Currently, I am facing a choice of encoding some information either in a binary vector or a normalized (Gaussian) floating point vector of the same length. For instance it could be in the format $[ 1, 0, 1]$ or $[0.998, 0, 0.002]$ (both these may represent the same data point depending on the encoding I use). If I use the former, I know that I am doomed to use the Jaccard similarity for measuring similarity, and for the latter, I can use efficient and effective methods like a kernel function. However, the binary encoding is less costly at the encoding step than the Gaussian vectors.

My question is whether there's an added advantage (disregarding the obvious setback on computing the floating point numbers) in using the latter over the former, perhaps in terms of accuracy and performance?

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    $\begingroup$ Are you actually asking about what are advantages of applying kernel function over computing Jaccard? It is a bit like apples and oranges to me. Also, why do you think you are doomed to use the Jaccard similarity with binary data? There exist many fine distance measures for them, not only Jaccard. $\endgroup$ – ttnphns Nov 17 '14 at 11:36
  • $\begingroup$ Any answer here is necessarily going to depend on the particular problem, so it's hard to comment on this in such a general setting. Speaking broadly, it's conceivable that the distinctions being thrown by processing to binary away matter, or not; you can only decide based on thinking about the nature of the problem combined with examining the data. $\endgroup$ – Dougal Jun 19 '15 at 8:17

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