Maximum Margin of Twin Spheres Support Vector Machine for Imbalanced Data Classification

Twin support vector machine (TSVM) finds two nonparallel planes by solving a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one as in the conventional support vector machine (SVM); this makes the learning speed of TSVM approximately four times faster than that of the standard SVM. One major limitation of TSVM is that it involves an expensive matrix inverse operation when solving the dual problem. In addition, TSVM is less effective when dealing with the imbalanced data. In this paper, we propose a maximum margin of twin spheres support vector machine (MMTSSVM) for imbalanced data classification. MMTSSVM only needs to find two homocentric spheres. On one hand, the small sphere captures as many samples in the majority class as possible; on the other hand, the large sphere pushes out most samples in the minority class by increasing the margin between two homocentric spheres. MMTSSVM involves a QPP and a linear programming problem as opposed to a pair of QPPs as in classical TSVM or a larger-sized QPP in SVM, thus it greatly increases the computational speed. More importantly, MMTSSVM avoids the matrix inverse operation. The property of parameters in MMTSSVM is discussed and testified by one artificial experiment. Experimental results on nine benchmark datasets demonstrate the effectiveness of the proposed MMTSSVM in comparison with state-of-the-art algorithms. Finally, we apply MMTSSVM into Alzheimer's disease medical experiment and also obtain a better experimental result.