Advanced source separation methods with applications to spatio-temporal datasets

Latent variable models are useful tools for statistical data analysis in many applications. Examples of popular models include factor analysis, state-space models and independent component analysis. These types of models can be used for solving the source separation problem in which the latent variables should have a meaningful interpretation and represent the actual sources generating data. Source separation methods is the main focus of this work. Bayesian statistical theory provides a principled way to learn latent variable models and therefore to solve the source separation problem. The first part of this work studies variational Bayesian methods and their application to different latent variable models. The properties of variational Bayesian methods are investigated both theoretically and experimentally using linear source separation models. A new nonlinear factor analysis model which restricts the generative mapping to the practically important case of post-nonlinear mixtures is presented. The variational Bayesian approach to learning nonlinear state-space models is studied as well. This method is applied to the practical problem of detecting changes in the dynamics of complex nonlinear processes. The main drawback of Bayesian methods is their high computational burden. This complicates their use for exploratory data analysis in which observed data regularities often suggest what kind of models could be tried. Therefore, the second part of this work proposes several faster source separation algorithms implemented in a common algorithmic framework. The proposed approaches separate the sources by analyzing their spectral contents, decoupling their dynamic models or by optimizing their prominent variance structures. These algorithms are applied to spatio-temporal datasets containing global climate measurements from a long period of time.reviewe

Exploratory source separation in biomedical systems

Contemporary science produces vast amounts of data. The analysis of this data is in a central role for all empirical sciences as well as humanities and arts using quantitative methods. One central role of an information scientist is to provide this research with sophisticated, computationally tractable data analysis tools. When the information scientist confronts a new target field of research producing data for her to analyse, she has two options: She may make some specific hypotheses, or guesses, on the contents of the data, and test these using statistical analysis. On the other hand, she may use general purpose statistical models to get a better insight into the data before making detailed hypotheses. Latent variable models present a case of such general models. In particular, such latent variable models are discussed where the measured data is generated by some hidden sources through some mapping. The task of source separation is to recover the sources. Additionally, one may be interested in the details of the generation process itself. We argue that when little is known of the target field, independent component analysis (ICA) serves as a valuable tool to solve a problem called blind source separation (BSS). BSS means solving a source separation problem with no, or at least very little, prior information. In case more is known of the target field, it is natural to incorporate the knowledge in the separation process. Hence, we also introduce methods for this incorporation. Finally, we suggest a general framework of denoising source separation (DSS) that can serve as a basis for algorithms ranging from almost blind approach to highly specialised and problem-tuned source separation algoritms. We show that certain ICA methods can be constructed in the DSS framework. This leads to new, more robust algorithms. It is natural to use the accumulated knowledge from applying BSS in a target field to devise more detailed source separation algorithms. We call this process exploratory source separation (ESS). We show that DSS serves as a practical and flexible framework to perform ESS, too. Biomedical systems, the nervous system, heart, etc., constitute arguably the most complex systems that human beings have ever studied. Furthermore, the contemporary physics and technology have made it possible to study these systems while they operate in near-natural conditions. The usage of these sophisticated instruments has resulted in a massive explosion of available data. In this thesis, we apply the developed source separation algorithms in the analysis of the human brain, using mainly magnetoencephalograms (MEG). The methods are directly usable for electroencephalograms (EEG) and with small adjustments for other imaging modalities, such as (functional) magnetic resonance imaging (fMRI), too.reviewe