Partitioning Mahalanobis D~2 to sharpen GIS classification

摘要

Mahalanobis D~2 is in common use to quantify habitat suitablility in maps prepared by GIS techniques. This paper demonstrates the utility of partitioning D~2 into a sum of orthogonal components. Geometrically each component is identified as the aquared distance, in standard maeasure, from a plane of closetst fit, as originally defined by K. Pearson. Thus, for some small k and nay 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 viariables, are instead defined in terms of combinations of variables which satisfy the equations of these k planes. As a result, species requirements admit to a trade-off among habitat variables so long as overall utility is maintained.