PCA的第一部分涵盖了99％的方差意义

本文介绍了PCA的第一部分涵盖了99％的方差意义的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

在PCA分析中，第一个成分占总方差的99％以上是什么意思/意味着什么? 我有一个大小为500X1000的特征向量，在该向量上我使用了Matlab的pca函数，该函数返回[coeff，score，latent，tsquared，explained].变量说明"返回每个组件所覆盖的方差百分比.

What does it mean/signify when the first component covers for more than 99% of the total variance in PCA analysis ? I have a feature vector of size 500X1000 on which I used Matlab's pca function which returns [coeff,score,latent,tsquared,explained]. The variable 'explained' returns the percentage of variance covered by each component.

推荐答案

explained告诉您仅使用该主要组件就可以多么准确地表示数据.就您而言，这意味着仅使用主要主成分，就可以非常准确地描述数据(达到99％).

The explained tells you how accurately you could represent the data by just using that principal component. In your case it means that just using the main principal component, you can describe very accurately (to a 99%) the data.

让我们举一个2D的例子.假设您有100x2数据，并且执行PCA.

Lets make a 2D example. Imagine you have data that is 100x2 and you do PCA.

结果可能是这样的(从互联网上获取)

the result could be something like this (taken from the internets)

此数据将为您提供大约90％的第一个主成分(图中PCA 1st尺寸的大绿色箭头)的explained值.

This data will give you an explained value for the first principal component (PCA 1st dimension big green arrow in the figure) of around 90%.

这是什么意思?

这意味着，如果将所有数据投影到该线上，则将以90％的精度重建这些点(当然，您将在PCA二维方向上丢失信息).

It means that if you project all your data to that line, you will reconstruct the points with 90% of accuracy (of course, you will loose the information in the PCA 2nd dimension direction).

在您的示例中，使用99％的像素表示，几乎所有蓝色的点都位于绿色大箭头上，绿色小箭头方向上的变化很小.

In your example, with 99% it visually means that almost all the points in blue are laying on the big green arrow, with very little variation in the small green arrow direction.

当然，用1000个尺寸而不是2个尺寸进行可视化要困难得多，但我希望您能理解.

Of course it is way more difficult to visualize with 1000 dimensions instead of 2, but I hope you understand.