Inexact implementation using Krylov subspace methods for large scale exponential discriminant analysis with applications to high dimensionality reduction problems
作者：
Highlights：
• We propose two Krylov subspace algorithms for solving the large matrix exponential eigenproblem effectively.
• We consider how to compute the involved matrix exponential-vector products efficiently, which is the key step in the Krylov subspace method.
• We compare the discriminant analysis criterion of EDA and that of LDA from a theoretical point of view.
• We establish a new relationship between the accuracy of the approximate eigenvectors and the distance to nearest neighbor classifier.
• We show why the matrix exponential eigenproblem can be solved approximately from a theoretical point of view.
摘要
Highlights•We propose two Krylov subspace algorithms for solving the large matrix exponential eigenproblem effectively.•We consider how to compute the involved matrix exponential-vector products efficiently, which is the key step in the Krylov subspace method.•We compare the discriminant analysis criterion of EDA and that of LDA from a theoretical point of view.•We establish a new relationship between the accuracy of the approximate eigenvectors and the distance to nearest neighbor classifier.•We show why the matrix exponential eigenproblem can be solved approximately from a theoretical point of view.
论文关键词：Dimensionality reduction,Linear discriminant analysis (LDA),Exponential discriminant analysis (EDA),Matrix exponential,Krylov subspace method
论文评审过程：Received 1 December 2015, Revised 26 May 2016, Accepted 20 August 2016, Available online 28 August 2016, Version of Record 12 March 2017.
论文官网地址：https://doi.org/10.1016/j.patcog.2016.08.020
