## Institut für Informatik und Computational Science

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Advances in biotechnologies rapidly increase the number of molecules of a cell which can be observed simultaneously. This includes expression levels of thousands or ten-thousands of genes as well as concentration levels of metabolites or proteins. Such Profile data, observed at different times or at different experimental conditions (e.g., heat or dry stress), show how the biological experiment is reflected on the molecular level. This information is helpful to understand the molecular behaviour and to identify molecules or combination of molecules that characterise specific biological condition (e.g., disease). This work shows the potentials of component extraction algorithms to identify the major factors which influenced the observed data. This can be the expected experimental factors such as the time or temperature as well as unexpected factors such as technical artefacts or even unknown biological behaviour. Extracting components means to reduce the very high-dimensional data to a small set of new variables termed components. Each component is a combination of all original variables. The classical approach for that purpose is the principal component analysis (PCA). It is shown that, in contrast to PCA which maximises the variance only, modern approaches such as independent component analysis (ICA) are more suitable for analysing molecular data. The condition of independence between components of ICA fits more naturally our assumption of individual (independent) factors which influence the data. This higher potential of ICA is demonstrated by a crossing experiment of the model plant Arabidopsis thaliana (Thale Cress). The experimental factors could be well identified and, in addition, ICA could even detect a technical artefact. However, in continuously observations such as in time experiments, the data show, in general, a nonlinear distribution. To analyse such nonlinear data, a nonlinear extension of PCA is used. This nonlinear PCA (NLPCA) is based on a neural network algorithm. The algorithm is adapted to be applicable to incomplete molecular data sets. Thus, it provides also the ability to estimate the missing data. The potential of nonlinear PCA to identify nonlinear factors is demonstrated by a cold stress experiment of Arabidopsis thaliana. The results of component analysis can be used to build a molecular network model. Since it includes functional dependencies it is termed functional network. Applied to the cold stress data, it is shown that functional networks are appropriate to visualise biological processes and thereby reveals molecular dynamics.

The goal of a Brain-Computer Interface (BCI) consists of the development of a unidirectional interface between a human and a computer to allow control of a device only via brain signals. While the BCI systems of almost all other groups require the user to be trained over several weeks or even months, the group of Prof. Dr. Klaus-Robert Müller in Berlin and Potsdam, which I belong to, was one of the first research groups in this field which used machine learning techniques on a large scale. The adaptivity of the processing system to the individual brain patterns of the subject confers huge advantages for the user. Thus BCI research is considered a hot topic in machine learning and computer science. It requires interdisciplinary cooperation between disparate fields such as neuroscience, since only by combining machine learning and signal processing techniques based on neurophysiological knowledge will the largest progress be made. In this work I particularly deal with my part of this project, which lies mainly in the area of computer science. I have considered the following three main points: <b>Establishing a performance measure based on information theory:</b> I have critically illuminated the assumptions of Shannon's information transfer rate for application in a BCI context. By establishing suitable coding strategies I was able to show that this theoretical measure approximates quite well to what is practically achieveable. <b>Transfer and development of suitable signal processing and machine learning techniques:</b> One substantial component of my work was to develop several machine learning and signal processing algorithms to improve the efficiency of a BCI. Based on the neurophysiological knowledge that several independent EEG features can be observed for some mental states, I have developed a method for combining different and maybe independent features which improved performance. In some cases the performance of the combination algorithm outperforms the best single performance by more than 50 %. Furthermore, I have theoretically and practically addressed via the development of suitable algorithms the question of the optimal number of classes which should be used for a BCI. It transpired that with BCI performances reported so far, three or four different mental states are optimal. For another extension I have combined ideas from signal processing with those of machine learning since a high gain can be achieved if the temporal filtering, i.e., the choice of frequency bands, is automatically adapted to each subject individually. <b>Implementation of the Berlin brain computer interface and realization of suitable experiments:</b> Finally a further substantial component of my work was to realize an online BCI system which includes the developed methods, but is also flexible enough to allow the simple realization of new algorithms and ideas. So far, bitrates of up to 40 bits per minute have been achieved with this system by absolutely untrained users which, compared to results of other groups, is highly successful.