Github user jkbradley commented on the issue: https://github.com/apache/spark/pull/15800 Limiting this discussion to MinHash: Say we construct a hash table of L x K functions (for doing both OR and AND amplification). For approxNearestNeighbors, we need to ask, "What is the best scalar value we can compute from these L*K values to approximate the distance between keys?" * I think this is one point of confusion in previous discussion: I am talking only about nearest neighbors, which sorts on a scalar estimate of distance. Things are different when you want to build a data structure with physical hash buckets. Assume that our LxK functions are chosen independently at random (which is what we are doing now). Then I claim that, to compare distances between 2 points (1 query + 1 in the dataset), there is no better way to combine these functions than to: * Compute LxK binary 0/1 indicators of whether the 2 points match on each hash function * Average these LxK 0/1 indicators Rough argument: * For a given scalar hash function (without amplification), there is no concept of "distance" between hash buckets. (This is different from P-Stable LSH.) * The distance metric we want to sort by is Jaccard similarity. * The average of these indicators is an efficient estimator (in the statistical sense) of the Jaccard similarity.
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