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Open AccessArticle

Association Factor for Identifying Linear and Nonlinear Correlations in Noisy Conditions

1
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
2
Deparments of Mathematics, College of Science and Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia
*
Author to whom correspondence should be addressed.
Current address: 150 W. University Blvd., Melbourne, FL 32901, USA.
Entropy 2020, 22(4), 440; https://doi.org/10.3390/e22040440
Received: 26 January 2020 / Revised: 4 April 2020 / Accepted: 6 April 2020 / Published: 13 April 2020
Background: In data analysis and machine learning, we often need to identify and quantify the correlation between variables. Although Pearson’s correlation coefficient has been widely used, its value is reliable only for linear relationships and Distance correlation was introduced to address this shortcoming. Methods: Distance correlation can identify linear and nonlinear correlations. However, its performance drops in noisy conditions. In this paper, we introduce the Association Factor (AF) as a robust method for identification and quantification of linear and nonlinear associations in noisy conditions. Results: To test the performance of the proposed Association Factor, we modeled several simulations of linear and nonlinear relationships in different noise conditions and computed Pearson’s correlation, Distance correlation, and the proposed Association Factor. Conclusion: Our results show that the proposed method is robust in two ways. First, it can identify both linear and nonlinear associations. Second, the proposed Association Factor is reliable in both noiseless and noisy conditions. View Full-Text
Keywords: association factor; Pearson’s correlation; distance correlation; maximal information coefficient (MIC); detrended fluctuation analysis (DFA); nonlinear relation; noisy relationship association factor; Pearson’s correlation; distance correlation; maximal information coefficient (MIC); detrended fluctuation analysis (DFA); nonlinear relation; noisy relationship
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MDPI and ACS Style

Kachouie, N.N.; Deebani, W. Association Factor for Identifying Linear and Nonlinear Correlations in Noisy Conditions. Entropy 2020, 22, 440.

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