Randomized Approaches for Nearest Neighbor Search in Metric Space When Computing the Pairwise Distance Is Extremely Expensive

Finding the closest object for a query in a database is a classical problem in computer science. For some modern biological applications, computing the similarity between two objects might be very time consuming. For example, it takes a long time to compute the edit distance between two whole chromosomes and the alignment cost of two 3D protein structures. In this paper, we study the nearest neighbor search problem in metric space, where the pair-wise distance between two objects in the database is known and we want to minimize the number of distances computed on-line between the query and objects in the database in order to find the closest object. We have designed two randomized approaches for indexing metric space databases, where objects are purely described by their distances with each other. Analysis and experiments show that our approaches only need to compute O(log n) objects in order to find the closest object, where n is the total number of objects in the database.

[1]  Christos Faloutsos,et al.  Similarity search without tears: the OMNI-family of all-purpose access methods , 2001, Proceedings 17th International Conference on Data Engineering.

[2]  D. Lipman,et al.  Improved tools for biological sequence comparison. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Luisa Micó,et al.  A new version of the nearest-neighbour approximating and eliminating search algorithm (AESA) with linear preprocessing time and memory requirements , 1994, Pattern Recognit. Lett..

[4]  Thomas L. Madden,et al.  Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. , 1997, Nucleic acids research.

[5]  Bin Ma,et al.  On the closest string and substring problems , 2002, JACM.

[6]  Juan Ramón Rico-Juan,et al.  Comparison of AESA and LAESA search algorithms using string and tree-edit-distances , 2003, Pattern Recognit. Lett..

[7]  Pavel Zezula,et al.  M-tree: An Efficient Access Method for Similarity Search in Metric Spaces , 1997, VLDB.

[8]  E. Ruiz.  An algorithm for finding nearest neighbours in (approximately) constant average time , 1986 .

[9]  Lusheng Wang,et al.  Efficient Algorithms for 3D Protein Substructure Identification , 2010, 2010 4th International Conference on Bioinformatics and Biomedical Engineering.

[10]  Pavel Zezula,et al.  Similarity Search: The Metric Space Approach (Advances in Database Systems) , 2005 .

[11]  Pavel Zezula,et al.  Similarity Search - The Metric Space Approach , 2005, Advances in Database Systems.

[12]  Gonzalo Navarro.  Searching in metric spaces by spatial approximation , 2002, The VLDB Journal.

[13]  Marvin B. Shapiro.  The choice of reference points in best-match file searching , 1977, CACM.

[14]  Mario A. Nascimento,et al.  Similarity Search and Dimensionality Reduction: Not All Dimensions Are Equally Useful , 2004, DASFAA.