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Proceedings Paper

Simplex shrink-wrap algorithm
Author(s): Daniel R. Fuhrmann
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Paper Abstract

An iterative algorithm for fitting a simplex around a set of data vectors is proposed. The algorithm is a gradient descent on an objective function defined on the vertices. This objective function is the sum of two terms: the first term is the volume of the simplex, which we would like to minimize, and the second term is a penalty term which has the effect of 'pushing' the faces of the simplex away from the data points. The gradient of each of these terms is determined analytically, and used in the gradient descent algorithm. The penalty term includes a multiplicative constant which approaches zero as the gradient descent algorithm progresses, causing the iterates to converge to the vertices of a simplex which fits tightly around the given data points. The performance of this algorithm is demonstrated using simulated data generated from real spectral libraries.

Paper Details

Date Published: 24 August 1999
PDF: 11 pages
Proc. SPIE 3718, Automatic Target Recognition IX, (24 August 1999); doi: 10.1117/12.359990
Show Author Affiliations
Daniel R. Fuhrmann, Washington Univ. (United States)

Published in SPIE Proceedings Vol. 3718:
Automatic Target Recognition IX
Firooz A. Sadjadi, Editor(s)

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