An Adaptive Weighted L_p Metric with Application to Optical Remote Sensing Classification Problems

摘要

In this contribution, a novel metric learning framework by jointly optimizing the feature space structural coherence manifested by the Cosine similarity measure and the error contribution induced by the Minkowski metric is presented with a loss function involving Mahalanobis distance measure governing the outlier robustness for maximal inter-sample and minimal intra-sample separation of the feature space vectors. The outlier's robustness and scale variation sensitivity of the proposed measure by exploiting the prior statistical entropy of the correlated feature components in weighing the different feature dimensions according to their degree of cohesion within the data clusters and the conceptual architecture for the optimality criterion in terms of the optimal Minkowski exponent, 'p_(optimal)' through semi-definite convex optimization with its lower and upper bounds of the proposed distance function have been discussed. Classification results involving special cases of the proposed distance measure on publicly available datasets validates the adequacy of the proposed methodology in remote sensing problems.