Major Description
Build all-pairs similarity algorithm via DIMSUM.
Given a dataset of sparse vector data, the all-pairs similarity problem is to find all similar vector pairs according to a similarity function such as cosine similarity, and a given similarity score threshold. Sometimes, this problem is called a “similarity join”.
The brute force approach of considering all pairs quickly breaks, since it scales quadratically. For example, for a million vectors, it is not feasible to check all roughly trillion pairs to see if they are above the similarity threshold. Having said that, there exist clever sampling techniques to focus the computational effort on those pairs that are above the similarity threshold, which makes the problem feasible.
DIMSUM has a single parameter (called gamma) to tradeoff computation time vs accuracy. Setting gamma from 1 to the largest magnitude allows tradeoff of computation vs accuracy from low computation to high accuracy. For a very large gamma, all cosine similarities are computed exactly with no sampling.
Current PR:
https://github.com/apache/spark/pull/1778
Justification for adding to MLlib:
- All-pairs similarity is missing from MLlib and has been requested several times, e.g. http://bit.ly/XAFGs8 and separately by Jeremy Freeman (see https://github.com/apache/spark/pull/1778#issuecomment-51300825)
- Algorithm is used in large-scale production at Twitter. e.g. see https://blog.twitter.com/2012/dimension-independent-similarity-computation-disco . Twitter also open-sourced their version in scalding: https://github.com/twitter/scalding/pull/833
- When used with the gamma parameter set high, this algorithm becomes the normalized gramian matrix, which is useful in RowMatrix alongside the computeGramianMatrix method already in RowMatrix
More details about usage at Twitter: https://blog.twitter.com/2014/all-pairs-similarity-via-dimsum
For correctness proof, see Theorem 4.3 in http://stanford.edu/~rezab/papers/dimsum.pdf
