Weighted and robust archetypal analysis
Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. T...
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| Veröffentlicht in: | Computational statistics & data analysis 2011-03, Vol.55 (3), p.1215-1225 |
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| container_title | Computational statistics & data analysis |
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| creator | Eugster, Manuel J.A. Leisch, Friedrich |
| description | Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. The original algorithm is adapted to be a robust M-estimator and an iteratively reweighted least squares fitting algorithm is presented. As a required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using an artificial example, a real world example and a detailed simulation study. |
| doi_str_mv | 10.1016/j.csda.2010.10.017 |
| format | Article |
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| ispartof | Computational statistics & data analysis, 2011-03, Vol.55 (3), p.1215-1225 |
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| language | eng |
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| source | RePEc; Elsevier ScienceDirect Journals Complete |
| subjects | Algorithms Boundaries Breakdown point Convex and discrete geometry Data points Data processing Exact sciences and technology General topics Geometry Hulls Hulls (structures) Iteratively reweighted least squares Least squares method M-estimator Mathematical models Mathematics Multivariate analysis Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Probability and statistics Robust archetypal analysis Robust archetypal analysis M-estimator Breakdown point Iteratively reweighted least squares Sciences and techniques of general use Statistics |
| title | Weighted and robust archetypal analysis |
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