# How to calculate the correlation coefficient between an array and a matrix?

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Nut 2016 年 5 月 25 日
コメント済み: Nut 2016 年 7 月 1 日
Hi,
I have a matrix A and a matrix B, with the same number of rows and a different number of columns. I need to calculate the correlation coefficient between each single columns of the matrix A and all the columns of the matrix B. For each column of A, the partial result will be an array, so I'm thinking to a matrix as final result.
Is there a way to do this avoiding the "for" cycle? Which is the most efficient way to do this? Could you suggest me the best syntax?
Finally, I have also to do the same with the mean squared error: again, in this second case, is it possible to avoid the "for" cycle?

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### 採用された回答

Tom Lane 2016 年 6 月 24 日
If you have the Statistics and Machine Learning Toolbox, it sounds like you want this:
>> x = randn(20,3);
>> y = x*[1 0;0 1;1 1];
>> corr(x,y)
ans =
0.9221 -0.1434
-0.2979 0.8438
0.6825 0.5606
I'm not sure what you mean by mean squared error. The following adds some noise to get z, then computes coefficients for predicting y from z, then computes the sum of squared differences between y and the predicted values for each column. Does this point you in the right direction?
>> z = x+randn(size(x))/100;
>> b
b =
0.9983 -0.0009
-0.0000 0.9964
1.0016 1.0049
>> sum((y-yhat).^2)
ans =
0.0025 0.0054
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Nut 2016 年 7 月 1 日
Thank you very much, Tom. corr is what I needed. Also what you said about mean squared error can help me, but more precisely I was wondering about a way to calculate it between each pairs of columns of the two matrices.
I would like to know if there is a way similar to "corr", to get a similar matrix containing the results for each pair, avoiding a "for" loop.
Thank you again!

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