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Association Factor for Identifying Linear and Nonlinear Correlations in Noisy Conditions
Nezamoddin N Kachouie1, Wejdan Deebani2
1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
The new Association Factor (AF) reliably identifies linear and nonlinear correlations, even in noisy data. This robust method outperforms Pearson's and Distance correlation in challenging conditions.
Area of Science:
- Data analysis and machine learning
- Statistical modeling
Background:
- Pearson's correlation coefficient is limited to linear relationships.
- Distance correlation identifies linear and nonlinear correlations but struggles with noisy data.
Purpose of the Study:
- Introduce the Association Factor (AF) for robust correlation analysis.
- Quantify linear and nonlinear associations in both clean and noisy datasets.
Main Methods:
- Simulated datasets with linear and nonlinear relationships under varying noise levels.
- Computed Pearson's correlation, Distance correlation, and the Association Factor.
Main Results:
- The Association Factor demonstrated robustness in identifying both linear and nonlinear associations.
- Performance of the Association Factor remained reliable across noiseless and noisy conditions.
Conclusions:
- The Association Factor is a robust and versatile tool for correlation analysis.
- AF offers improved reliability over existing methods in the presence of noise.
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