Human brain contains a large amount of neurons connecting to each other, therefore, forming a large and complex network. It is fundamentally important to map network connectivity of brain systems for understanding functions and dysfunctions of human brain. Magnetic resonance imaging (MRI) is the most powerful non-invasive neuroimaging tool examining both structures and functions of human brain. Currently, a major bottleneck in human brain mapping is understanding the relationship between brain

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... unctions/behaviour and the human nervous system. To address this problem, researchers start to use features derived from MRI and graph theory to understand patterns of structural and functional brain network connectivity. This PhD project aims at significantly improving the accuracy of brain network connectivity modelling and prediction, thereby enabling better understanding of human brain. Specifically, this PhD project is built upon on the recent success of deep learning, which is used as a major tool for brain network modelling and analysis. Graph is a mathematical representation of brain networks. A central and unsolved challenge of applying deep learning on graphs is how to incorporate dynamics and structures of networks with the learning process. This PhD project will develop a probabilistic graph model to model neural dynamics of human brain (Aim 1). Conventional dynamical modelling approaches are mostly based on sliding windows that are subject to the choice of parameters and window length. To overcome this problem, we propose a regularization-based hidden Markov model (HMM) to estimate dynamical interactions of functional brain network connectivity at a group level. Neuroscience is entering 'big data' era with the advance of neuroimaging techniques and massive data collection. Deep learning has shown great success in big data analytics. However, deep learning has been rarely used for brain network connectivity analysis due to its statistical limitations on irregular-structured network data. To address these problems, we develop a spectral parameterized convolutional neural network (SCNN) to learn brain network connectivity data and predict mental disorders (Aim 2). Inferring functional connections of whole brain poses a great challenge in neuroscience, Most of current network generative models rely on a predefined connection formation to estimate complex patterns of interconnections in the neurological system. Because it is unclear how brain is organized to support high-levels functions, predefined connection formation is unable to provide enough system-specific details about brain mechanisms. Therefore, we propose a graph-based generative adversarial network (GAN) combining with a topological decision tree to infer functional connections of human brain and generate interpretable features (Aim 3). Using a deep learning on graph approach to analyse brain network connectivity will enable an accurate and efficient network modelling and analysis, thereby increasing the throughput of neuroscience study. Publications included in this thesis 1. [93] Xingjuan Li, Yu Li, Xue Li, Predicting Clinical Outcomes of Alzheimer's Disease from Complex Brain Networks, Advanced Data Mining and Applications, 2017 Acknowledgments First and foremost, I thank my principal advisor, Xue Li. Everyone knows that Xue is a brilliant scientist, but fewer know the depth of his dedication to his graduate students. Xue always puts his students first, and I am grateful for all the long conversations in his office, and for the fun and inspiring lab that he creates. Xue brings excitement to all the research that he touches, and he has profoundly influenced me as a researcher and as a person. I also express my thanks to my associated advisor, Yu Li, for his generous support, and his valuable and in-depth guidance for my PhD study and research. In the past days, I learned a lot from him. With his help, I learned how to discover fresh and intriguing research topics, and how to write good papers.