東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ null ]

切換: 標籤 | MARC模式 | ISBD

FindBook

Google Book

Amazon

博客來

Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data./
作者:	Zhao, Qi.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2022,
面頁冊數:	160 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
Contained By:	Dissertations Abstracts International84-01B.
標題:	Computer science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29212654
ISBN:	9798837516245

Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data.
Zhao, Qi.

Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data. - Ann Arbor : ProQuest Dissertations & Theses, 2022 - 160 p.

Source: Dissertations Abstracts International, Volume: 84-01, Section: B.

Thesis (Ph.D.)--University of California, San Diego, 2022.

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

Recently there has been an increasing number of learning problems arising in complex data domains, like graph-structured data, such as social networks and knowledge graphs. Various machine learning approaches have been developed to handle different kinds of data like PointNet for point clouds and graph neural networks for graph-structured data. At the same time, to tame the complexity in data, geometry and topology form natural platforms. In particular, computational geometry and the emerging field of topological data analysis (TDA) have been effective at capturing hidden structure and shape features from data, as well as providing efficient algorithms for them. In this thesis, we aim to integrate geometric ideas and topological concepts with machine learning pipelines to further augment their power and performance. In the first part of the thesis, we show how topological ideas, in particular, the so-called persistent homology, can help with analyzing graph-structured data. Persistent homology provides a flexible and versatile way to summarize complex shapes (including graphs) by a simple multiscale summary. In the first line of work, we designed an effective metric learning approach for persistence-based summaries of graphs, and showed how this improved graph classification tasks. In the second line, we show how topological summaries can be used to further improve graph neural networks' performance.In the second part, we investigate how geometric algorithmic ideas can be combined with neural networks (NNs) to tackle hard optimization problems in geometric setting. In recent years, NNs have shown promise in helping solve combinatorial optimization problems. However, such approaches often tend to be ad hoc. Instead of solving problems in a completely data-driven manner using NNs, we propose to design mixed algorithmic-NN frameworks, where NNs are used as components within an algorithmic framework. In particular, this allows us to leverage elegant algorithmic ideas for problems in geometric setting to develop learning-based frameworks solving optimization problems efficiently in practice, but also with theoretical guarantees. We demonstrate our proposed mixed algorithmic-NN frameworks over two problems: Maximum-independent set (and several other graph problems) for intersection graphs in Euclidean setting, and computing (rectilinear) Minimum Steiner Tree for points in Euclidean setting.

ISBN: 9798837516245Subjects--Topical Terms:

523869
Computer science.
Subjects--Index Terms:

Combinatorial optimization problems

Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data.
LDR:03630nmm a2200349 4500 001 2352264
005 20221118093859.5
008 241004s2022 ||||||||||||||||| ||eng d
020 $a 9798837516245
035 $a (MiAaPQ)AAI29212654
035 $a AAI29212654
040 $a MiAaPQ $c MiAaPQ
100 1 $a Zhao, Qi. $3 3217728
245 1 0 $a Combining Geometric and Topological Ideas with Machine Learning for Analyzing Complex Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2022
300 $a 160 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-01, Section: B.
500 $a Advisor: Wang, Yusu;Chaudhuri, Kamalika.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2022.
506 $a This item must not be sold to any third party vendors.
520 $a Recently there has been an increasing number of learning problems arising in complex data domains, like graph-structured data, such as social networks and knowledge graphs. Various machine learning approaches have been developed to handle different kinds of data like PointNet for point clouds and graph neural networks for graph-structured data. At the same time, to tame the complexity in data, geometry and topology form natural platforms. In particular, computational geometry and the emerging field of topological data analysis (TDA) have been effective at capturing hidden structure and shape features from data, as well as providing efficient algorithms for them. In this thesis, we aim to integrate geometric ideas and topological concepts with machine learning pipelines to further augment their power and performance. In the first part of the thesis, we show how topological ideas, in particular, the so-called persistent homology, can help with analyzing graph-structured data. Persistent homology provides a flexible and versatile way to summarize complex shapes (including graphs) by a simple multiscale summary. In the first line of work, we designed an effective metric learning approach for persistence-based summaries of graphs, and showed how this improved graph classification tasks. In the second line, we show how topological summaries can be used to further improve graph neural networks' performance.In the second part, we investigate how geometric algorithmic ideas can be combined with neural networks (NNs) to tackle hard optimization problems in geometric setting. In recent years, NNs have shown promise in helping solve combinatorial optimization problems. However, such approaches often tend to be ad hoc. Instead of solving problems in a completely data-driven manner using NNs, we propose to design mixed algorithmic-NN frameworks, where NNs are used as components within an algorithmic framework. In particular, this allows us to leverage elegant algorithmic ideas for problems in geometric setting to develop learning-based frameworks solving optimization problems efficiently in practice, but also with theoretical guarantees. We demonstrate our proposed mixed algorithmic-NN frameworks over two problems: Maximum-independent set (and several other graph problems) for intersection graphs in Euclidean setting, and computing (rectilinear) Minimum Steiner Tree for points in Euclidean setting.
590 $a School code: 0033.
650 4 $a Computer science. $3 523869
653 $a Combinatorial optimization problems
653 $a Computational geometry
653 $a Graph neural networks
653 $a Machine learning
653 $a Topological data analysis
690 $a 0984
710 2 $a University of California, San Diego. $b Computer Science and Engineering. $3 1018473
773 0 $t Dissertations Abstracts International $g 84-01B.
790 $a 0033
791 $a Ph.D.
792 $a 2022
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29212654