Towards high-dimensional data analysis in air quality research

Analysis of chemical constituents from mass spectrometry of aerosols involves non-negative matrix factorization, an approximation of high-dimensional data in lower-dimensional space. The associated optimization problem is non-convex, resulting in crude approximation errors that are not accessible to scientists. To address this shortcoming, we introduce a new methodology for user-guided error-aware data factorization that entails an assessment of the amount of information contributed by each dimension of the approximation, an effective combination of visualization techniques to highlight, filter, and analyze error features, as well as a novel means to interactively refine factorizations. A case study and the domain-expert feedback provided by the collaborating atmospheric scientists illustrate that our method effectively communicates errors of such numerical optimization results and facilitates the computation of high-quality data factorizations in a simple and intuitive manner.