Doctor's Theses (authored and supervised):
"Non-Gaussian Feature Extraction for Complex Data";
Supervisor, Reviewer: K. Nordhausen, U. Schmock, P. Ilmonen;
E105 - Institut für Stochastik und Wirtschaftsmathematik,
oral examination: 2021-10-12.
In recent years, the size and complexity of the available data have grown rapidly, making visualization and exploratory data analysis very diﬃcult. Therefore, researchers have proposed many methods to reduce the dimensionality of the data, by ﬁnding suitable data transformations that map the observed (measured) covariates into a smaller set of features, which hopefully then contain all the relevant or discriminatory information while simultaneously eliminating redundancies, and noise. Due to their simplicity, linear data
transformations have been of special interest, and are very often obtained using the projection pursuit, a family of methods searching for, mostly univariate, projections of the data which maximize a predeﬁned objective function, also known as projection index. Given
the assumption that the data are a mixture of low-dimensional, non-Gaussian signal and independent high-dimensional Gaussian noise, the appropriate statistical framework is the non-Gaussian components analysis (NGCA) model. Finding the non-Gaussian components of the data is often considered as an important preprocessing step for eﬃcient data analysis, thus making the aim of the feature extraction within the NGCA model to project the data onto a subspace that contains only the signal. Therefore, the aim of the thesis is to ﬁrst study the feature extraction, as well as the estimation of the dimension of the feature subspace, under the multivariate non-Gaussian component model, with a special focus on homoscedastic Gaussian mixture model with two classes and the projection pursuit, and then to further extend the obtained methods to accommodate for the data which naturally allows a matrix representation such as e.g. grayscale images.
non-Gaussian component analysis; Gaussian mixture models; matrix-variate distributions; dimension reduction
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.