Positive Matrix Factorization of Large Aerosol Mass Spectrometry Datasets Using Error-Weighted Randomized Hierarchical Alternating Least Squares
Benjamin Sapper1,Daven Henze1,Manjula Canagaratna2,and Harald Stark3,4Benjamin Sapper et al.Benjamin Sapper1,Daven Henze1,Manjula Canagaratna2,and Harald Stark3,4
1University of Colorado Boulder, 11 Engineering Dr, Boulder, CO 80309, United States
2Aerodyne Research, 45 Manning Road, Billerica, MA 01821, United States
3Center for Aerosol and Cloud Chemistry, Aerodyne Research Inc., 45 Manning Road, Billerica, MA 01821
4Department of Chemistry and Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, Colorado 80309, United States
1University of Colorado Boulder, 11 Engineering Dr, Boulder, CO 80309, United States
2Aerodyne Research, 45 Manning Road, Billerica, MA 01821, United States
3Center for Aerosol and Cloud Chemistry, Aerodyne Research Inc., 45 Manning Road, Billerica, MA 01821
4Department of Chemistry and Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, Colorado 80309, United States
Received: 05 Nov 2022 – Discussion started: 20 Dec 2022
Abstract. Weighted positive matrix factorization (PMF) has been used by scientists to find small sets of underlying factors in environmental data. However, as the size of the data has grown, increasing computational costs have made it impractical to use traditional methods for this factorization. In this paper, we present a new weighting method to dramatically decrease computational costs for these traditional algorithms. We then apply this weighting method with the Randomized Hierarchical Alternating Least Squares (RHALS) algorithm to a large environmental dataset, where we show that interpretable factors can be reproduced using these methods. We show this algorithm results in a computational speedup of 38, 67, and 634 compared to the Multiplicative Update (MU), deterministic Hierarchical Alternating Least Squares (HALS), and non-negative Alternating Least Squares (ALS) algorithms, respectively. We also investigate rotational ambiguity in the solution, and present a simple “pulling” method to rotate a set of factors. This method is shown to find alternative solutions, and in some cases, lower the weighted residual error of the algorithm.
Positive Matrix Factorization (PMF) has been used by atmospheric scientists to extract underlying factors present in large datasets. This paper presents a new technique for weighted PMF that drastically reduces the computational costs of previously developed algorithms. We use this technique to deliver interpretative factors and solution diagnostics from an atmospheric chemistry dataset.
Positive Matrix Factorization (PMF) has been used by atmospheric scientists to extract...