Principal Component Pursuit for Pattern Identification in Environmental Mixtures
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Environmental health researchers often aim to identify sources/behaviors that give rise to potentially harmful exposures. We adapted principal component pursuit (PCP)-a robust 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 exposure patterns across pollutants and a sparse matrix isolating unique exposure events. We adapted PCP to accommodate non-negative and 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 compared PCP-LOD to principal component analysis (PCA) to evaluate performance. We next applied PCP-LOD to a mixture of 21 persistent organic pollutants (POPs) measured in 1,000 U.S. adults from the 2001-2002 National Health and Nutrition Examination Survey. We applied singular value decomposition to the estimated low-rank matrix to characterize the patterns. 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 achieved lower relative predictive error than PCA for all simulated datasets with up to 50 outperformed PCA only when noise was low. In the POP mixture, PCP-LOD identified a rank-three underlying structure and separated 6 unique events. One pattern represented comprehensive exposure to all POPs. The other patterns grouped chemicals based on known structure and toxicity. PCP-LOD serves as a useful tool to express multi-dimensional exposures as consistent patterns that, if found to be related to adverse health, are amenable to targeted interventions.
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