matlab里面的求协方差函数
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一:matlab里面关于方差和协方差的几点需要注意的
求均值的函数:mean
求方差的函数:var
标准差:
方差:
求协方差的函数:cov
1 如果a,b是向量,则:
cov(a,b)相当于是[D(a),cov(a,b);cov(b,a),D(b)],其中D(a)和D(b)分别代表了a,b的方差。cov(a,b)和cov(b,a)分别代表了两者之间的协方差
举例:
>> a=[1.1 2.2 3 4.5 0.8]a = 1.1000 2.2000 3.0000 4.5000 0.8000>> b=[1.3 2.4 2.1 5 3.3]b = 1.3000 2.4000 2.1000 5.0000 3.3000>> cov(a,b)ans = 2.2570 1.3595 1.3595 1.9970
其中,对角线的值是两个向量的方差,斜对角线的是两个向量之间的协方差
2 如果a,b是矩阵,则:
cov(a,b)相当于是cov(a(:),b(:)),举例说明:
>> a=randn(4);>> aa = -0.4326 -1.1465 0.3273 -0.5883 -1.6656 1.1909 0.1746 2.1832 0.1253 1.1892 -0.1867 -0.1364 0.2877 -0.0376 0.7258 0.1139>> b=randn(4);>> bb = 1.0668 0.2944 -0.6918 -1.4410 0.0593 -1.3362 0.8580 0.5711 -0.0956 0.7143 1.2540 -0.3999 -0.8323 1.6236 -1.5937 0.6900>> cov(a,b)ans = 0.8513 -0.0860 -0.0860 1.0129/////////////////////////////////////////////////////////////////////////////>> a(:)ans = -0.4326 -1.6656 0.1253 0.2877 -1.1465 1.1909 1.1892 -0.0376 0.3273 0.1746 -0.1867 0.7258 -0.5883 2.1832 -0.1364 0.1139>> b(:)ans = 1.0668 0.0593 -0.0956 -0.8323 0.2944 -1.3362 0.7143 1.6236 -0.6918 0.8580 1.2540 -1.5937 -1.4410 0.5711 -0.3999 0.6900>> cov(a(:),b(:))ans = 0.8513 -0.0860 -0.0860 1.0129
另外,matlab里面关于cov函数的说明解释的很详细:
cov(x), if x is a vector, returns the variance of x. For matrix input X, where each row is an observation, and each column is a variable, cov(X) is the covariance matrix. diag(cov(X)) is a vector of variances for each column, and sqrt(diag(cov(X))) is a vector of standard deviations. cov(X,Y), where X and Y are matrices with the same number of elements, is equivalent to cov([X(:) Y(:)]).
cov(x) or cov(x,y) normalizes by N – 1, if N > 1, where N is the number of observations. This makes cov(X) the best unbiased estimate of the covariance matrix if the observations are from a normal distribution. For N = 1, cov normalizes by N.
cov(x,1) or cov(x,y,1) normalizes by N and produces the second moment matrix of the observations about their mean. cov(X,Y,0) is the same as cov(X,Y) and cov(X,0) is the same as cov(X).
其使用示例可见:http://www.mathworks.cn/cn/help/matlab/ref/cov.html?searchHighlight=cov
参考:
http://pinkyjie.com/2010/08/31/covariance/
http://www.cnblogs.com/cvlabs/archive/2010/05/08/1730319.html
http://blog.csdn.net/faceRec/article/details/1697362
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