An Improved Lanczos Algorithm for Principal Component Analysis
Xuansheng Wang, Beidun Chen, Jianqiang Sheng, Hongying Zheng, Tangren Dan, Xianfeng Wu · 2020
In this paper, we propose an improved Lanczos algorithm for principal component analysis. This algorithm is to get a low rank approximation which is identical to truncated singular valued decomposition, but it is much cheaper. Since this algorithm is only an extension of Lanczos algorithm to improve its approximation capabilities, we call it extended Lanczos algorithm, and it can keep the computational cost and get much better results in principal component analysis. From numerical experiments, we can demonstrate that our method can work effectively.