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Unformatted text preview: 1 LocalitySensitive Hashing Basic Technique HammingLSH Applications 2 Finding Similar Pairs ◆ Suppose we have in main memory data representing a large number of objects. ◗ May be the objects themselves (e.g., summaries of faces). ◗ May be signatures as in minhashing. ◆ We want to compare each to each, finding those pairs that are sufficiently similar. 3 Candidate Generation From Minhash Signatures ◆ Pick a similarity threshold s , a fraction < 1. ◆ A pair of columns c and d is a candidate pair if their signatures agree in at least fraction s of the rows. ◗ I.e., M ( i, c ) = M ( i, d ) for at least fraction s values of i . 4 Candidate Generation  (2) ◆ For images, a pair of vectors is a candidate if they differ by at most a small threshold t in at least s % of the components. ◆ For entity records, a pair is a candidate if the sum of similarity scores of corresponding components exceeds a threshold. 5 The Problem with Checking for Candidates ◆ While the signatures of all columns may fit in main memory, comparing the signatures of all pairs of columns is quadratic in the number of columns. ◆ Example : 10 6 columns implies 5*10 11 comparisons. ◆ At 1 microsecond/comparison: 6 days. 6 Solutions 1. DivideComputeMerge (DCM) uses external sorting, merging. 2. LocalitySensitive Hashing (LSH) can be carried out in main memory, but admits some false negatives. 3. Hamming LSH  a variant LSH method. 7 DivideComputeMerge ◆ Designed for “shingles” and docs. ◆ At each stage, divide data into batches that fit in main memory. ◆ Operate on individual batches and write out partial results to disk. ◆ Merge partial results from disk. 8 doc1: s11,s12,…,s1k doc2: s21,s22,…,s2k … DCM Steps s11,doc1 s12,doc1 … s1k,doc1 s21,doc2 … Invert t1,doc11 t1,doc12 … t2,doc21 t2,doc22 … sort on shingleId doc11,doc12,1 doc11,doc13,1 … doc21,doc22,1 … Invert and pair doc11,doc12,1 doc11,doc12,1 … doc11,doc13,1 … sort on <docId1, docId2> doc11,doc12,2 doc11,doc13,10 … Merge 9...
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 Fall '09

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