PCA的数学原理
数学算法俱乐部
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· 2021-07-09
日期 : 2021年07月08日
正文共 :7172字
PCA(Principal Component Analysis)是一种常用的数据分析方法。PCA通过线性变换将原始数据变换为一组各维度线性无关的表示,可用于提取数据的主要特征分量,常用于高维数据的降维。网上关于PCA的文章有很多,但是大多数只描述了PCA的分析过程,而没有讲述其中的原理。这篇文章的目的是介绍PCA的基本数学原理,帮助读者了解PCA的工作机制是什么。
当然我并不打算把文章写成纯数学文章,而是希望用直观和易懂的方式叙述PCA的数学原理,所以整个文章不会引入严格的数学推导。希望读者在看完这篇文章后能更好的明白PCA的工作原理。
数据的向量表示及降维问题
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向量的表示及基变换
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协方差矩阵及优化目标
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算法及实例
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进一步讨论
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