Sparse least square twin support vector machine with adaptive norm

By promoting the parallel hyperplanes to non-parallel ones in SVM, twin support vector machines (TWSVM) have attracted more attention. There are many modifications of them. However, most of the modifications minimize the loss function subject to the I ₂-norm or I ₁-norm penalty. These methods are non-adaptive since their penalty forms are fixed and pre-determined for any types of data. To overcome the above shortcoming, we propose l _p norm least square twin support vector machine (l _p LSTSVM). Our new model is an adaptive learning procedure with l _p -norm (0<p<1), where p is viewed as an adjustable parameter and can be automatically chosen by data. By adjusting the parameter p, l _p LSTSVM can not only select relevant features but also improve the classification accuracy. The solutions of the optimization problems in l _p LSTSVM are obtained by solving a series systems of linear equations (LEs) and the lower bounds of the solution is established which is extremely helpful for feature selection. Experiments carried out on several standard UCI data sets and synthetic data sets show the feasibility and effectiveness of the proposed method.