InvMap and Witness Simplicial Variational Auto-Encoders
Variational auto-encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Machine Learning and Knowledge Extraction |
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| Online Access: | https://www.mdpi.com/2504-4990/5/1/14 |
| _version_ | 1827748965961957376 |
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| author | Aniss Aiman Medbouhi Vladislav Polianskii Anastasia Varava Danica Kragic |
| author_facet | Aniss Aiman Medbouhi Vladislav Polianskii Anastasia Varava Danica Kragic |
| author_sort | Aniss Aiman Medbouhi |
| collection | DOAJ |
| description | Variational auto-encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the simplicial auto-encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a dataset better than a standard VAE. |
| first_indexed | 2024-03-11T06:16:18Z |
| format | Article |
| id | doaj.art-6fe4d4f9cf01452ea81890add99e010f |
| institution | Directory Open Access Journal |
| issn | 2504-4990 |
| language | English |
| last_indexed | 2024-03-11T06:16:18Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machine Learning and Knowledge Extraction |
| spelling | doaj.art-6fe4d4f9cf01452ea81890add99e010f2023-11-17T12:16:54ZengMDPI AGMachine Learning and Knowledge Extraction2504-49902023-02-015119923610.3390/make5010014InvMap and Witness Simplicial Variational Auto-EncodersAniss Aiman Medbouhi0Vladislav Polianskii1Anastasia Varava2Danica Kragic3Division of Robotics Perception and Learning, Department of Intelligent Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, SE-100 44 Stockholm, SwedenDivision of Robotics Perception and Learning, Department of Intelligent Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, SE-100 44 Stockholm, SwedenDivision of Robotics Perception and Learning, Department of Intelligent Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, SE-100 44 Stockholm, SwedenDivision of Robotics Perception and Learning, Department of Intelligent Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, SE-100 44 Stockholm, SwedenVariational auto-encoders (VAEs) are deep generative models used for unsupervised learning, however their standard version is not topology-aware in practice since the data topology may not be taken into consideration. In this paper, we propose two different approaches with the aim to preserve the topological structure between the input space and the latent representation of a VAE. Firstly, we introduce InvMap-VAE as a way to turn any dimensionality reduction technique, given an embedding it produces, into a generative model within a VAE framework providing an inverse mapping into original space. Secondly, we propose the Witness Simplicial VAE as an extension of the simplicial auto-encoder to the variational setup using a witness complex for computing the simplicial regularization, and we motivate this method theoretically using tools from algebraic topology. The Witness Simplicial VAE is independent of any dimensionality reduction technique and together with its extension, Isolandmarks Witness Simplicial VAE, preserves the persistent Betti numbers of a dataset better than a standard VAE.https://www.mdpi.com/2504-4990/5/1/14variational auto-encodertopological machine learningnon-linear dimensionality reductiontopological data analysisdata visualizationrepresentation learning |
| spellingShingle | Aniss Aiman Medbouhi Vladislav Polianskii Anastasia Varava Danica Kragic InvMap and Witness Simplicial Variational Auto-Encoders Machine Learning and Knowledge Extraction variational auto-encoder topological machine learning non-linear dimensionality reduction topological data analysis data visualization representation learning |
| title | InvMap and Witness Simplicial Variational Auto-Encoders |
| title_full | InvMap and Witness Simplicial Variational Auto-Encoders |
| title_fullStr | InvMap and Witness Simplicial Variational Auto-Encoders |
| title_full_unstemmed | InvMap and Witness Simplicial Variational Auto-Encoders |
| title_short | InvMap and Witness Simplicial Variational Auto-Encoders |
| title_sort | invmap and witness simplicial variational auto encoders |
| topic | variational auto-encoder topological machine learning non-linear dimensionality reduction topological data analysis data visualization representation learning |
| url | https://www.mdpi.com/2504-4990/5/1/14 |
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