Optimally Weighted PCA for High-Dimensional Heteroscedastic Data

Understand

Modern data are increasingly both high-dimensional and heteroscedastic.

• This paper considers the challenge of estimating underlying principal components from high-dimensional data with noise that is heteroscedastic across samples, i.e., some samples are noisier than others.
• Such heteroscedasticity naturally arises, e.g., when combining data from diverse sources or sensors.
• A natural way to account for this heteroscedasticity is to give noisier blocks of samples less weight in PCA by using the leading eigenvectors of a weighted sample covariance matrix.