Geometric decision rules for instance-based learning problems

Binay Bhattacharya, Kaustav Mukherjee, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In the typical nonparametric approach to classification in instance-based learning and data mining, random data (the training set of patterns) are collected and used to design a decision rule (classifier). One of the most well known such rules is the k-nearest neighbor decision rule (also known as lazy learning) in which an unknown pattern is classified into the majority class among the k-nearest neighbors in the training set. This rule gives low error rates when the training set is large. However, in practice it is desired to store as little of the training data as possible, without sacrificing the performance. It is well known that thinning (condensing) the training set with the Gabriel proximity graph is a viable partial solution to the problem. However, this brings up the problem of efficiently computing the Gabriel graph of large training data sets in high dimensional spaces. In this paper we report on a new approach to the instance-based learning problem. The new approach combines five tools: first, editing the data using Wilson-Gabriel-editing to smooth the decision boundary, second, applying Gabriel-thinning to the edited set, third, filtering this output with the ICF algorithm of Brighton and Mellish, fourth, using the Gabriel-neighbor decision rule to classify new incoming queries, and fifth, using a new data structure that allows the efficient computation of approximate Gabriel graphs in high dimensional spaces. Extensive experiments suggest that our approach is the best on the market.

Original languageEnglish (US)
Title of host publicationPattern Recognition and Machine Intelligence - First International Conference, PReMI 2005, Proceedings
Number of pages10
StatePublished - 2005
Event1st International Conference on Pattern Recognition and Machine Intelligence, PReMI 2005 - Kolkata, India
Duration: Dec 20 2005Dec 22 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3776 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other1st International Conference on Pattern Recognition and Machine Intelligence, PReMI 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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