TREPH: A Plug-In Topological Layer for Graph Neural Networks
Topological Data Analysis (TDA) is an approach to analyzing the shape of data using techniques from algebraic topology. The staple of TDA is Persistent Homology (PH). Recent years have seen a trend of combining PH and Graph Neural Networks (GNNs) in an end-to-end manner to capture topological featur...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/2/331 |
| _version_ | 1797621092195500032 |
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| author | Xue Ye Fang Sun Shiming Xiang |
| author_facet | Xue Ye Fang Sun Shiming Xiang |
| author_sort | Xue Ye |
| collection | DOAJ |
| description | Topological Data Analysis (TDA) is an approach to analyzing the shape of data using techniques from algebraic topology. The staple of TDA is Persistent Homology (PH). Recent years have seen a trend of combining PH and Graph Neural Networks (GNNs) in an end-to-end manner to capture topological features from graph data. Though effective, these methods are limited by the shortcomings of PH: incomplete topological information and irregular output format. Extended Persistent Homology (EPH), as a variant of PH, addresses these problems elegantly. In this paper, we propose a plug-in topological layer for GNNs, termed Topological Representation with Extended Persistent Homology (TREPH). Taking advantage of the uniformity of EPH, a novel aggregation mechanism is designed to collate topological features of different dimensions to the local positions determining their living processes. The proposed layer is provably differentiable and more expressive than PH-based representations, which in turn is strictly stronger than message-passing GNNs in expressive power. Experiments on real-world graph classification tasks demonstrate the competitiveness of TREPH compared with the state-of-the-art approaches. |
| first_indexed | 2024-03-11T08:51:48Z |
| format | Article |
| id | doaj.art-6493c89694774327bcbbe39dddcbd39f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T08:51:48Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6493c89694774327bcbbe39dddcbd39f2023-11-16T20:24:01ZengMDPI AGEntropy1099-43002023-02-0125233110.3390/e25020331TREPH: A Plug-In Topological Layer for Graph Neural NetworksXue Ye0Fang Sun1Shiming Xiang2National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, ChinaSchool of Mathematical Sciences, Capital Normal University, Beijing 100048, ChinaNational Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, ChinaTopological Data Analysis (TDA) is an approach to analyzing the shape of data using techniques from algebraic topology. The staple of TDA is Persistent Homology (PH). Recent years have seen a trend of combining PH and Graph Neural Networks (GNNs) in an end-to-end manner to capture topological features from graph data. Though effective, these methods are limited by the shortcomings of PH: incomplete topological information and irregular output format. Extended Persistent Homology (EPH), as a variant of PH, addresses these problems elegantly. In this paper, we propose a plug-in topological layer for GNNs, termed Topological Representation with Extended Persistent Homology (TREPH). Taking advantage of the uniformity of EPH, a novel aggregation mechanism is designed to collate topological features of different dimensions to the local positions determining their living processes. The proposed layer is provably differentiable and more expressive than PH-based representations, which in turn is strictly stronger than message-passing GNNs in expressive power. Experiments on real-world graph classification tasks demonstrate the competitiveness of TREPH compared with the state-of-the-art approaches.https://www.mdpi.com/1099-4300/25/2/331graph neural networkgraph representation learningtopological data analysisextended persistent homology |
| spellingShingle | Xue Ye Fang Sun Shiming Xiang TREPH: A Plug-In Topological Layer for Graph Neural Networks Entropy graph neural network graph representation learning topological data analysis extended persistent homology |
| title | TREPH: A Plug-In Topological Layer for Graph Neural Networks |
| title_full | TREPH: A Plug-In Topological Layer for Graph Neural Networks |
| title_fullStr | TREPH: A Plug-In Topological Layer for Graph Neural Networks |
| title_full_unstemmed | TREPH: A Plug-In Topological Layer for Graph Neural Networks |
| title_short | TREPH: A Plug-In Topological Layer for Graph Neural Networks |
| title_sort | treph a plug in topological layer for graph neural networks |
| topic | graph neural network graph representation learning topological data analysis extended persistent homology |
| url | https://www.mdpi.com/1099-4300/25/2/331 |
| work_keys_str_mv | AT xueye trephaplugintopologicallayerforgraphneuralnetworks AT fangsun trephaplugintopologicallayerforgraphneuralnetworks AT shimingxiang trephaplugintopologicallayerforgraphneuralnetworks |