D Distance Sampling

where a and b are twomultivariate observations, Σ− is the inverse of the variance-covariance matrix and (a − b) ′ is the transpose of vector (a − b). e Mahalanobis distance is designed to take into account the correlation between all variables (attributes) of the observations under consideration. For uncorre-lated variables, the Mahalanobis distance reduces to the Euclidean distance for standardized data. As an example, consider a set of points x inR that have the constant distance r from the origin, that is, (, ).en, the set of points having the property dMahalanobis(, x) = r is an ellipse.eMahalanobis distance is a positive denite quadratic form x′Ax, where the matrix A = Σ−. Distance measures or metrics are members of a broader concept called similarity measures (or dissimi