Exploratory Analysis of Highly Dimensional Data: Parametric Methods for Dimensionality Reduction, Visualization and Feature Extraction with Applications in Computational Biology

Abstract

Recent advances in experimental technologies have facilitated the gathering of data with thousands of variables. Because of this, modern data analysis tasks often encounter high dimensional data, which are challenging to analyse. Such analysis is made more difficult with the lack of ground-truth. In this thesis, I have explored two aspects of high-dimensional exploratory data analysis: 1) Dimensionality Reduction and Visualization of high-dimensional data to gain insights into the structure of the data and, 2) Extraction and interpretation of feature subsets (motifs) which explain the structure of high-dimensional data. I have presented methods that are built on concepts of Neural Networks - a powerful modern branch of optimization techniques. Through my work, I have shown that using relatively infrequently used variants of neural networks and building on their concepts (e.g. vector quantization and Hebbian Learning) we can produce powerful dimensionality reduction methods that address major gap areas of research. I have further shown that using unsupervised deep neural networks with contextual regularization, we can produce a framework to extract minimal motifs that optimally reconstruct complex nonlinear structures present in high dimensional data.