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POLatent Semantic Analysis in Python discrepancy
 

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  1. POLatent Semantic Analysis in Python discrepancy
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    <p>I'm trying to follow the <a href="http://en.wikipedia.org/wiki/Latent_semantic_analysis" rel="nofollow">Wikipedia Article on latent semantic indexing</a> in Python using the following code:</p> <pre><code>documentTermMatrix = array([[ 0., 1., 0., 1., 1., 0., 1.], [ 0., 1., 1., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0., 1., 1.], [ 0., 0., 0., 1., 0., 0., 0.], [ 0., 1., 1., 0., 0., 0., 0.], [ 1., 0., 0., 1., 0., 0., 0.], [ 0., 0., 0., 0., 1., 1., 0.], [ 0., 0., 1., 1., 0., 0., 0.], [ 1., 0., 0., 1., 0., 0., 0.]]) u,s,vt = linalg.svd(documentTermMatrix, full_matrices=False) sigma = diag(s) ## remove extra dimensions... numberOfDimensions = 4 for i in range(4, len(sigma) -1): sigma[i][i] = 0 queryVector = array([[ 0.], # same as first column in documentTermMatrix [ 0.], [ 0.], [ 0.], [ 0.], [ 1.], [ 0.], [ 0.], [ 1.]]) </code></pre> <p>How the math says it should work:</p> <pre><code>dtMatrixToQueryAgainst = dot(u, dot(s,vt)) queryVector = dot(inv(s), dot(transpose(u), queryVector)) similarityToFirst = cosineDistance(queryVector, dtMatrixToQueryAgainst[:,0] # gives 'matrices are not aligned' error. should be 1 because they're the same </code></pre> <p>What does work, with math that looks incorrect: ( from <a href="http://www.gototheboard.com/articles/An_Example_of_Latent_Semantic_Indexing" rel="nofollow">here</a>)</p> <pre><code>dtMatrixToQueryAgainst = dot(s, vt) queryVector = dot(transpose(u), queryVector) similarityToFirst = cosineDistance(queryVector, dtMatrixToQueryAgainsst[:,0]) # gives 1, which is correct </code></pre> <p>Why does route work, and the first not, when everything I can find about the math of LSA shows the first as correct? I feel like I'm missing something obvious...</p>
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    1. COWhat does `## remove extra dimensions...` involve?
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    3. COat `u,s,vt = linalg.svd(a, full_matrices=False)`, where is `a` comming from???
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