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POWhat's wrong with my PCA?
 

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  1. POWhat's wrong with my PCA?
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    <p>My code:</p> <pre><code>from numpy import * def pca(orig_data): data = array(orig_data) data = (data - data.mean(axis=0)) / data.std(axis=0) u, s, v = linalg.svd(data) print s #should be s**2 instead! print v def load_iris(path): lines = [] with open(path) as input_file: lines = input_file.readlines() data = [] for line in lines: cur_line = line.rstrip().split(',') cur_line = cur_line[:-1] cur_line = [float(elem) for elem in cur_line] data.append(array(cur_line)) return array(data) if __name__ == '__main__': data = load_iris('iris.data') pca(data) </code></pre> <p>The iris dataset: <a href="http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data" rel="noreferrer">http://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data</a></p> <p>Output:</p> <pre><code>[ 20.89551896 11.75513248 4.7013819 1.75816839] [[ 0.52237162 -0.26335492 0.58125401 0.56561105] [-0.37231836 -0.92555649 -0.02109478 -0.06541577] [ 0.72101681 -0.24203288 -0.14089226 -0.6338014 ] [ 0.26199559 -0.12413481 -0.80115427 0.52354627]] </code></pre> <p>Desired Output:<br> Eigenvalues - <code>[2.9108 0.9212 0.1474 0.0206]</code><br> Principal Components - <code>Same as I got but transposed</code> so okay I guess </p> <p>Also, what's with the output of the linalg.eig function? According to the PCA description on wikipedia, I'm supposed to this:</p> <pre><code>cov_mat = cov(orig_data) val, vec = linalg.eig(cov_mat) print val </code></pre> <p>But it doesn't really match the output in the tutorials I found online. Plus, if I have 4 dimensions, I thought I should have 4 eigenvalues and not 150 like the eig gives me. Am I doing something wrong?</p> <p><strong>edit</strong>: I've noticed that the values differ by 150, which is the number of elements in the dataset. Also, the eigenvalues are supposed to add to be equal to the number of dimensions, in this case, 4. What I don't understand is why this difference is happening. If I simply divided the eigenvalues by <code>len(data)</code> I could get the result I want, but I don't understand why. Either way the proportion of the eigenvalues isn't altered, but they are important to me so I'd like to understand what's going on.</p>
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    1. USSteve Tjoa
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    1. COThey are not incorrect. Eigenvalues/eigenvectors are not completely determined (can vary by any scale factor, or even have signs). The actual value you get out depends on the algorithm. (If you do a search you will find a lot of similar queries about obaining eigenvalues with 'wrong' sign which probably explain the issue better).
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      1. POWhat's wrong with my PCA?
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