Topological Properties
topological properties
Learning the structure and investigating the geometry of complex networks
Networks are widely used as mathematical models of complex systems across many scientific disciplines, and in particular within neuroscience. In this talk, we introduce two aspects of our collaborative research: (1) machine learning and networks, and (2) graph dimensionality. Machine learning and networks. Decades of work have produced a vast corpus of research characterising the topological, combinatorial, statistical and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network. We have developed hcga, a framework for highly comparative analysis of graph data sets that computes several thousands of graph features from any given network. Taking inspiration from hctsa, hcga offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterisation of graph data sets. We show that hcga outperforms other methodologies (including deep learning) on supervised classification tasks on benchmark data sets whilst retaining the interpretability of network features, which we exemplify on a dataset of neuronal morphologies images. Graph dimensionality. Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. Deviating from approaches based on fractals, here, we present a new framework to define intrinsic notions of dimension on networks, the relative, local and global dimension. We showcase our method on various physical systems.
Generative models of the human connectome
The human brain is a complex network of neuronal connections. The precise arrangement of these connections, otherwise known as the topology of the network, is crucial to its functioning. Recent efforts to understand how the complex topology of the brain has emerged have used generative mathematical models, which grow synthetic networks according to specific wiring rules. Evidence suggests that a wiring rule which emulates a trade-off between connection costs and functional benefits can produce networks that capture essential topological properties of brain networks. In this webinar, Professor Alex Fornito and Dr Stuart Oldham will discuss these previous findings, as well as their own efforts in creating more physiologically constrained generative models. Professor Alex Fornito is Head of the Brain Mapping and Modelling Research Program at the Turner Institute for Brain and Mental Health. His research focuses on developing new imaging techniques for mapping human brain connectivity and applying these methods to shed light on brain function in health and disease. Dr Stuart Oldham is a Research Fellow at the Turner Institute for Brain and Mental Health and a Research Officer at the Murdoch Children’s Research Institute. He is interested in characterising the organisation of human brain networks, with particular focus on how this organisation develops, using neuroimaging and computational tools.