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recently I have read this paper, A Survey of text similarity approaches, and I discovered that there are a lot of algorithms that can be used to measure similarity.

At present I am applying the method of soft similarity (link to the paper: Soft similarity and soft cosine):

"Our idea is more general: we propose to modify the manner of calculation of similarity in Vector Space Model taking into account similarity of features. If we apply this idea to the cosine measure, then the “soft cosine measure” is introduced, as opposed to traditional “hard cosine”, which ignores similarity of features. Note that when we consider similarity of each pair of features, it is equivalent to introducing new features in the VSM. Essentially, we have a matrix of similarity between pairs of features and all these features represent new dimensions in the VSM. [...] The next question is how to measure similarity between features. In general, the measuring of similarity depends on the nature of the features. In our case, we compare features using the Levenshtein distance [6], taking advantage of the fact that they are usually strings in case of natural language processing"

I am working on vectors trying to align Language1 and the same language in leet form. My question here is: are there any other distance measures that I can test a part from the here mentioned Levenshtein distance and the cosine distance? and why should I prefer one from another?

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