Pentti Paatero, Sirkka Juntto*

Matrix factorization methods for physical sciences ("Factor Analysis") are applicable to many problems where a number of "spectra" have been measured in similar situations or of similar samples consisting of same (perhaps unknown) costituents in different proportions. Examples: chromatographic "spectra", aerosol size distributions, compositions of environmental samples, Auger spectra measured after various heat treatments of the same sample.

A new method "PMF" or "Positive Matrix Factorization" is developed and studied in the present work. The essential features of PMF are:

The methods has been developed both for two-dimensional and for three-dimensional data arrays. The 3-way model is often called PARAFAC. The present 3-way solution is much more efficent than the customary solutions of the PARAFAC problem and produces error estimates for the results.

In 1996, theoretical and computational aspects of the method have been studied, and journal articles have been written and submitted. Measurements of pollution in the Arctic air have been analyzed in order to determine the sources of pollution. Development of a generalized "Multilinear" program has been started. This program will allow that different mathematical models may be computed by individual users by using the same program, without rewriting the program in any way at all.

A new application of factor analytic models is studied: analysis of almost-periodic time series. Many environmental data sets
have this property. A demonstration analysis has been performed of carbon monoxide data. Daily and weekly patterns are observed; these patterns are related to traffic intensity at different times.

* Finnish Meteorological Institute