Representation learning and algorithms in hyperbolic spaces
Abstract/Contents
- Abstract
- Graph embedding methods aim at learning representations of nodes that preserve graph properties (e.g., graph distances). These embeddings can then be used in downstream applications such as clustering, visualization, nearest neighbor search and classification tasks. Most machine learning algorithms learn embeddings in standard Euclidean spaces. Recent research shows promise for more faithful embeddings by leveraging non-Euclidean geometries, such as hyperbolic or spherical geometries. In particular, trees can be embedded almost perfectly into two-dimensional hyperbolic spaces, while this is not possible in Euclidean spaces of any dimension. In this thesis, we develop machine learning models that operate in hyperbolic spaces. We start by introducing hyperbolic representation learning methods for hierarchical graphs, including methods for multi relational graphs or graphs with node features. We demonstrate the benefits of these hyperbolic representations compared to their Euclidean counterparts on a variety of link prediction benchmark datasets. We then design algorithms that operate on these hyperbolic representations. We first propose a method for hierarchical clustering in hyperbolic space, which can be used to solve any similarity-based hierarchical clustering problem with gradient-descent. We then propose a generalization of Principal Component Analysis for hyperbolic inputs, and show that it yields improved low-dimensional representations and data visualizations compared to previous manifold dimensionality reduction methods.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Chami, Ines |
|---|---|
| Degree supervisor | Ré, Christopher |
| Thesis advisor | Ré, Christopher |
| Thesis advisor | Guibas, Leonidas J |
| Thesis advisor | Leskovec, Jurij |
| Degree committee member | Guibas, Leonidas J |
| Degree committee member | Leskovec, Jurij |
| Associated with | Stanford University, Department of Computational and Mathematical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Ines Chami. |
|---|---|
| Note | Submitted to the Department of Computational and Mathematical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/bj040rx3340 |
Access conditions
- Copyright
- © 2021 by Ines Chami
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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