Sparsity introduction in Bayesian Autocorrelation Matrix factorization for organic aerosol source apportionment

The Positive Matrix Factorisation (PMF) algorithm (Paatero and Tapper, 1994) has been the most widely used receptor model for a long time and has only recently been challenged with new methodologies. The novel Bayesian auto-correlated matrix factorisation method (BAMF, Rusanen et al. 2024) integrates an auto-correlation term emulating real-world pollutant sources time evolution has produced higher accuracy compared to PMF. However, both PMF and BAMF struggle to provide well-separated profiles manifested as mixed time series contributions.

 A sparsity-handling algorithm named horseshoe (HS) regularisation has beenapplied to BAMF in order to improve profile determination. The horseshoe application pushes some parameters to be close to zero and others to have large values (Piironen and Vehtari, 2017). The BAMF+HS method reduces the dimensionality of the problem by suppressing the non-significant species for each profile. The resulting profiles are expected to be less noisy and better representing the nature of the atmospheric pollution sources. Figure 1 shows the effect of BAMF+HS (in orange) compared to the regular BAMF (in blue) and the PMF (in green) on a toy dataset, consisting on an oversimplified dataset with very sparse profiles. The BAMF+HS results show contributions pushed to zero, making the profiles closer to the truth (in black) with respect to the less sparse results of BAMF and PMF. This same comparison has been carried out on realistic synthetic datasets to show the effectiveness of sparsity introduction into source apportionment.

Figure 1. Comparison to truth of source apportionment profiles resulting from three different receptor models for a toy dataset.

Acknowledgement: This work is supported by the European Union's Horizon Europe research and innovation programme under the Marie Skłodowska-Curie Postdoctoral Fellowship Programme, SMASH co-funded under the grant agreement No. 101081355. The SMASH project is co-funded by the Republic of Slovenia and the European Union from the European Regional Development Fund. K.R.D. acknowledges support by SNSF Ambizione grant PZPGP2_201992.

References

Piironen, J., & Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors.

Rusanen, A., Björklund, A., Manousakas, M., Jiang, J., Kulmala, M. T., Puolamäki, K., & Daellenbach, K. R. (2023). Atmospheric Measurement Techniques Discussions, 2023, 1-28.

Paatero, P., & Tapper, U. (1994). Environmetrics, 5(2), 111-126.