'pca' vs 'svd' or 'eig' functions

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Pranav Aggarwal
Pranav Aggarwal 2021-3-16
评论： Pranav Aggarwal 2021-3-18
Hi,
I am trying to generate the principal components from a set of data. However, i get an entirely different result when i use the 'pca' function compared to the 'eig' function. The 'eig' function gives the same results as the 'svd' function for my data.
I am using the raw data as input into the 'pca' function.
For 'eig' - I am calculating the correlation matrix and then using that as input into the 'eig' function.
I am very puzzled on why i get different results and would be grateful for your help! Code below:
testmat = rand(20,5);
testcorrelMat = corr(testmat);
testeig = eig(testcorrelMat);
testsvd = svd(testcorrelMat);
[testcoeff, ~, testlatent] = pca(testmat);
[sort(testsvd), sort(testeig), sort(testlatent)]

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采纳的回答

the cyclist
the cyclist 2021-3-16
Ran in:
You will get the same result from pca() if you standardize the input data first:
rng default
testmat = rand(20,5);
% Standardize the data
testmat = (testmat - mean(testmat))./std(testmat);
testcorrelMat = corr(testmat);
testeig = eig(testcorrelMat);
testsvd = svd(testcorrelMat);
[testcoeff, ~, testlatent] = pca(testmat);
[sort(testsvd), sort(testeig), sort(testlatent)]
ans = 5×3
0.2238 0.2238 0.2238 0.6422 0.6422 0.6422 0.8504 0.8504 0.8504 1.4606 1.4606 1.4606 1.8229 1.8229 1.8229
  2 个评论
Steven Lord
Steven Lord 2021-3-16
Ran in:
To normalize the data you can use the normalize function to normalize by 'zscore' (which is the default normalization method.)
rng default
testmat = rand(20,5);
% Standardize the data
testmat = normalize(testmat);
testcorrelMat = corr(testmat);
testeig = eig(testcorrelMat);
testsvd = svd(testcorrelMat);
[testcoeff, ~, testlatent] = pca(testmat);
results = [sort(testsvd), sort(testeig), sort(testlatent)]
results = 5×3
0.2238 0.2238 0.2238 0.6422 0.6422 0.6422 0.8504 0.8504 0.8504 1.4606 1.4606 1.4606 1.8229 1.8229 1.8229
format longg
results - results(:, 1)
ans = 5×3
0 1.11022302462516e-16 -1.94289029309402e-16 0 4.44089209850063e-16 -9.99200722162641e-16 0 -1.11022302462516e-16 3.33066907387547e-16 0 -1.33226762955019e-15 -1.55431223447522e-15 0 0 -8.88178419700125e-16
Looks pretty good to me.
Pranav Aggarwal
Pranav Aggarwal 2021-3-18
Thanks Steven and 'the cyclist' - solved!

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