2000-01-01
https://scigraph.springernature.com/explorer/license/
335-346
An Algorithm for Positive-Breakdown Regression Based on Concentration Steps
chapters
2000
https://link.springer.com/10.1007%2F978-3-642-58250-9_27
false
2019-04-16T09:46
chapter
Positive-breakdown regression is able to extract previously unknown patterns or substructures from the data. Here we will focus on least trimmed squares (LTS) regression, which is based on the subset of h cases (out of n) whose least squares fit possesses the smallest sum of squared residuals. The coverage h may be set between n/2 and n. The computation time of existing LTS algorithms grows too much with the size of the data set. In this paper we develop a new algorithm called FAST-LTS. The basic idea is the ‘concentration step’, which is based on a new inequality involving order statistics and sums of squared residuals. Further reductions of the computation time are obtained by techniques which we call ‘selective iteration’ and ‘nested extensions’. We also use an intercept adjustment technique to improve the precision. For small data sets FAST-LTS typically finds the exact LTS, whereas for larger data sets it gives more accurate results than existing algorithms for LTS and is faster by orders of magnitude. This allows us to apply FAST-LTS to large datasets.
en
Data Analysis
978-3-642-58250-9
978-3-540-67731-4
Springer Nature - SN SciGraph project
Otto
Opitz
10.1007/978-3-642-58250-9_27
doi
dimensions_id
pub.1043348595
Wolfgang
Gaul
Artificial Intelligence and Image Processing
Van Driessen
Katrien
Martin
Schader
Peter J.
Rousseeuw
Department of Mathematics and Computer Science, University of Antwerp (UIA), B-2610, Wilrijk, Belgium
University of Antwerp
Faculty of Applied Economics, University of Antwerp (UFSIA), B-2000, Antwerp, Belgium
Information and Computing Sciences
readcube_id
ce7c88b22ef519d8ff4addd69b5ce7fe9a370423ed1a4c6c463364304b498a0e
Berlin, Heidelberg
Springer Berlin Heidelberg