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Representation Learning and Algorithms in Hyperbolic Spaces.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Representation Learning and Algorithms in Hyperbolic Spaces./
Author:	Chami, Ines.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	193 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
Subject:	Taxonomy. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28688401
ISBN:	9798544204398

Representation Learning and Algorithms in Hyperbolic Spaces.
Chami, Ines.

Representation Learning and Algorithms in Hyperbolic Spaces. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 193 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--Stanford University, 2021.

This item must not be sold to any third party vendors.

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.

ISBN: 9798544204398Subjects--Topical Terms:

3556303
Taxonomy.

Representation Learning and Algorithms in Hyperbolic Spaces.
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245 1 0 $a Representation Learning and Algorithms in Hyperbolic Spaces.
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300 $a 193 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Re, Christopher.
502 $a Thesis (Ph.D.)--Stanford University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a 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.
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650 4 $a Algorithms. $3 536374
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650 4 $a Graph representations. $3 3560730
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650 4 $a Artificial intelligence. $3 516317
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