How many kinds of Distance Function can we use?

I was reading stuffs about pattern recognition. Recently I want to make a survey of methods to evaluate similarities of vectors. As far as I know, there are Euclidean distances, Mahalanobis distances and Cosine Distance. Can anyone present some mor开发者_开发技巧e names or keywords to search?

Also mutual neighbor distance (MND), Minkowski metric, Hausdorff distance, conceptual similarity, normalized Google distance, KL divergence, Spearman’s rank correlation, and Lin similarity. (Not all of these are vector based.)

I highly recommend Pattern Classification by Duda, Hart, and Stork for further reading. It is extensively cited.

Pearson, Manhatten, Gower, Jaccard, Tanimoto, Russel Rao, Dice, Kulczynski, Simple Matching, Levenshtein

You can define your own distance metrics too, so I would say there can be A LOT of possible distance metrics. Now if those metrics are good or have any meaning is another story.

Hamming distance