A Probabilistic Spell for the Curse of Dimensionality

Range searches in metric spaces can be very di cult if the space is \high dimensional", i.e. when the histogram of distances has a large mean and a small variance. The so-called \curse of dimensionality" (well known in vector spaces) is also observed in metric spaces, and the term refers to the odd situation where using an index for proximity searching may be worse (in total elapsed time) than an exhaustive search. There are at least two reasons behind the curse of dimensionality: a large search radius and/or a high intrinsic dimension of the metric space. We present a general probabilistic framework that allows us to reduce the e ective search radius of the search and which gets more e ective as the dimension grows. The technique is based on probabilistically stretching the triangle inequality. We apply the technique to a particular class of indexing algorithms, even though it could be generalized to any indexing algorithm using the triangle inequality. We present an approx...

• Type: Conference
• Year: 2001
• Where: ALENEX
• Authors: Edgar Chávez, Gonzalo Navarro
• Keywords: ALENEX 2001, ALENEX 2007, Metric Space, Search Radius, Triangle Inequality