Abstract

Abstract The metric space model abstracts many proximity search problems, from nearest-neighborclassifiers to textual and multimedia information retrieval. In this context, an index is a data structure that speeds up proximity queries. However, indexes lose their efficiency as the intrinsicdata dimensionality increases. In this paper we present a simple index called list of clusters (LC), which is based on a compact partitioning of the data set. The LC is shown to require little space,to be suitable both for main and secondary memory implementations, and most importantly, to be very resistant to the intrinsic dimensionality of the data set. In this aspect our structure isunbeaten. We finish with a discussion of the role of unbalancing in metric space searching, and how it permits trading memory space for construction time. 1 Introduction The problem of proximity searching has received much attention in recent times, due to an increasing interest in manipulating and retrieving the more and more common multimedia data. Multimedia data have to be classified, forecasted, filtered, organized, and so on. Their manipulation poses new challenges to classifiers and function approximators. The well-known k-nearest neighbor (knn) classifier is a favorite candidate for this task for being simple enough and well understood. One of the main obstacles, however, of using this classifier for massive data classification is its linear complexity to find a set of k neighbors for a given query.

Citations

508	Multidimensional access methods - Gaede, Günther - 1998
472	Voronoi diagrams: A survey of a fundamental geometric data structure - Aurenhammer - 1991
447	M-tree: an efficient access method for similarity search in metric spaces - Ciaccia, Patella, et al. - 1997
284	Searching in metric spaces - Chávez, Navarro, et al. - 2001
225	Data structures and algorithms for nearest neighbor search in general metric spaces - Yianilos - 1993
203	Searching in high-dimensional spaces: index structures for improving the performance of multimedia databases - Bohm, Berchtold, et al. - 2001
159	Near neighbor search in large metric spaces - Brin - 1995
142	Satisfying general proximity/similarity queries with metric trees - Uhlmann - 1991
118	Index-driven similarity search in metric spaces - Hjaltason, Samet - 2003
117	Some approaches to best-match file searching - Burkhard, Keller - 1973
111	A simple algorithm for nearest neighbor search in high dimensions - Nene, Nayar - 1997
110	Distance-based indexing for high-dimensional metric spaces - Bozkaya, Özgsoyoglu - 1997
62	Searching in metric spaces by spatial approximation - Navarro
58	Proximity matching using fixed-queries trees - Baeza-Yates, Cunto, et al.
55	An algorithm for finding nearest neighbors in (approximately) constant average time - Vidal - 1986
42	A new version of the nearestneighbor approximating and eliminating search algorithm (AESA) with linear preprocessing time and memory requirements - Mico, Oncina, et al. - 1994
40	A data structure and an algorithm for the nearest point problem - Kalantari, McDonald - 1983
26	Fixed queries array: A fast and economical data structure for proximity searching - Chávez, Marroquín, et al.
24	neighbor search in large metric spaces - Near - 1995
24	D-index: Distance searching index for metric data sets - Dohnal, Gennaro, et al.
22	Incremental Similarity Search in Multimedia Databases - Hjaltason, Samet - 2000
18	Spaghettis: an array based algorithm for similarity queries in metric spaces - Chávez, Marroquín, et al. - 1999
18	An effective clustering algorithm to index high dimensional metric spaces - Chávez, Navarro
17	Voronoi trees and clustering problems - Dehne, Noltemeier - 1987
15	Handbook of Algorithms and Data Structures. Addison-Wesley, 2nd edition - Gonnet, Baeza-Yates - 1991
14	A fast branch and bound nearest neighbor classifier in metric spaces - Mic'o, Oncina, et al. - 1996
10	Proximity queries in metric spaces - Ch'avez, Marroqu'in - 1997
10	Monotonous Bisector Trees -- a tool for efficient partitioning of complex schenes of geometric objects - Nolteimer, Verbarg, et al. - 1992