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I have a Latent Dirichlet Allocation (LDA) model with $K$ topics trained on a corpus with $M$ documents. Due to my hyper parameter configurations, the output topic distributions for each document is heavily distributed on only 3-6 topics and all the rest are close to zero ($K$~$\mathcal{O}(100)$). What I mean by this, is that the 3-6 highest contributing topics for all documents is orders of magnitude (about 6 orders) greater than the rest of the topic contributions.

If I use the Jensen-Shannon distance to compute the similarity between documents, I need to store all values of the topic distribution as non-zero, even the very small values of the non contributing topics, because Jensen-Shannon divides by each discrete value in the distribution. This requires a lot of storage and is inefficient.

If, however, I store the topic distributions of each document as a sparse matrix (the 3-6 highest contributing topics are non-zero and the rest are zero) where each row is a unique document and each column is a topic, then this uses far less space. But I can no longer use the Jensen-Shannon metric, because we would be dividing by 0. In this case:

Can I use the euclidean distance between documents topic distributions to compare similarity between documents?

Using the euclidean distance would require far less storage and is extremely fast to compute.

I appreciate that Jensen-Shannon is one of the "correct" metrics to compare discrete probability distributions, as well as the Bhattacharyya distance and Hellinger distance. But ultimately, the output of LDA is a discrete topic distribution for each doucment - each document is a vector (or point) in a $K$ dimensional space. By this argument, is it valid to use the euclidean distance to calcualte documents similarities? Is there something blatantly wrong with this method?

I have tested the euclidean distance to compare documents, and yielded good results, which works well for my industrial application. But I want to know the academics behind such a method. Thanks in advance!

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  • $\begingroup$ It's not theoretically grounded. How did the Hellinger and Bhattacharyya distances compare? $\endgroup$ – Emre Nov 17 '17 at 19:38
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Euclidean distance -by which in this application, I assume you mean the euclidean distance in an $n$-dimensional space defined by the distribution of document contents among $n$ topics considered, is a valid measure to use in comparing the topics represented within two documents.

What you're doing by applying this method is quantifying a topic frequency difference within this newly defined space, and so interpretation of these quanta will require analysis of the space. For example, what euclidean distance indicates that documents are relatively similar?

In distiction, the normalized result of something like the hellinger distance provides an easily interperable framework by which to evaluate the results- a score of 0 indicates no overlap in the distribution over the topics in question of the two documents, and a 1, perfect overlap.

For the efficiency concerns, it's not clear to me why you couldn't truncate your topics considered to the crucial topics and then calculate any of the metrics on the distributions over ony those topics, rather than the entire universe of considered topics.

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