Big Data Analytics and Information Science for Business and Biomedical Applications

The analysis of Big Data in biomedical as well as business and financial research has drawn much attention from researchers worldwide. This book provides a platform for the deep discussion of state-of-the-art statistical methods developed for the analysis of Big Data in these areas. Both applied and theoretical contributions are showcased

Predictive decoding of neural data

In the last five decades the number of techniques available for non-invasive functional imaging has increased dramatically. Researchers today can choose from a variety of imaging modalities that include EEG, MEG, PET, SPECT, MRI, and fMRI. This doctoral dissertation offers a methodology for the reliable analysis of neural data at different levels of investigation. By using statistical learning algorithms the proposed approach allows single-trial analysis of various neural data by decoding them into variables of interest. Unbiased testing of the decoder on new samples of the data provides a generalization assessment of decoding performance reliability. Through consecutive analysis of the constructed decoder\u27s sensitivity it is possible to identify neural signal components relevant to the task of interest. The proposed methodology accounts for covariance and causality structures present in the signal. This feature makes it more powerful than conventional univariate methods which currently dominate the neuroscience field. Chapter 2 describes the generic approach toward the analysis of neural data using statistical learning algorithms. Chapter 3 presents an analysis of results from four neural data modalities: extracellular recordings, EEG, MEG, and fMRI. These examples demonstrate the ability of the approach to reveal neural data components which cannot be uncovered with conventional methods. A further extension of the methodology, Chapter 4 is used to analyze data from multiple neural data modalities: EEG and fMRI. The reliable mapping of data from one modality into the other provides a better understanding of the underlying neural processes. By allowing the spatial-temporal exploration of neural signals under loose modeling assumptions, it removes potential bias in the analysis of neural data due to otherwise possible forward model misspecification. The proposed methodology has been formalized into a free and open source Python framework for statistical learning based data analysis. This framework, PyMVPA, is described in Chapter 5

The smoothness constraint in spatially informed minimum norm approaches for the reconstruction of neuroelectromagnetic sources

Neuronal processes in the brain give rise to electromagnetic signals that can be measured by means of EEG/MEG. However, the ambiguity of the bioelectromagnetic inverse problem limits the localizability of the underlying generators. The solution of the inverse problem requires additional assumptions. A very common method is to model brain activity using distributed sources. In that case, a large number of equivalent current dipoles covers the volume in which activity is expected (usually the cortex). Reconstruction methods on the basis of distributed sources allow the incorporation of additional information on the functional similarity between sources (i.e. information on the spatial structure of brain activity). This kind of information can be derived from prior knowledge, for instance from the subdivision of the cortex into distinct functional areas (i.e. parcellations) or from fMRI. The work presented here is based on a previously published method that combines a general smoothness constraint with priori knowledge on the (binary) similarity between neighboring sources by means of a 2nd order spatial derivative operator (PatchLORETA). The first part of this work addressed the systematic evaluation on how the integration of prior knowledge into the derivative operator affects the estimation of a priori assumed source covariances. It turned out that the method introduced incorrect prior assumptions. Consequently, some extensions were proposed to generalize the approach. These are an additional normalization operator and an additional parameter to encode arbitrary mutual similarity between neighbors. Moreover, a technique was developed to adjust the correlation structure according to a desired smoothness level. The final method (called informed LORETA) is particularly suited for the use of functio-anatomical boundaries. The second part addressed the systematic evaluation of the question whether the use of prior knowledge (derived from parcellations) can improve source localization. This was done using Monte-Carlo simulations. A main focus was the evaluation on how potential errors / uncertainties in the prior knowledge influence the reconstruction performance. Finally, informed LORETA was used for the localization of auditory evoked potentials from experimental data. It turned out that spatially informed methods provide very plausible reconstruction results.EEG/MEG ermöglicht die Messung elektrischer Gehirnaktivität, die durch neuronale Prozesse im Gehirn hervorgerufen wird. Die Lokalisierbarkeit der Aktivität ist aufgrund der fehlenden Eindeutigkeit des bioelektromagnetischen inversen Problems allerdings eingeschränkt. Zur Lösung sind Zusatzannahmen erforderlich. Eine Klasse von Lösungsverfahren basiert auf der Verwendung verteilter Quellenmodelle. Dabei werden im gesamten wahrscheinlichen Quellraum (typischerweise im Cortex) Stromdipole modelliert, um schließlich eine räumliche Verteilung der Dipolstärken zu bestimmen. Dieser Ansatz erlaubt es, Zusatzannahmen über die funktionelle Ähnlichkeit zwischen den Dipolen (d.h. über die räumliche Strukturierung von Gehirnaktivität) zu formulieren. Derartiges Wissen kann zum Beispiel aus der Unterteilung des Cortex in funktional unterschiedliche Areale (Parzellierungen) oder mittels fMRI gewonnen werden. Diese Arbeit befasst sich mit einer bereits zuvor publizierten Technik, bei der Zusatzwissen über die funktionelle Ähnlichkeit benachbarter Quellen in einen Differentialoperator integriert und mit einer allgemeinen Glattheitsannahme kombiniert wird (PatchLORETA). Im ersten Teil dieser Arbeit wurde systematisch untersucht, wie sich eine derartige Integration auf die tatsächliche Korrelationsstruktur auswirkt. Dabei wurden verschiedene Probleme identifiziert, die zu fehlerhaften a priori Annahmen führen. Aus diesem Grund wurde die Methode um einen Normalisierungsoperator, lokale Ähnlichkeitsparameter, und ein Verfahren zur Einstellung einer definierten Glattheitsannahme erweitert. Im Ergebnis liegt ein als informed LORETA bezeichnetes Verfahren vor, in das grundsätzlich beliebige Ähnlichkeitsinformation eingebunden werden kann. Es ist besonders zur Integration funktio-anatomischer Grenzen geeignet. Im zweiten Teil dieser Arbeit wurde die Nutzbarkeit informierter linearer inverser Verfahren mithilfe von Monte-Carlo-Simulationen und unter Verwendung von Parzellierungen systematisch untersucht. Im Fokus stand dabei vor allem der Einfluss möglicher Fehler im Zusatzwissen auf die Rekonstruktionsqualität. Abschließend wurde informed LORETA zur Lokalisierung auditorisch evozierter Aktivität aus EEG/MEG-Daten eingesetzt. Dabei konnte gezeigt werden, dass die Plausibilität der rekonstruierten Quellenverteilung durch die Integration von Zusatzwissen deutlich gesteigert werden kann

Bayesian inversion in biomedical imaging

Biomedizinische Bildgebung ist zu einer Schlüsseltechnik geworden, Struktur oder Funktion lebender Organismen nicht-invasiv zu untersuchen. Relevante Informationen aus den gemessenen Daten zu rekonstruieren erfordert neben mathematischer Modellierung und numerischer Simulation das verlässliche Lösen schlecht gestellter inverser Probleme. Um dies zu erreichen müssen zusätzliche a-priori Informationen über die zu rekonstruierende Größe formuliert und in die algorithmischen Lösungsverfahren einbezogen werden. Bayesianische Invertierung ist eine spezielle mathematische Methodik dies zu tun. Die vorliegende Arbeit entwickelt eine aktuelle Übersicht Bayesianischer Invertierung und demonstriert die vorgestellten Konzepte und Algorithmen in verschiedenen numerischen Studien, darunter anspruchsvolle Anwendungen aus der biomedizinischen Bildgebung mit experimentellen Daten. Ein Schwerpunkt liegt dabei auf der Verwendung von Dünnbesetztheit/Sparsity als a-priori Information.Biomedical imaging techniques became a key technology to assess the structure or function of living organisms in a non-invasive way. Besides innovations in the instrumentation, the development of new and improved methods for processing and analysis of the measured data has become a vital field of research. Building on traditional signal processing, this area nowadays also comprises mathematical modeling, numerical simulation and inverse problems. The latter describes the reconstruction of quantities of interest from measured data and a given generative model. Unfortunately, most inverse problems are ill-posed, which means that a robust and reliable reconstruction is not possible unless additional a-priori information on the quantity of interest is incorporated into the solution method. Bayesian inversion is a mathematical methodology to formulate and employ a-priori information in computational schemes to solve the inverse problem. This thesis develops a recent overview on Bayesian inversion and exemplifies the presented concepts and algorithms in various numerical studies including challenging biomedical imaging applications with experimental data. A particular focus is on using sparsity as a-priori information within the Bayesian framework. <br

Neuroelectromagnetic imaging of correlated sources using a novel subspace penalized sparse learning

Localization of brain signal sources from EEG/MEG has been an active area of research [1]. Currently, there exists a variety of approaches such as MUSIC [2], M-SBL [3], and etc. These algorithms have been applied for various clinical examples and demonstrated excellent performances. However, when the unknown sources are highly correlated, the conventional algorithms often exhibit spurious reconstructions. To address the problem, this paper proposes a new algorithm that generalizes M-SBL by exploiting the fundamental subspace geometry in the multiple measurement problem (MMV). Experimental results using simulation and real phantom data show that the proposed algorithm outperforms the existing methods even under a highly correlated source condition