Weighted least squares projection twin support vector machines with local information

Recently proposed least squares projection twin support vector machine (LSPTSVM), as a variant of projection twin support vector machine (PTSVM), attempts to further enhance the performance of PTSVM, whose solution follows from solving two sets of linear equations whereas PTSVM needs to solve two quadratic programming problems along with two sets of linear equations. Unfortunately, LSPTSVM fails to exploit the underlying correlation or similarity information between any pair of data points with the same labels that may be important for classification performance as much as possible. To mitigate the above deficiency, in this paper, we propose a novel binary classifier based on LSPTSVM, called weighted least squares projection support vector machine with local information (LIWLSPTSVM). Compared to LSPTSVM, LIWLSPTSVM mines as much underlying similarity information within samples as possible by computing the relative density degree for each data point according to the weights of the intra-class graph of training set. Because of measuring the importance of samples in the same class by density weighting method, weighted mean, instead of standard mean in LSPTSVM, is used as the class mean. Moreover, LIWLSPTSVM successfully inherits the merit of the LSPTSVM, and it has a special case of LSPTSVM when the relative density degree of each point is degenerated to one. The experimental results on toy as well as publicly available datasets confirm the effectiveness of our method.