Date of Award
12-11-2023
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Computer Science
First Advisor
Shihao Ji
Abstract
In light of the groundbreaking achievements of convolutional neural networks (CNNs) in 2D image processing, there has been a pronounced interest in adapting these methods to non-Euclidean data, such as graphs and 3D geometric data. Point clouds, in particular, present unique challenges as they are sparse, unordered, and locality-sensitive, making the adaptation of CNNs to point cloud processing a non-trivial task. Similar challenges are encountered in the context of graph data. Consequently, the exploration of extending successful neural processing paradigms from 2D images to these non-Euclidean domains has emerged as a vibrant and dynamic research area.
This thesis focuses on advancing graph neural networks (GNNs) and analyzing 3D point clouds, emphasizing sparsification, classification and generation. For graph neural networks, a significant contribution is the introduction of Sparse Graph Attention Networks (SGAT), integrating a sparse attention mechanism into graph attention networks (GATs) through $L_0$-norm regularization. SGAT excels in edge removal (50\%-80\% on large graphs), enhancing interpretability without compromising performance on assortative graphs and improving it on disassortative graphs. In 3D point cloud analysis, an autoregressive approach, APSNet, formulates task-oriented point cloud sampling as a sequential generation process, and develops an attention-based point cloud sampling network that optimally samples 8 points out of 1024, tailoring the process for tasks like 3D point cloud classification, reconstruction, and registration. Extending into a non-autoregressive method, PTSNet, a point transformer, utilizes a transformer-based dynamic query generator. This innovation enables PTSNet to capture long-range correlations, mitigating issues like gradient vanishing and reducing duplicate samples compared to LSTM-based methods. Lastly, the thesis proposes GDPNet, first hybrid Generative and Discriminative PointNet, extending the Joint Energy-based Model (JEM) for point cloud generation and classification. GDPNet retains strong discriminative power of modern PointNet classifiers, while generating point cloud samples rivaling state-of-the-art generative approaches.
DOI
https://doi.org/10.57709/36381722
Recommended Citation
Ye, Yang, "On the Analysis of Non-euclidean data: Sparsification, Classification and Generation." Dissertation, Georgia State University, 2023.
doi: https://doi.org/10.57709/36381722
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