Principal Component Pursuit for Pattern Identification in Environmental Mixtures

Background: Environmental health researchers often aim to identify sources or behaviors that give rise to potentially harmful environmental exposures. Objective: We adapted principal component pursuit (PCP)—a robust and well-established technique for dimensionality reduction in computer vision and signal processing—to identify patterns in environmental mixtures. PCP decomposes the exposure mixture into a low-rank matrix containing consistent patterns of exposure across pollutants and a sparse matrix isolating unique or extreme exposure events. Methods: We adapted PCP to accommodate nonnegative data, missing data, and values below a given limit of detection (LOD). We simulated data to represent environmental mixtures of two sizes with increasing proportions <LOD and three noise structures. We applied PCP-LOD to evaluate its performance in comparison with principal component analysis (PCA). We next applied principal component pursuit with limit of detection (PCP-LOD) to an exposure mixture of 21 persistent organic pollutants (POPs) measured in 1,000 U.S. adults from the 2001–2002 National Health and Nutrition Examination Survey (NHANES). We applied singular value decomposition to the estimated low-rank matrix to characterize the patterns. Results: PCP-LOD recovered the true number of patterns through cross-validation for all simulations; based on an a priori specified criterion, PCA recovered the true number of patterns in 32% of simulations. PCP-LOD achieved lower relative predictive error than PCA for all simulated data sets with up to 50% of the data <LOD. When 75% of values were <LOD, PCP-LOD outperformed PCA only when noise was low. In the POP mixture, PCP-LOD identified a rank-three underlying structure and separated 6% of values as extreme events. One pattern represented comprehensive exposure to all POPs. The other patterns grouped chemicals based on known structure and toxicity. Discussion: PCP-LOD serves as a useful tool to express multidimensional exposures as consistent patterns that, if found to be related to adverse health, are amenable to targeted public health messaging. https://doi.org/10.1289/EHP10479