求解大样本核主成分分析模型的Lanczos算法  

Lanczos Algorithm for Kernel Principle Component Analysis on Large Scale Samples

作　　者：陈永良[1] 林楠[1] 李学斌[1] 

机构地区：[1]吉林大学综合信息矿产预测研究所,长春130026

出　　处：《吉林大学学报（地球科学版）》2010年第1期222-226,共5页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学基金项目(40872193)

摘　　要：求解核主成分分析模型的技术关键是确定核矩阵端部的较大特征对。把求解大规模对称矩阵端部特征对问题的基本方法——Lanczos算法应用于核主成分分析模型的求解,设计了大样本核主成分分析模型求解的实用算法。在clapack和nu-TRLan两个软件包的基础上,开发了大样本核主成分分析模型求解算法的VC++程序。用高光谱遥感图像数据进行模型求解算法的应用试验研究,证明了大样本核主成分分析模型求解算法的实用性。The key technique for solving the problem of kernel principle component analysis is to determine the several biggest eigenpairs of the kernel matrix. Lanczos algorithm is applied to the problem. Basing on the method, along with the thick-restart strategy, a highly effective algorithm is laid out. A corresponding visual C＋＋ program for computing the parameters of a kernel component analysis model on large scale samples is developed on clapack and nu-TRLan software packages. Experiments are conducted to process hyperspectral remote sensing images to get the kernel principle components. The results illustrate the practicability of the algorithm in computing the parameters of a kernel principle component analysis model for large scale samples.

关 键 词：大样本 核主成分分析 LANCZOS算法 Thick-重启动策略 

分 类 号：P628[天文地球—地质矿产勘探]