Toy example dataset for testing PCA implementation

Question

I want to check my implementation of dimensionality reduction with PCA, so I'm looking for a test case. I have found other implementations on the web as well, so I will be comparing with those too.

Can anyone give me a test case, where I have an $N \times D_1$ data matrix and I want to keep $D_2$ components after PCA, so let's say $N = 4$, $D_1 = 5$ and $D_2 = 3$, in other words, I have 5 features from 4 samples, and I want to do PCA and keep 3 components. Given that PCA does not have any randomness, a dataset should give the same output in different implementations of PCA, right?

If anyone is interested, what I'm doing (in MATLAB) is:

[COEFF,SCORE,latent] = princomp(data);
D2 = min(find((cumsum(latent)./sum(latent))>0.9)); % or simply 3 for this case
reduced_testdata = bsxfun(@minus, testdata, mean(traindata)) * COEFF;

P.S: examples for other dimensionality reduction methods (like LDA and CCA) are also very welcome, as they can help me or other users to check their code as well.

Answer 1

Since you are using Matlab, you can use hald:

% From http://www.mathworks.com/help/stats/princomp.html
load hald;
[pc,score,latent,tsquare] = princomp(ingredients);

or cities, amongst others.

Given that PCA does not have any randomness, a dataset should give the same output in different implementations of PCA, right?

Right, but there could be differences in rounding, some corner cases, and some functions might not sort by descending principal component scores.