Abstract
Pearson product-moment correlation coefficient represents a fundamental measure of similarity between two data vectors. In various applications, it is meaningful to consider its weighted version known as the weighted Pearson correlation coefficient. Its properties are studied in this theoretical paper; these include the robustness to rounding, as it is an important issue in approximate neurocomputing, or specific robustness properties for the context of template matching in image analysis. For a highly robust correlation coefficient inspired by the least weighted estimator, properties are derived and novel hypothesis tests are proposed. This robust measure is recommendable particularly for data contaminated by outliers (not only) in the context of image analysis.
The research was supported by the grant 22-02067S “Approximate Neurocomputing” of the Czech Science Foundation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alsahafi, Y.S., Kassem, M.A., Hosny, K.M.: Skin-Net: a novel deep residual network for skin lesions classification using multilevel feature extraction and cross-channel correlation with detection of outlier. J. Big Data 10, 105 (2023)
Azar, J., Makhoul, A., Barhamgi, M., Couturier, R.: An energy efficient IoT data compression approach for edge machine learning. Futur. Gener. Comput. Syst. 96, 168–175 (2019)
Bilan, S., Yuzhakov, S.: Pattern Recognition Based on Parallel Shift Technology. CRC Press, Boca Raton (2018)
Böhringer, S., de Jong, M.A.: Quantification of facial traits. Front. Genet. 10, 397 (2019)
Borenstein, M., Hedges, L.V., Higgins, J.P.T., Rothstein, H.R.: Introduction to Meta-analysis, 2nd edn. Wiley, Chichester (2021)
Botvinik-Nezer, R., Holzmeister, F., Camerer, C.F., Dreber, A., Huber, J., et al.: Variability in the analysis of a single neuroimaging dataset by many teams. Nature 582, 84–88 (2020)
Čížek, P.: Semiparametrically weighted robust estimation of regression models. Comput. Stat. Data Anal. 55, 774–788 (2011)
Delaigle, A., Hall, P.: Achieving near perfect classification for functional data. J. Roy. Stat. Soc. 74, 267–286 (2012)
Ferrari, C., Berretti, S., Bimbo, A.D.: Discovering identity specific activation patterns in deep descriptors for template based face recognition. 14th IEEE International Conference on Automatic Face & Gesture Recognition (FG 2019), pp. 1–5 (2019)
Gamel, S.A., Hassan, E., El-Rashidy, N., Talaat, F.M.: Exploring the effects of pandemics on transportation through correlations and deep learning techniques. Multimed. Tools Appl. (2023)
Gao, B., Spratling, M.W.: Robust template matching via hierarchical convolutional features from a shape biased CNN. In: Yao, J., Xiao, Y., You, P., Sun, G. (eds.) The International Conference on Image, Vision and Intelligent Systems (ICIVIS 2021). LNEE, vol. 813, pp. 333–344. Springer, Singapore (2022). https://doi.org/10.1007/978-981-16-6963-7_31
Guyll, M., Madon, S., Yang, Y., Wells, G.: Validity of forensic cartridge-case comparisons. Psychol. Cogn. Sci. 120, e2210428120 (2023)
Jurečková, J., Picek, J., Schindler, M.: Robust Statistical Methods with R, 2nd edn. CRC Press, Boca Raton (2019)
Kalina, J.: Robust coefficients of correlation or spatial autocorrelation based on implicit weighting. J. Korean Stat. Soc. 51, 1247–1267 (2022)
Kalina, J., Matonoha, C.: A sparse pair-preserving centroid-based supervised learning method for high-dimensional biomedical data or images. Biocybern. Biomed. Eng. 40, 774–786 (2020)
Kalina, J., Tichavský, J.: On robust estimation of error variance in (highly) robust regression. Meas. Sci. Rev. 20, 6–14 (2020)
Naeem, A., Anees, T., Ahmed, K.T., Naqvi, R.A., Ahmad, S., Whangbo, T.: Deep learned vectors formation using auto-correlation, scaling, and derivations with CNN for complex and huge image retrieval. Complex Intell. Syst. 9, 1729–1751 (2023)
Rao, C.R.: Linear Statistical Inference and Its Applications. Wiley, New York (2002)
Rather, A.A., Chachoo, M.A.: Robust correlation estimation and UMAP assisted topological analysis of omics data for disease subtyping. Comput. Biol. Med. 155, 106640 (2023)
Saleh, A.K.M.E., Picek, J., Kalina, J.: R-estimation of the parameters of a multiple regression model with measurement errors. Metrika 75, 311–328 (2012)
Sun, L., Sun, H., Wang, J., Wu, S., Zhao, Y., Xu, Y.: Breast mass detection in mammography based on image template matching and CNN. Sensors 2021, 2855 (2021)
Sze, V., Chen, Y.H., Yang, T.J., Emer, J.S.: Efficient Processing of Deep Neural Networks. Morgan & Claypool Publishers, San Rafael (2020)
Víšek, J.Á.: Consistency of the least weighted squares under heteroscedasticity. Kybernetika 47, 179–206 (2011)
Yang, H., Zheng, K., Li, J.: Open set recognition of underwater acoustic targets based on GRU-CAE collaborative deep learning network. Appl. Acoust. 193, 108774 (2022)
Acknowledgements
The authors are grateful to Jakub Krett for numerical experiments motivating this work and to Jiří Šíma and Václav Šmídl for discussion about Sect. 2.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Kalina, J., Vidnerová, P. (2023). Properties of the Weighted and Robust Implicitly Weighted Correlation Coefficients. In: Iliadis, L., Papaleonidas, A., Angelov, P., Jayne, C. (eds) Artificial Neural Networks and Machine Learning – ICANN 2023. ICANN 2023. Lecture Notes in Computer Science, vol 14262. Springer, Cham. https://doi.org/10.1007/978-3-031-44201-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-031-44201-8_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-44200-1
Online ISBN: 978-3-031-44201-8
eBook Packages: Computer ScienceComputer Science (R0)