Good question Yaakov, I am also would like to know the answer. Thank you for the question.

Thank you Aparna,

I would like to see academic papers that suggest better similarity measures than the well-known basic cosine distance function (with proofs).

There is a wide range of distance measures to choose from. However, one is not necessarily better than the other -- it really depends on the application.

To list a few,

• Jaccard distance
• L2 norm (Euclidean distance)
• L1 norm (Manhattan distance)
• Cosine distance
• Hamming distance

Apart from the usual list dynamic time warping (DTW) has been gaining increasing attention over the last decade, especially in the field of biometrics.

http://www.umass.edu/landeco/teaching/multivariate/readings/McCune.and.Grace.2002.chapter6.pdf

Dear Dr HaCohen-Kerner

I can save you a little trouble. If you go to the following link

https://en.wikipedia.org/wiki/Qualitative_variation

you will find a variety of measures. I am optomistic that at least one of these might be of use to you. 

Dear David,

Thank you for the wonderful link.

What are your research domains?

Best wishes,

Yaakov

Dear Yaakov HaCohen-Kerner,

I came across the following link. I exactly don't know whether it will be helpful or not. But still..

http://dataaspirant.com/2015/04/11/five-most-popular-similarity-measures-implementation-in-python/