Abstract

As the amount of data being generated keeps growing, there is an increasing demand for adaptable approaches that can effectively extract the overall trends while also maintaining subject-specific information from large-scale datasets. Modeling complex and high-dimensional data presents significant challenges across healthcare, human action recognition, and speech recognition.
In this dissertation, we develop a bounded multivariate generalized Gaussian mixture model (BMGGMM) integrated with independent component analysis (ICA) to effectively capture the correlated features in multivariate data. While independent vector analysis (IVA) extends ICA to handle multiple datasets by leveraging inter-dataset dependencies and preserving their correlation structures, it suffers from limitations when dealing with complex datasets. To overcome this, we propose a novel blind source separation (BSS) method that combines IVA with the BMGGMM framework, enabling robust modeling of complex data distributions with varying shapes and dimensions. Second, we introduced the integration of the ICA-BMGGMM and IVA-BMGGMM to the hidden Markov model (HMM) to boost their performance in terms of source separation. The performance of IVA deteriorates as the number of datasets and sources increases. To address this limitation, we propose the adaptive constrained IVA (acIVAMGGMM) and bounded acIVAMGGMM techniques. These methods integrate multiple reference signals into the IVA function and adaptively control the reference-estimated source relations. Finally, we introduce a new approach, ICA and IVA for common subspace analysis (ICABMGGMM-CS) and IVABMGGMM-CS, designed for the subspace analysis of multi-subject fMRI data. These methods leverage the strengths of both ICA and IVA while effectively addressing the challenges posed by high dimensions.