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2015 IEEE International Conference on Data Mining (ICDM) (2015)
Atlantic City, NJ, USA
Nov. 14, 2015 to Nov. 17, 2015
ISSN: 1550-4786
ISBN: 978-1-4673-9503-8
pp: 11-20
Given two sets of vectors, A = {a1→, . . . , am→} and B = {b1→, . . . , bn→}, our problem is to find the top-t dot products, i.e., the largest |ai→ bj→| among all possible pairs. This is a fundamental mathematical problem that appears in numerous data applications involving similarity search, link prediction, and collaborative filtering. We propose a sampling-based approach that avoids direct computation of all mn dot products. We select diamonds (i.e., four-cycles) from the weighted tripartite representation of A and B. The probability of selecting a diamond corresponding to pair (i, j) is proportional to (ai→ bj→)2, amplifying the focus on the largest-magnitude entries. Experimental results indicate that diamond sampling is orders of magnitude faster than direct computation and requires far fewer samples than any competing approach. We also apply diamond sampling to the special case of maximum inner product search, and get significantly better results than the state-of-theart hashing methods.
Diamonds, Indexes, Search problems, Manganese, Sparse matrices, Data mining, Collaboration

G. Ballard, T. G. Kolda, A. Pinar and C. Seshadhri, "Diamond Sampling for Approximate Maximum All-Pairs Dot-Product (MAD) Search," 2015 IEEE International Conference on Data Mining (ICDM), Atlantic City, NJ, USA, 2015, pp. 11-20.
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