主成分分析与线性判别分析降维比较

Dimension Reduction Comparison between PCA and LDA

摘要: 主成分分析(PCA)和线性判别分析(LDA)是机器学习领域中常用的降维方法。本文针对矩阵型数据结构，将一维的降维方法PCA和LDA推广为二维PCA和二维LDA，2DPCA和2DLDA对矩阵型数据进行降维处理时，克服了维数灾难的问题。实验研究表明，对比降维效果和分类错误率，2DLDA相比2DPCA是一种更为出色的降维分类方法。

Abstract: Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are commonly used in machine learning. In this paper, we extend PCA and LDA to 2DPCA and 2DLDA, 2DPCA and 2DLDA are directly to reduce the dimension on the original matrix data structure, overcoming the problem of the curse of dimensionality. Empirical research suggests that 2DLDA is a better dimensionality reduction classification method than 2DPCA compared with the effect of dimension reduction and the error rate of classification.