Order Statistics Correlation Coefficient as a Novel Association Measurement With Applications to Biosignal Analysis

• Published in: IEEE transactions on signal processing Vol. 55; no. 12; pp. 5552 - 5563
• Main Authors: Weichao Xu, Chunqi Chang, Hung, Y.S., Kwan, S.K., Chin Wan Fung, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Area measurement; Atrial fibrillation; atrial flutter; Biological and medical sciences; Coefficients; Computerized, statistical medical data processing and models in biomedicine; concomitant; Correlation coefficients; Derivation; Exact sciences and technology; Fibrillation; Information, signal and communications theory; Kendall's tau; Mathematical models; Medical management aid. Diagnosis aid; Medical sciences; Mutual information; nonlinear association measure; Nonlinearity; order statistics; Pearson's coefficient; Performance evaluation; rearrangement inequality; Robustness; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Spearman's rho; Statistical analysis; Statistics; Technological innovation; Telecommunications and information theory; Time measurement; Time series analysis; Transformations; order statistics; Pearson's coefficient; Spearman's rho; Atrial fibrillation; atrial flutter; rearrangement inequality; nonlinear association measure; Kendall's tau; concomitant; Correlation coefficient; Order statistic; Non linear transformation; Correlation method; Statistical method; High sensitivity; Noise immunity; Robustness; Delay time; Diagnostic aid; Signal analysis
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.899374

In this paper, we propose a novel correlation coefficient based on order statistics and rearrangement inequality. The proposed coefficient represents a compromise between the Pearson's linear coefficient and the two rank-based coefficients, namely Spearman's rho and Kendall's tau. Theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients. Experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank-based coefficients when measuring linear associations; whereas it is well able to detect monotone nonlinear associations like the two rank-based coefficients. Extensive statistical analyses also suggest that our new coefficient has superior anti-noise robustness, small biasedness, high sensitivity to changes in association, accurate time-delay detection ability, fast computational speed, and robustness under monotone nonlinear transformations.