Combinatorial Framework for Similarity Search

—We present an overview of the combinatorial framework for similarity search. An algorithm is combinatorial if only direct comparisons between two pairwise similarity values are allowed. Namely, the input dataset is represented by a comparison oracle that given any three points x, y, z answers whether y or z is closer to x. We assume that the similarity order of the dataset satisfies the four variations of the following disorder inequality: if x is the a’th most similar object to y and y is the b’th most similar object to z, then x is among the D(a + b) most similar objects to z, where D is a relatively small disorder constant. Combinatorial algorithms for nearest neighbor search have two important advantages: (1) they do not map similarity values to artificial distance values and do not use triangle inequality for the latter, and (2) they work for arbitrarily complicated data representations and similarity functions. Ranwalk, the first known combinatorial solution for nearest...

• Type: Conference
• Year: 2009
• Where: SISAP
• Authors: Yury Lifshits
• Keywords: Combinatorial, Combinatorial Nets, Data Mining, Nearest Neighbor, SISAP 2009