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  1. PO
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    <p>You decomposed the wrong matrix.</p> <p>Principal Component Analysis requires manipulating the eigenvectors/eigenvalues of the <strong><em>covariance matrix</em></strong>, not the data itself. The covariance matrix, created from an m x n data matrix, will be an m x m matrix with ones along the main diagonal.</p> <p>You can indeed use the <em>cov</em> function, but you need further manipulation of your data. It's probably a little easier to use a similar function, <strong><em>corrcoef</em></strong>:</p> <pre><code>import numpy as NP import numpy.linalg as LA # a simulated data set with 8 data points, each point having five features data = NP.random.randint(0, 10, 40).reshape(8, 5) # usually a good idea to mean center your data first: data -= NP.mean(data, axis=0) # calculate the covariance matrix C = NP.corrcoef(data, rowvar=0) # returns an m x m matrix, or here a 5 x 5 matrix) # now get the eigenvalues/eigenvectors of C: eval, evec = LA.eig(C) </code></pre> <p>To get the eigenvectors/eigenvalues, I did not decompose the covariance matrix using SVD, though, you certainly can. My preference is to calculate them using <em>eig</em> in NumPy's (or SciPy's) LA module--it is a little easier to work with than <em>svd</em>, the return values are the eigenvectors and eigenvalues themselves, and nothing else. By contrast, as you know, <em>svd</em> doesn't return these these directly.</p> <p>Granted the SVD function will decompose any matrix, not just square ones (to which the <em>eig</em> function is limited); however when doing PCA, you'll always have a square matrix to decompose, regardless of the form that your data is in. This is obvious because the matrix you are decomposing in PCA is a <em>covariance matrix</em>, which by definition is always square (i.e., the columns are the individual data points of the original matrix, likewise for the rows, and each cell is the covariance of those two points, as evidenced by the ones down the main diagonal--a given data point has perfect covariance with itself).</p>
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    1. POWhat's wrong with my PCA?
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    1. POWhat's wrong with my PCA?
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    1. COSometimes it is worth calculating the means and standard deviations separately, and then calculating covariance. This is useful if, for example, one wants to reverse the process after manipulating the principal components.
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    2. COI agree--in this case, the OP seemed to want something that 'just worked', and i find doing it this way (often) simpler, particular when working from the command line.
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    3. COI think this is wrong. As you say PCA results in the eigenvalues/vectors of the covariance matrix, but in almost every case I've seen these can be obtained by performing SVD on the (de-meaned) data matrix itself. This performs much better since it removes the need to calculate the full covariance matrix, and is also more numerically stable (I don't know the details but I understand SVD is more stable than eig). Can't find a more accessible description but you can see here: http://public.lanl.gov/mewall/kluwer2002.html This is the method used in every serious implementation I have seen.
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