Matlab中的Pearson系数和协方差计算

问题描述

我想在Matlab中计算皮尔逊相关系数(不使用Matlab的corr功能).

I want to calculate Pearson's correlation coefficent in Matlab (without using Matlab's corr function).

简而言之，我有两个向量A和B(每个向量均为1x100)，我正在尝试像这样计算皮尔逊系数:

Simply, I have two vectors A and B (each of them is 1x100) and I am trying to calculate the Pearson's coefficient like this:

P = cov(x, y)/std(x, 1)std(y,1)

我正在使用Matlab的cov和std函数.我没有得到的是，cov函数返回一个像这样的方阵:

I am using Matlab's cov and std functions. What I don't get is, the cov function returns me a square matrix like this:

corrAB =
    0.8000    0.2000
    0.2000    4.8000

但是我希望有一个单一的数字作为协方差，所以我可以得出一个单一的P(皮尔逊系数)数字.我想念的是什么?

But I expect a single number as the covariance so I can come up with a single P (pearson's coefficient) number. What is the point I'm missing?

推荐答案

我认为您只是对协方差和协方差矩阵感到困惑，而且数学符号和MATLAB的函数输入看起来确实很相似.在数学中，cov(x,y)表示两个变量的 协方差 x和y.在MATLAB中，cov(x,y)计算x的 ="a href =" http://en.wikipedia.org/wiki/Covariance_matrix"rel =" noreferrer>协方差矩阵 和y. cov是函数，而x和y是输入.

I think you're just confused with covariance and covariance matrix, and the mathematical notation and MATLAB's function inputs do look similar. In math, cov(x,y) means the covariance of the two variables x and y. In MATLAB, cov(x,y) calculates the covariance matrix of x and y. Here cov is a function and x and y are the inputs.

为了更清楚一点，让我用C表示协方差. MATLAB的cov(x,y)返回格式为

Just to make it clearer, let me denote the covariance by C. MATLAB's cov(x,y) returns a matrix of the form

C_xx    C_xy
C_yx    C_yy

正如RichC所指出的，您需要非对角线C_xy(请注意，对于实变量x和y，C_xy=C_yx).一个为您提供两个变量x和y的皮尔逊系数的MATLAB脚本为:

As RichC pointed out, you need the off-diagonals, C_xy (note that C_xy=C_yx for real variables x and y). A MATLAB script that gives you the Pearson's coefficient for two variables x and y, is:

C=cov(x,y);
p=C(2)/(std(x)*std(y));

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