AZADKIA-CHATTERJEE'S CORRELATION COEFFICIENT ADAPTS TO MANIFOLD DATA
Annals of Applied Probability, ISSN: 1050-5164, Vol: 34, Issue: 6, Page: 5172-5210
2024
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Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Article Description
In their seminal work, Azadkia and Chatterjee (Ann. Statist. 49 (2021) 3070-3102) initiated graph-based methods for measuring variable dependence strength. By appealing to nearest neighbor graphs based on the Euclidean metric, they gave an elegant solution to a problem of Rényi (Acta Math. Acad. Sci. Hung. 10 (1959) 441-451). This idea was later developed in Deb, Ghosal and Sen (2020) (https://arxiv.org/abs/2010.01768) and the authors there proved that, quite interestingly, Azadkia and Chatterjee's correlation coefficient can automatically adapt to the manifold structure of the data. This paper furthers their study in terms of calculating the statistic's limiting variance under independence-showing that it only depends on the manifold dimension-and extending this distribution-free property to a class of metrics beyond the Euclidean.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85212532279&origin=inward; http://dx.doi.org/10.1214/24-aap2088; https://projecteuclid.org/journals/annals-of-applied-probability/volume-34/issue-6/AzadkiaChatterjees-correlation-coefficient-adapts-to-manifold-data/10.1214/24-AAP2088.full; https://dx.doi.org/10.1214/24-aap2088; https://projecteuclid.org/access-suspended
Institute of Mathematical Statistics
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