基于QR分解的稀疏LSSVM算法

传统最小二乘支持向量机(LSSVM)一般通过随机选择部分样本得到核矩阵的低秩近似提高解的稀疏性, 为了使该近似分解用尽可能小的低秩矩阵更好地近似原核矩阵, 提出一种]基于正交三角(QR)分解的QRP-LSSVM稀疏算法. 采用QR分解保持正交的特性挑选差异更大的样本, 迭代地精选核矩阵的部分列得到核矩阵的Nystr-m型低秩近似, 并利用分解结果快速求得最小二乘支持向量机的稀疏解. 实验分析表明, 该算法在不牺牲分类性能的前提下可得到更稀疏的解, 甚至在稀疏水平不超过0.05%的情况下准确率也较高, 可有效解决大规模训练问题.

Sparse LSSVM Algorithm Based on QR Factorization

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 makethe 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 ofkernel 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.