Integrating machine learning approaches into network science: Exemplary applications and novel algorithms.

The goal of this PhD thesis is to exemplify how methods to model complex systems, mainly the language of complex network science, and machine learning approaches can profit from each other. Thereby it deals with several projects arising from concrete questions to different complex systems from multiple fields of science. An introductory chapter explains important clustering algorithms and blind source separation (BSS) techniques. Then it reviews the basic concepts of complex network science, and in particular discusses community detection, i.e. the identification of more densely interconnected subgraphs, the classical interface between the two disciplines. Following the trend beyond the well studied standard graphs in the network field, chapter 2 focuses on network analysis in the presence of self-loops. It develops two measures of node centrality that are applicable to weighted directed graphs and explicitly incorporate the role of such self-loops. Our main application comes from empirical economics and focuses on the networks of commodity flows between business sectors. Applying our centrality measures to such data from a wide set of countries we uncover salient characteristics of the structures of these national economies. Comparison of the countries by a clustering according to their sectors’ centralities then reveals geographical proximity and similar developmental status. Chapter 3 goes beyond network analysis and exemplifies how to bridge the gap between interaction topology and system dynamics. It investigates the connection between the topology of hierarchical networks and the solutions of according dynamical systems, when the dynamics are modeled by two types of differential equations. These are generic models for biological signal transduction and therefore of high relevance for mathematical biology. For given topology the system's dynamics are determined by an interplay of the single parameters. We describe this by algebraic expressions which we call effective parameters and demonstrate how they can be directly inferred from the interaction topology only. Further, we discuss the impact of the effective parameters on parameter estimation. Matrix factorization techniques provide efficient tools for the detailed analysis of large-scale biological and biomedical data. While underlying algorithms usually work fully blindly, chapter 4 proposes the GraDe algorithm, the first matrix factorization algorithm that is based on prior knowledge. Prior knowledge is thereby encoded in a weighted directed graph model. We prove identifiability in our factorization model, where we pose constraints that are based on the novel concept of graph-delayed correlations. In simulations with artificial signals and real-world data, we demonstrate applicability and robustness of the proposed approach. Applying GraDe to gene-expression data from a time-course microarray experiment on IL-6 stimulated hepatocytes results in new biological insights. Chapter 5 develops a novel community detection method that allows detection of overlapping communities in k-partite graphs, networks with nodes of different kinds. It determines for each node a fuzzy degree-of-membership to each community and additionally estimates a weighted backbone graph connecting the communities. The algorithm is fast and efficient, mimicking the multiplicative update rules often employed in non-negative matrix factorization. We demonstrate its applicability in the real-world example of a gene-disease-protein complex graph. Employing functional annotations we show that the detected communities and their connecting backbone are biologically reasonable. The final chapter formulates perspectives for novel developments in the BSS field. The estimation of latent causes in biological systems is an upcoming challenge and crucial for the interpretation of any systems biology experiment. We demonstrate that for special cases of metabolic and gene regulatory networks this task leads to linear BSS problems and show how novel non-linear mixing models arise from more complex situations. By reconstructing latent causes from artificial data we give proof of principles that this strategy is indeed practicable