Abstract: The traditional least squares support vector machine (LSSVM) obtained the low rank of kernel matrix by randomly choosing a part of samples to improve the sparsity of solution. In order to make the approximate decomposition of low rank matrix as small as possible to approximate the original kernel matrix, we proposed QRPLSSVM sparse algorithm based on QR factorization. Using the orthogonal feature of QR factorization to choose some samples with a big diversity, we iteratively selected some columns of the kernel matrix to get Nystrm type low rank approximation of kernel matrix, and used decomposition results to get the sparse solution of LSSVM quickly.  The experimental analyses show  that the proposed algorithm can get more sparse solutions without sacrificing the classification performance, and even get higher accuracy with the sparsity level less than 0.05%, and it can solve largescale training problems effectively.

Key words: sparse least square support vector machine (LSSVM), sparse solution, QR factorization