Abstract
This work consists of a summary of the studied two linear
matrix methods, the Extreme Value Estimation Method (EVE)
and the Positive Matrix Factorization method (PMF), and
eight original papers. The summary discusses theoretical
aspects of the methods and gives a motivation to the
demonstrated applications. The papers give problem
dependent details and a more thorough theoretical
treatment of the methods.
The EVE method is a special approach to the analysis of
linear illposed problems. The special features of the
program are indicated by analyzing data with different
information contents and by analyzing measured data from
different instruments. Especially, the EVE method is
applied to the deconvolution of proton induced Xray
spectra and to the inversion of aerosol size
distributions from size segregating devices. Inversion of
aerosol size distributions from diffusion battery and low
pressure impactor measurements is demonstrated.
A new factor analytical method is presented. The Positive
Matrix Factorization (PMF) method produces nonnegative
factors and optimally takes into account error estimates
of the data values. Thus, PMF is more suitable to the
analysis of physical or chemical data than the customary
methods of factor analysis. e.g. Principal Component
Analysis (PCA). The present method is applied to the
analysis of an artificial source receptor modeling data
and to the source identification of bulk wet deposition
in Finland. The PMF method can be modified to take into
account instrument specific effects during the
factorization task. This feature is demonstrated by
analyzing repetitive diffusion battery measurements.
Original language  English 

Qualification  Doctor Degree 
Awarding Institution 

Supervisors/Advisors 

Award date  2 May 1995 
Place of Publication  Espoo 
Publisher  
Print ISBNs  9513847608 
Publication status  Published  1995 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 factor analysis
 matrix methods
 Extreme Value Estimation Method
 inversion
 Positive Matrix Factorization
 theses
 computer applications
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Tapper, U. (1995). Solution of linear inversion problems and factor analytic problems with matrix based models: Dissertation. VTT Technical Research Centre of Finland.