Deep Learning on Graph-structured Data

John Boaz T. Lee, Worcester Polytechnic Institute

Abstract

In recent years, deep learning has made a significant impact in various fields – helping to push the state-of-the-art forward in many application domains. Convolutional Neural Networks (CNN) have been applied successfully to tasks such as visual object detection, image super-resolution, and video action recognition while Long Short-term Memory (LSTM) and Transformer networks have been used to solve a variety of challenging tasks in natural language processing. However, these popular deep learning architectures (i.e., CNNs, LSTMs, and Transformers) can only handle data that can be represented as grids or sequences. Due to this limitation, many existing deep learning approaches do not generalize to problem domains where the data is represented as graphs – social networks in social network analysis or molecular graphs in chemoinformatics, for instance. The goal of this thesis is to help bridge the gap by studying deep learning solutions that can handle graph data naturally. In particular, we explore deep learning-based approaches in the following areas. 1. Graph Attention. In the real-world, graphs can be both large – with many complex patterns – and noisy which can pose a problem for effective graph mining. An effective way to deal with this issue is to use an attention-based deep learning model. An attention mechanism allows the model to focus on task-relevant parts of the graph which helps the model make better decisions. We introduce a model for graph classification which uses an attention-guided walk to bias exploration towards more task-relevant parts of the graph. For the task of node classification, we study a different model – one with an attention mechanism which allows each node to select the most task-relevant neighborhood to integrate information from. 2. Graph Representation Learning. Graph representation learning seeks to learn a mapping that embeds nodes, and even entire graphs, as points in a low-dimensional continuous space. The function is optimized such that the geometric distance between objects in the embedding space reflect some sort of similarity based on the structure of the original graph(s). We study the problem of learning time-respecting embeddings for nodes in a dynamic network. 3. Brain Network Discovery. One of the fundamental tasks in functional brain analysis is the task of brain network discovery. The brain is a complex structure which is made up of various brain regions, many of which interact with each other. The objective of brain network discovery is two-fold. First, we wish to partition voxels – from a functional Magnetic Resonance Imaging scan – into functionally and spatially cohesive regions (i.e., nodes). Second, we want to identify the relationships (i.e., edges) between the discovered regions. We introduce a deep learning model which learns to construct a group-cohesive partition of voxels from the scans of multiple individuals in the same group. We then introduce a second model which can recover a hierarchical set of brain regions, allowing us to examine the functional organization of the brain at different levels of granularity. Finally, we propose a model for the problem of unified and group-contrasting edge discovery which aims to discover discriminative brain networks that can help us to better distinguish between samples from different classes.