WIT Press


Partitioning Mahalanobis D^2 To Sharpen GIS Classification

Price

Free (open access)

Paper DOI

10.2495/MIS000181

Volume

24

Pages

10

Published

2000

Size

886 kb

Author(s)

J.E. Dunn & L. Duncan

Abstract

Partitioning Mahalanobis D^ to sharpen GIS classification J.E. Dunn & L. Duncan Department of Mathematical Sciences University of Arkansas, U.S.A. Abstract Mahalanobis D^ is in common use to quantify habitat suitability in maps prepared by GIS techniques. This paper demonstrates the utility of partitioning D^ into a sum of orthogonal components. Geometrically each component is identified as the squared distance, in standard measure, from a plane of closest fit, as originally defined by K. Pearson. Thus, for some small k and any vector measurement, the sum of the k components corresponding to the k smallest, nonzero eigenvalues of the covariance matrix reflects the squared distance of the measurement from the intersection of k hyperplanes in the p-dimensional measurement space. Species requirements, rather than being defined in terms of individual measured variables, are instead defined in terms of combinations of variables which satisfy the equations of these k planes. As

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