Solution of linear inversion problems and factor analytic problems with matrix based models: Dissertation

Research output: ThesisDissertationCollection of Articles

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 ill-posed 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 X-ray 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 non-negative 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 languageEnglish
QualificationDoctor Degree
Awarding Institution
  • University of Helsinki
Supervisors/Advisors
  • Paatero, Pentti, Supervisor, External person
Award date2 May 1995
Place of PublicationEspoo
Publisher
Print ISBNs951-38-4760-8
Publication statusPublished - 1995
MoE publication typeG5 Doctoral dissertation (article)

Fingerprint

matrix
estimation method
inversion
method
particle size
wet deposition
deconvolution
factor analysis
low pressure
analytical method
principal component analysis
modeling
analysis

Keywords

  • factor analysis
  • matrix methods
  • Extreme Value Estimation Method
  • inversion
  • Positive Matrix Factorization
  • theses
  • computer applications

Cite this

@phdthesis{31a35110347e4a68b397e578fc01bdb6,
title = "Solution of linear inversion problems and factor analytic problems with matrix based models: Dissertation",
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 ill-posed 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 X-ray 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 non-negative 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.",
keywords = "factor analysis, matrix methods, Extreme Value Estimation Method, inversion, Positive Matrix Factorization, theses, computer applications",
author = "Unto Tapper",
note = "Project code: LVI1009 Project code: KET44221",
year = "1995",
language = "English",
isbn = "951-38-4760-8",
series = "VTT Publications",
publisher = "VTT Technical Research Centre of Finland",
number = "222",
address = "Finland",
school = "University of Helsinki",

}

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: ThesisDissertationCollection 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

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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 ill-posed 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 X-ray 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 non-negative 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 ill-posed 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 X-ray 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 non-negative 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

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KW - computer applications

M3 - Dissertation

SN - 951-38-4760-8

T3 - VTT Publications

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CY - Espoo

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