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    <p>That all looks right, up to the last step. The usual notation for SVD is that it returns three matrices A = USV*. S is a diagonal matrix (meaning all zero off the diagonal) that, in this case, basically gives a measure of how much each dimension captures of the original data. The numbers ("singular values") will go down, and you can look for a drop-off for how many dimensions are useful. Otherwise, you'll want to just choose an arbitrary number N for how many dimensions to take.</p> <p>Here I get a little fuzzy. The coordinates of the terms (words) in the reduced-dimension space is either in U or V, I think depending on whether they are in the rows or columns of the input matrix. Off hand, I think the coordinates for the words will be the rows of U. i.e. the first row of U corresponds to the first row of the input matrix, i.e. the first word. Then you just take the first N columns of that row as the word's coordinate in the reduced space.</p> <p>HTH</p> <p>Update:</p> <p>This process so far doesn't tell you exactly how to pick out tags. I've never heard of anyone using LSI to choose tags (a machine learning algorithm might be more suited to the task, like, say, decision trees). LSI tells you whether two words are similar. That's a long way from assigning tags.</p> <p>There are two tasks- a) what are the set of tags to use? b) how to choose the best three tags?. I don't have much of a sense of how LSI is going to help you answer (a). You can choose the set of tags by hand. But, if you're using LSI, the tags probably should be words that occur in the documents. Then for (b), you want to pick out the tags that are closest to words found in the document. You could experiment with a few ways of implementing that. Choose the three tags that are closest to <em>any</em> word in the document, where closeness is measured by the cosine similarity (see Wikipedia) between the tag's coordinate (its row in U) and the word's coordinate (its row in U).</p>
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    1. POLSA - Latent Semantic Analysis - How to code it in PHP?
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    1. USJosh Tauberer
    1. USJosh Tauberer
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    1. COThank you. My main problem is: How can I determine which words I should chose? Assuming that I always want to have 3 tags: What do I have to do?
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      1. UScaw
    2. COThanks. Maybe I've misunderstood something and LSA isn't used to find tags. But if I have a set of tags, e.g. "Sports, Politics, World", then you can surely use LSA to find the best matching tag, right?
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    3. CO"But if I have a set of tags, e.g. "Sports, Politics, World","... No. That's not what LSA is for at all really. If you had those tags, and a corpus of articles about those topics, it would make more sense to use a Bayesian classfier. What LSA is for is to say, "the words: baseball, yankees, A-Rod tend to co-occur, and probably reflect some underlying structure, therefore other articles having baseball in them might be related to the same underlying topics". LSA is just factor analysis.
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      1. USGregg Lind
 

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