I have been using Latent Dirichlet Analysis for a while but I am a bit confounded as to it's practical ability to compare two documents. It is of course ideal for classification when you want to see in what category a certain document or word belongs, but in content comparison I am at my wits end.

An inferred document yields a distribution over n topics, summing to one.

Using Kolmogorov-Smirnov was recommended somewhere, but it has the annoying property of giving two identical distributions a very high score, even if they do not make sense. Two words not in the dictionary will give a perfect match, which is of course absurd.

The normalized dot product actually works very well because it punishes flat distributions (trivial documents), but I thought there would be a better one.

Any suggestion is appreciated.


1 Answer 1


There's numerous approaches to this. For a pair of documents, the Kullback Leibler divergence of their respective topic distributions is probably the most common and straight-forward.

See page 12 of Probabilistic Topic Models by Styvers and Griffiths for a discussion of the KL divergence approach, as well as several others.

  • $\begingroup$ As far as I can see, my particular problem of TRIVIAL identical distributions is not solved by Shannen-Jensen / Kullback-Leibler. Look!! Sum_i[ ln(Pi/Qi) * Pi] means that all precisely similar ps and qs make it ln(1) * whatever = 0. It measures closeness only too good, because it assumes that information in itself has no variance-properties. Very weird since Shannon was an information theorist. Or am I missing something big? Stats appears to be too tough for me.. $\endgroup$
    – user19795
    Commented Jan 21, 2013 at 8:11

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