IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2402.00543.html
   My bibliography  Save this paper

The extension of Pearson correlation coefficient, measuring noise, and selecting features

Author

Listed:
  • Reza Salimi
  • Kamran Pakizeh

Abstract

Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations. Specifically, a multivariable version of the correlation coefficient can greatly contribute to better assessment of the risk in a multi-asset investment portfolio. Needless to say, the correlation coefficient is derived from another concept: covariance. Even though covariance can be extended naturally by its mathematical formula, such an extension is to no use. Making matters worse, the correlation coefficient can never be extended based on its mathematical definition. In this article, we briefly explore random matrix theory to extend the notion of Pearson's correlation coefficient to an arbitrary number of variables. Then, we show that how useful this measure is at gauging noise, thereby selecting features particularly in classification.

Suggested Citation

  • Reza Salimi & Kamran Pakizeh, 2024. "The extension of Pearson correlation coefficient, measuring noise, and selecting features," Papers 2402.00543, arXiv.org.
    • Handle: RePEc:arx:papers:2402.00543
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2402.00543
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
    2. P. Robert & Y. Escoufier, 1976. "A Unifying Tool for Linear Multivariate Statistical Methods: The RV‐Coefficient," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 257-265, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cling, Jean-Pierre & Delecourt, Clément, 2022. "Interlinkages between the Sustainable Development Goals," World Development Perspectives, Elsevier, vol. 25(C).
    2. Delimiro Visbal-Cadavid & Mónica Martínez-Gómez & Rolando Escorcia-Caballero, 2020. "Exploring University Performance through Multiple Factor Analysis: A Case Study," Sustainability, MDPI, vol. 12(3), pages 1-24, January.
    3. Florence Jacquet & A Aboul-Naga & Bernard Hubert, 2020. "The contribution of ARIMNet to address livestock systems resilience in the Mediterranean region," Post-Print hal-03625860, HAL.
    4. Rauf Ahmad, M., 2019. "A significance test of the RV coefficient in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 116-130.
    5. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2013. "Measuring Association and Dependence Between Random Vectors," LIDAM Discussion Papers ISBA 2013026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Roberta De Vito & Ruggero Bellio & Lorenzo Trippa & Giovanni Parmigiani, 2019. "Multi‐study factor analysis," Biometrics, The International Biometric Society, vol. 75(1), pages 337-346, March.
    7. Carmen C. Rodríguez-Martínez & Mitzi Cubilla-Montilla & Purificación Vicente-Galindo & Purificación Galindo-Villardón, 2023. "X-STATIS: A Multivariate Approach to Characterize the Evolution of E-Participation, from a Global Perspective," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    8. Dorota Toczydlowska & Gareth W. Peters, 2018. "Financial Big Data Solutions for State Space Panel Regression in Interest Rate Dynamics," Econometrics, MDPI, vol. 6(3), pages 1-45, July.
    9. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    10. Haouès-Jouve Sinda & Lemonsu Aude & Gauvrau Benoit & Amossé Alexandre & Can Arnaud & Carrissimo Bertrand & Gaudio Noémie & Hidalgo Julia & Lopez-Rieu Claudia & Chouillou Delphine & Richard Isabelle, 2022. "Cross-analysis for the assessment of urban environmental quality: An interdisciplinary and participative approach," Environment and Planning B, , vol. 49(3), pages 1024-1047, March.
    11. Górecki Tomasz & Krzyśko Mirosław & Ratajczak Waldemar & Wołyński Waldemar, 2016. "An Extension of the Classical Distance Correlation Coefficient for Multivariate Functional Data with Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 449-466, September.
    12. Jean-Pierre Rossi & Maxime Nardin & Martin Godefroid & Manuela Ruiz-Diaz & Anne-Sophie Sergent & Alejandro Martinez-Meier & Luc Pâques & Philippe Rozenberg, 2014. "Dissecting the Space-Time Structure of Tree-Ring Datasets Using the Partial Triadic Analysis," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-13, September.
    13. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Papageorgiou, Ioulia & Moustaki, Irini, 2019. "Sampling of pairs in pairwise likelihood estimation for latent variable models with categorical observed variables," LSE Research Online Documents on Economics 87592, London School of Economics and Political Science, LSE Library.
    15. Sneha Vishwanath & Alexandre G de Brevern & Narayanaswamy Srinivasan, 2018. "Same but not alike: Structure, flexibility and energetics of domains in multi-domain proteins are influenced by the presence of other domains," PLOS Computational Biology, Public Library of Science, vol. 14(2), pages 1-26, February.
    16. A. Iodice D’Enza & A. Markos & F. Palumbo, 2022. "Chunk-wise regularised PCA-based imputation of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 365-386, June.
    17. Mansooreh Kazemilari & Maman Abdurachman Djauhari & Zuhaimy Ismail, 2016. "Foreign Exchange Market Performance: Evidence from Bivariate Time Series Approach," Papers 1608.07694, arXiv.org.
    18. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    19. Bavaud, François, 2023. "Exact first moments of the RV coefficient by invariant orthogonal integration," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    20. Svetlana V Shinkareva & Robert A Mason & Vicente L Malave & Wei Wang & Tom M Mitchell & Marcel Adam Just, 2008. "Using fMRI Brain Activation to Identify Cognitive States Associated with Perception of Tools and Dwellings," PLOS ONE, Public Library of Science, vol. 3(1), pages 1-9, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2402.00543. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.