Publication
Title
Fast robust correlation for high-dimensional data
Author
Abstract
The product moment covariance matrix is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately, the product moment covariance and the corresponding Pearson correlation are very susceptible to outliers (anomalies) in the data. Several robust estimators of covariance matrices have been developed, but few are suitable for the ultrahigh-dimensional data that are becoming more prevalent nowadays. For that one needs methods whose computation scales well with the dimension, are guaranteed to yield a positive semidefinite matrix, and are sufficiently robust to outliers as well as sufficiently accurate in the statistical sense of low variability. We construct such methods using data transformations. The resulting approach is simple, fast, and widely applicable. We study its robustness by deriving influence functions and breakdown values, and computing the mean squared error on contaminated data. Using these results we select a method that performs well overall. This also allows us to construct a faster version of the DetectDeviatingCells method (Rousseeuw and Van den Bossche Citation2018) to detect cellwise outliers, which can deal with much higher dimensions. The approach is illustrated on genomic data with 12,600 variables and color video data with 920,000 dimensions. Supplementary materials for this article are available online.
Language
English
Source (journal)
Technometrics : a journal of statistics for the physical, chemical, and engineering sciences. - Washington, D.C., 1959, currens
Publication
Washington, D.C. : 2021
ISSN
0040-1706 [print]
1537-2723 [online]
DOI
10.1080/00401706.2019.1677270
Volume/pages
63 :2 (2021) , p. 184-198
Pubmed ID
000493638500001
Full text (Publisher's DOI)
Full text (open access)
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Creation 27.02.2024
Last edited 28.02.2024
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