Principal component analysis using QR decomposition
Principal component analysis using QR decomposition
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DOI：
10.1007/s13042-012-0131-7
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发表时间：
2013-12-01
影响因子：
5.6
通讯作者：
Miyano, Satoru
中科院分区：
文献类型：
--
作者：
Sharma, Alok;Paliwal, Kuldip K.;Miyano, Satoru
本文提出了基于QR的主成分分析（PCA）方法。与基于奇异值分解（SVD）的PCA方法类似，该方法具有数值稳定性。我们已经进行了分析比较，以及数值比较（在Matlab软件上），以研究我们的方法的性能（在计算复杂度方面）。基于SVD的PCA的计算复杂度约为14 dn（2）次浮点运算（其中d是特征空间的维数，n是训练特征向量的数量）;而基于QR的PCA的计算复杂度约为2dn（2）+ 2dth次浮点运算（其中t是数据协方差矩阵的秩，h是缩减特征空间的维数）。据观察，基于QR的PCA在计算复杂度方面更有效。
In this paper we present QR based principal component analysis (PCA) method. Similar to the singular value decomposition (SVD) based PCA method this method is numerically stable. We have carried out analytical comparison as well as numerical comparison (on Matlab software) to investigate the performance (in terms of computational complexity) of our method. The computational complexity of SVD based PCA is around 14dn(2) flops (where d is the dimensionality of feature space and n is the number of training feature vectors); whereas the computational complexity of QR based PCA is around 2dn(2) + 2dth flops (where t is the rank of data covariance matrix and h is the dimensionality of reduced feature space). It is observed that the QR based PCA is more efficient in terms of computational complexity.