Partitioning Mahalanobis D^2 To Sharpen GIS
Classification
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
Keywords
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