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I have set of documents as follows where each document has set of words that represents the content of it.

Doc1: {fish, moose, wildlife, hunting, bears, polar}
Doc2: {energy, fuel, costs, oil, gas}
Doc3: {wildlife, hunt, polar, fishing}

So, if I look at my documents I can deduce that Doc1 and Doc3 are very much similar.

I want distance metrics for bag-of-words. I followed some tutorials in Gensim about how to do it. However, as I understand, initially they train a model and then use that model to calculate the Hellinger Distance. However, in my case, I do not have any training data. Hence, please let me know how to achieve this with no training data.

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As u said that one has to train a model in order to calculate Hellinger distance. I am not sure that which model u are talking about but for now I assume that u might have thinking about the latent model so according to me there is not mandatory to train a latent model to produce a document vector. one can create a document vector from the directly word-doc matrix and can calculate Hellinger distance. One simple trick is that I used is first calculate a bag of word representation after getting doc-word matrix by gensim utilities. kindly review it and let me know your opinion.

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