data samples. Unlike TWSVM which solves a pair of quadratic programming problem (QPP), the proposed RRFLSTSVM method solves a pair of system of linear equations and hence is computationally efficient. Experimental and statistical analysis show the efficacy of the proposed RRFLSTSVM method.