Fast robust correlation for high-dimensional data

TL;DR

This paper introduces a fast, robust method for estimating covariance in high-dimensional data, addressing outlier sensitivity and computational challenges, with applications to genomic and video data.

Contribution

The authors develop a simple, scalable approach for robust covariance estimation using data transformations, suitable for ultrahigh-dimensional data, and improve outlier detection methods.

Findings

Method performs well in robustness and accuracy

Applicable to data with thousands to hundreds of thousands of variables

Demonstrated on genomic and video datasets

Abstract

The product moment covariance 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 measures of covariance 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 covariance 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, 2018) to detect cellwise outliers, that can deal with much higher dimensions. The approach is illustrated on genomic data with 12,000 variables and color video data with 920,000 dimensions.