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

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)]

Answer 1

[the cyclist]

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

[Steven Lord]

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]

Thanks Steven and 'the cyclist' - solved!