Abstract
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) 
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Keywords
 factor analysis
 matrix methods
 Extreme Value Estimation Method
 inversion
 Positive Matrix Factorization
 theses
 computer applications
Cite this
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Solution of linear inversion problems and factor analytic problems with matrix based models : Dissertation. / Tapper, Unto.
Espoo : VTT Technical Research Centre of Finland, 1995. 159 p.Research output: Thesis › Dissertation › Collection of Articles
TY  THES
T1  Solution of linear inversion problems and factor analytic problems with matrix based models
T2  Dissertation
AU  Tapper, Unto
N1  Project code: LVI1009 Project code: KET44221
PY  1995
Y1  1995
N2  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.
AB  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.
KW  factor analysis
KW  matrix methods
KW  Extreme Value Estimation Method
KW  inversion
KW  Positive Matrix Factorization
KW  theses
KW  computer applications
M3  Dissertation
SN  9513847608
T3  VTT Publications
PB  VTT Technical Research Centre of Finland
CY  Espoo
ER 