![]() In this way they attempt to describe more sophisticated and nonlinear relations among feature vectors. Given a set of x k observation vectors ( k = 1., I) of dimension J, the q-PMD between vectors x i and x j is calculated by first mapping each x k into all polynomial terms of order q or less, which are included in vector z k, and then calculating the MD between z i and z j using the covariance matrix obtained from the reference population of polynomial term mappings. Those authors formulated the q-order PMD ( q-PMD) as follows. ![]() They use the PMD for classifying path regions in images of natural outdoor environments. Grudic and Mulligan (2006) have shown that the MD may not tightly follow a learning data set, and substituted it by the Polynomial Mahalanobis distance (PMD), which is obtained by mapping the measurement space into high order polynomial terms. It weights the distance calculation according to the statistical variation of each component using the covariance matrix of the observed sample. The Mahalanobis distance is a common metric that attempts to capture the non-isotropic properties of a J-dimensional feature space. Mabel Sánchez, in Computer Aided Chemical Engineering, 2012 2 Methodology
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