Heuristic Search Algorithms for the Minimum Volume Ellipsoid

David L. Wood, David M Rocke

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

A method of robust estimation of multivariate location and shape that has attracted a lot of attention recently is Rousseeuw’s minimum volume ellipsoid estimator (MVE). This estimator has a high breakdown point but is difficult to compute successfully. In this article, we apply methods of heuristic search to this problem, including simulated annealing, genetic algorithms, and tabu search, and compare the results to the undirected random search algorithm that is often cited. Heuristic search provides several effective algorithms that are far more computationally efficient than random search. Furthermore, random search, as currently implemented, is shown to be ineffective for larger problems.

Original languageEnglish (US)
Pages (from-to)69-95
Number of pages27
JournalJournal of Computational and Graphical Statistics
Volume2
Issue number1
DOIs
StatePublished - 1993

Fingerprint

Minimum Volume Ellipsoid
Random Search
Heuristic Search
Heuristic algorithm
Search Algorithm
Estimator
Breakdown Point
Robust Estimation
Tabu Search
Simulated Annealing
Genetic Algorithm
Heuristic search

Keywords

  • Breakdown point
  • Genetic algorithms
  • Multivariate location and shape
  • Robust estimation
  • Simulated annealing
  • Tabu search

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Heuristic Search Algorithms for the Minimum Volume Ellipsoid. / Wood, David L.; Rocke, David M.

In: Journal of Computational and Graphical Statistics, Vol. 2, No. 1, 1993, p. 69-95.

Research output: Contribution to journalArticle

@article{94b2476105dc4fc8a47d10a652ff58a3,
title = "Heuristic Search Algorithms for the Minimum Volume Ellipsoid",
abstract = "A method of robust estimation of multivariate location and shape that has attracted a lot of attention recently is Rousseeuw’s minimum volume ellipsoid estimator (MVE). This estimator has a high breakdown point but is difficult to compute successfully. In this article, we apply methods of heuristic search to this problem, including simulated annealing, genetic algorithms, and tabu search, and compare the results to the undirected random search algorithm that is often cited. Heuristic search provides several effective algorithms that are far more computationally efficient than random search. Furthermore, random search, as currently implemented, is shown to be ineffective for larger problems.",
keywords = "Breakdown point, Genetic algorithms, Multivariate location and shape, Robust estimation, Simulated annealing, Tabu search",
author = "Wood, {David L.} and Rocke, {David M}",
year = "1993",
doi = "10.1080/10618600.1993.10474600",
language = "English (US)",
volume = "2",
pages = "69--95",
journal = "Journal of Computational and Graphical Statistics",
issn = "1061-8600",
publisher = "American Statistical Association",
number = "1",

}

TY - JOUR

T1 - Heuristic Search Algorithms for the Minimum Volume Ellipsoid

AU - Wood, David L.

AU - Rocke, David M

PY - 1993

Y1 - 1993

N2 - A method of robust estimation of multivariate location and shape that has attracted a lot of attention recently is Rousseeuw’s minimum volume ellipsoid estimator (MVE). This estimator has a high breakdown point but is difficult to compute successfully. In this article, we apply methods of heuristic search to this problem, including simulated annealing, genetic algorithms, and tabu search, and compare the results to the undirected random search algorithm that is often cited. Heuristic search provides several effective algorithms that are far more computationally efficient than random search. Furthermore, random search, as currently implemented, is shown to be ineffective for larger problems.

AB - A method of robust estimation of multivariate location and shape that has attracted a lot of attention recently is Rousseeuw’s minimum volume ellipsoid estimator (MVE). This estimator has a high breakdown point but is difficult to compute successfully. In this article, we apply methods of heuristic search to this problem, including simulated annealing, genetic algorithms, and tabu search, and compare the results to the undirected random search algorithm that is often cited. Heuristic search provides several effective algorithms that are far more computationally efficient than random search. Furthermore, random search, as currently implemented, is shown to be ineffective for larger problems.

KW - Breakdown point

KW - Genetic algorithms

KW - Multivariate location and shape

KW - Robust estimation

KW - Simulated annealing

KW - Tabu search

UR - http://www.scopus.com/inward/record.url?scp=0002102675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002102675&partnerID=8YFLogxK

U2 - 10.1080/10618600.1993.10474600

DO - 10.1080/10618600.1993.10474600

M3 - Article

AN - SCOPUS:0002102675

VL - 2

SP - 69

EP - 95

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 1

ER -