Department of Statistics and Actuarial Science

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Browsing Department of Statistics and Actuarial Science by browse.metadata.advisor "Bakker, Hans-Peter"

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    Validation of independent components using a hypothesis testing approach
    (Stellenbosch : Stellenbosch University, 2020-12) De Koker, Corine; Hofmeyr, David; Bakker, Hans-Peter
    ENGLISH ABSTRACT: The main focus of this thesis is the validation of Independent Component Analysis (ICA), a popular technique used in signal processing. In a typical application, the purpose of ICA is to extract non-Gaussian signals representing the source signals from observed signals that are mixtures of the source signals in the case where the source signals are unavailable or unknown. This thesis only considers the FastICA implementation of ICA in the case where the number of source signals are equal to the number of mixture signals, and where any additive noise can be neglected. The FastICA algorithm extracts non-Gaussian signals through the maxmisation of negentropy. The more non-Gaussian the source signals, the more closely the signals extracted using FastICA represent the source signals. Amongst other things, this thesis demonstrates a novel approach using hypothesis testing with negentropy as a test statistic to determine the degree of non-Gaussianity of the source signals. The results from the hypothesis test mentioned previously were compared to the results from a second hypothesis test which uses a measure suggested by Himberg et al. (2004) that measures the compactness of the clusters of estimates of ICA components. The clustering visualisation methods proposed by Himberg et al. (2004) were also executed in this thesis and provided visual support for the results from the hypothesis tests. Both hypothesis tests were performed on three different datasets. The first dataset contained mixtures of only non-Gaussian signals. The second dataset contained mixtures of three non-Gaussian and three Gaussian signals, while the third dataset contained mixtures of only Gaussian signals. Both hypothesis tests rejected the null hypothesis that each of the source signals contained in the dataset are Gaussian when applied to the first dataset, which is in line with our expectations. The results from both hypothesis tests indicated the presence of three Gaussian and three non-Gaussian source signals in the second dataset. Regarding the third dataset, both hypothesis tests rejected about 5% of the signals extracted by the FastICA algorithm, which was as expected since a significance level of 5% was used. Therefore, our results provide evidence that hypothesis testing could potentially be used as an alternative method to indicate the degree of non-Gaussianity of mixtures of source signals. Key words: ICA; Hypothesis testing; non-Gaussianity