I am implementing a PCA algorithm in MATLAB. I see two different approaches to calculating the covariance matrix:
C = sampleMat.' * sampleMat ./ nSamples; and
C = cov(data); What is the difference between these two methods?
PS 1: When I use cov(data) is that unnecessary:
meanSample = mean(data,1); data = data - repmat(data, nSamples, 1); PS 2:
At first approach should I use nSamples or nSamples - 1?
In short: cov mainly just adds convenience to the bare formula.
If you type
edit cov You'll see a lot of stuff, with these lines all the way at the bottom:
xc = bsxfun(@minus,x,sum(x,1)/m); % Remove mean if flag xy = (xc' * xc) / m; else xy = (xc' * xc) / (m-1); % DEFAULT end which is essentially the same as your first line, save for the subtraction of the column-means.
Read the wiki on sample covariances to see why there is a minus-one in the default path.
Note however that your first line uses normal transpose (.'), whereas the cov-version uses conjugate-transpose ('). This will make the output of cov different in the context of complex-valued data.
Also note that cov is a function call to a non-built in function. That means that there will be a (possibly severe) performance penalty when using cov in a loop; Matlab's JIT compiler cannot accelerate non-built in functions.
cov. If you need to do it hundreds of times in a loop, with different data sets, etc., using the bare formula will be much faster and is overall the better trade-off. As mentioned above: the output of cov will only be different from your first attempt, if your data is complex-valued. If it only contains real values, the outputs will be identical.