Robust Coefficients of Correlation or Spatial Autocorrelation Based on Implicit Weighting

Abstract

Pearson product-moment correlation coefficient represents a fundamental tool for measuring linear association between two data vectors. In various applications, it is often reasonable to consider its weighted version known as the weighted correlation coefficient. This paper starts with theoretical considerations related to properties of the weighted correlation coefficient, particularly to its local robustness and relationship to other similarity measures. Inspired by the least weighted squares regression estimator, a robust correlation coefficient is investigated here together with its spatial autocorrelation extension. Finally, the considered methods are investigated in two image processing tasks.