Probabilistic Rank Correlation - A New Rank and Comparison Based Correlation Coefficient with a Simple, Pragmatic Transitivity Condition

Probabilistic Rank Correlation - A New Rank and Comparison Based Correlation Coefficient with a Simple, Pragmatic Transitivity Condition

Ruiting Lian Changle Zhou Ben Goertzel 

Fujian Provincial Key Laboratory of Brain-like Intelligent Systems, Department of Cognitive Science, Xiamen University, Xiamen, China

Hanson Robotics Open Cog Foundation709C, 7/F Bio-Informatics Centre 2 Science Park West Avenue Shatin, Hong Kong, China

Page: 
476-496
|
DOI: 
https://doi.org/10.18280/ama_a.540403
Received: 
10 August 2017
|
Accepted: 
30 October 2017
|
Published: 
31 December 2017
| Citation

OPEN ACCESS

Abstract: 

A novel measure of correlation between data sets is proposed based on applying the notion of “probabilistic support” to compare the pairwise comparisons of measurements. Probabilistic Rank Correlation (PRC) is a crisp instantiation of this idea, in the spirit of traditional rank correlations. It is shown that, under broad conditions, Probabilistic Rank Correlations has a strong, elegant transitivity property. The practical application of the PRC is also illustrated.

Keywords: 

Correlation, Transitivity, Probabilistic support, Probabilistic Rank Correlation, Correlation measure

1. Introductions
2. Transitivity of Correlation
3. Probabilistic Rank Correlation
4. Algebraic Properties of Symmetric and Asymmetric Probabilistic Support
5. Comparison with Kendall Correlation
6. A Simple Sufficient Condition for Transitivity of the Probabilistic Rank Correlation
7. A Less Stringent Transitivity Condition
8. Handling Equally Ranked Values
9. Practical Examples
10. Conclusion
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