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Robust coefficients of correlation or spatial autocorrelation based on implicit weighting

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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.

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Acknowledgements

The author would like to thank Patrik Janáček for technical help and the reviewers for constructive advice. Figure 2 is reprinted from Biocybernetics and Biomedical Engineering, vol. 40, J. Kalina and C. Matonoha, “A sparse pair-preserving centroid-based supervised learning method for high-dimensional biomedical data or images”, pp. 774–786, 2020, with permission from Elsevier.

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  1. The Czech Academy of Sciences, Institute of Computer Science, Pod Vodárenskou věží 2, 182 07, Prague 8, Czech Republic

    Jan Kalina

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Correspondence to Jan Kalina.

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The research was supported by the project GA22-02067S (“Approximate Neurocomputing”) of the Czech Science Foundation.

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Kalina, J. Robust coefficients of correlation or spatial autocorrelation based on implicit weighting. J. Korean Stat. Soc. 51, 1247–1267 (2022). https://doi.org/10.1007/s42952-022-00184-2

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