Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem

Details Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem

2008-10-22

arxiv.org/abs/0810.4182v1

Computer Science

Information Theory

Manuscript submitted to IEEE Transactions on Information Theory on March 3, 2007; revised August 27, 2007

Scientific paper

Consider the problem of finding high dimensional approximate nearest neighbors, where the data is generated by some known probabilistic model. We will investigate a large natural class of algorithms which we call bucketing codes. We will define bucketing information, prove that it bounds the performance of all bucketing codes, and that the bucketing information bound can be asymptotically attained by randomly constructed bucketing codes. For example suppose we have n Bernoulli(1/2) very long (length d-->infinity) sequences of bits. Let n-2m sequences be completely independent, while the remaining 2m sequences are composed of m independent pairs. The interdependence within each pair is that their bits agree with probability 1/20. Moreover if one sequence out of each pair belongs to a a known set of n^{(2p-1)^{2}-\epsilon} sequences, than pairing can be done using order n comparisons!

Affiliated with

Also associated with

No associations

Rating

Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bucketing Coding and Information Theory for the Statistical High Dimensional Nearest Neighbor Problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-680002