zoukankan      html  css  js  c++  java
  • Generalized Low Rank Approximation of Matrices

    Generalized Low Rank Approximations of Matrices


    JIEPING YE*jieping@cs.umn.edu
    Department of Computer Science & Engineering,University of Minnesota-Twin Cities, Minneapolis, MN 55455, USA

    Published online:12 August 2005


            Abstract.The problem of computing low rank approximations of matrices is considered. The novel aspect of our approach is that the low rank approximations are on a collection of matrices. We formulate this as an optimization problem, which aims to minimize the reconstruction (approximation) error. To the best of our knowledge, the optimization problem proposed in this paper does not admit a closed form solution. We thus derive an iterative algorithm, namely GLRAM, which stands for the Generalized Low Rank Approximations of Matrices. GLRAM reduces the reconstruction error sequentially, and the resulting approximation is thus improved during successive iterations. Experimental results show that the algorithm converges rapidly. 

           We have conducted extensive experiments on image data to evaluate the effectiveness of the proposed algorithm and compare the computed low rank approximations with those obtained from traditional Singular Value Decomposition (SVD) based methods. The comparison is based on the reconstruction error, misclassification error rate,and computation time. Results show that GLRAM is competitive with SVD for classification, while it has a muchlower computation cost. However, GLRAM results in a larger reconstruction error than SVD. To further reduce the reconstruction error, we study the combination of GLRAM and SVD, namely GLRAM + SVD, where SVD is repreceded by GLRAM. Results show that when using the same number of reduced dimensions, GLRAM+SVD achievessignificant reduction of the reconstruction error as compared to GLRAM, while keeping the computation cost low.






  • 相关阅读:
    failed: unacceptable content-type: text/html
    iOS button点击更换图片
    支付宝ios SDK官方下载页面
    xcode6 中使用OC代码时,在NSObject的子类中报错
    CocoaPods安装和使用教程
    Mac 下安装Ruby环境
    iOS .a与.framewofk
    Couldn't find preset "es2015" relative to directory问题解决
    yarn依赖管理工具的使用
    java.io.IOException: Could not delete path 'D:mycode eactnativeSecondTestandroidappuildgeneratedsource eleaseandroidsupportv7
  • 原文地址:https://www.cnblogs.com/engineerLF/p/5393027.html
Copyright © 2011-2022 走看看