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

Unto Tapper

    Research output: ThesisDissertationCollection of Articles


    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
    • Paatero, Pentti, Supervisor, External person
    Award date2 May 1995
    Place of PublicationEspoo
    Print ISBNs951-38-4760-8
    Publication statusPublished - 1995
    MoE publication typeG5 Doctoral dissertation (article)


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


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