Graph-Based Data Mining in Neuroimaging of Neurological Diseases

Abstract

The human brain is one of the most complex network systems. Understanding the organization of the brain is crucial for the diagnosis and treatment of brain disorders. Recent advances in neuroimaging enable a non-invasive in vivo observation of the structural and functional behaviors of the human brain. However, it is challenging to find meaningful structures from the high-dimensional imaging data and develop robust frameworks for the detection of brain diseases, especially Alzheimer's disease (AD). To tackle these challenges, we investigate brain imaging data from a network perspective in this dissertation.

We first analyze a high-resolution brain network targeting the hippocampal area based on amyloid depositions. We improve the quality of the positron emission tomography (PET) images with a deblurring algorithm and segment the hippocampal area into subregions. We find that the network features clearly indicate the stages of AD.

Then, we propose a spectral graph regression model (GRM) to learn brain network structures. The proposed GRM regards the imaging data as smooth signals on an unknown graph. By solving inverse problems, a more physiologically meaningful brain network is estimated in comparison with the state-of-the-art method. We also study the sample complexity of learning graphical models with block structures.

Next, we develop a matched signal detection (MSD) theory for signals with intrinsic structures described by weighted graphs. To model different real data, we present hypothesis tests by considering low-pass, variation bounded, and random signals on graphs. Real data evaluations demonstrate the effectiveness of the method. Moreover, we introduce an AD detection framework by exploiting deep learning and brain network structures. The classification accuracy of a targeted autoencoder network combing with network information is much higher than that of traditional approaches.

Finally, we present a network diffusion model with sources to localize the origins of AD. By imposing a sparsity constraint on the number of sources, we solve the inverse problem efficiently. In addition, we precisely predict the changes of brain atrophy patterns through this model.