CMB - Projekt

Linear Unmixing

Application to Air Pollution Data

Researchers: Prof. Johannes Staehelin (Institute for Atmospheric and Climate Science), Dr. Werner Stahel, Marcel Wolbers.

Abstract:

Monitoring stations collect data on a number m of chemical compounds automatically in short intervals. We study several sets of one year of hourly data on around 17 volatile organic compounds (VOC). Such data can be used to identify and quantify the contributions of several sources of emission, even if they are unknown.

Suppose that the pollution is generated by a small number p<m of sources, each of which emits constant proportions of the m different chemical compounds. These (unknown) proportions are collected into the ``source profiles''. The observed data vectors (profiles) must then be linear combinations of these source profiles and are therefore contained in a p-dimensional subspace. The idea is described by a Factor Analysis Model with special requirements on the suitable factors (on the ``oblique rotation'' in factor analytic jargon).

In this project, we developed a model as well as graphical and numerical tools for finding the sources and their contributions.

The most important results are:

Linear Unmixing of Multivariate Observations: A Structural Model. By Marcel Wolbers and Werner Stahel. Journal of the American Statistical Society (JASA) 100, 1328-1342 (December 2005)
Remarks on the paper (PDF) (postscript)
Linear Unmixing of Multivariate Observations. By Marcel Wolbers, PhD thesis. The thesis contains additional material, mainly on a functional model.
A Strategy for Analyzing Linear Mixing Data (PDF). By Werner Stahel. Describes R functions and how to use them.
Here are the slides of a talk introducing the ideas (PDF) / (postscript).