Non-Gaussian feature extraction for complex data

Abstract

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.