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The Freaky Torus

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Important usage condition: Use and redistribution are governed by CC BY-SA 4.0. Review and comply with the license before using the data.
Persistent identifier
doi:10.60507/FK2/LORXU7
Published version
1.0
Publication date
2023-06-29
License
CC BY-SA 4.0

Description

This dataset contains the Python code to compute samples on our shape space Freaky Torus of deformed tori, a synthetic shape space with factors S¹×S¹×T² The first factor, an S¹, controls the deformation of the latitudinal cross-section into a rotated ellipse. The next factor, another S¹, controls the deformation of the longitudinal cross-section into a rotated ellipse. The third factor, a two-dimensional flat torus T², controls the position of a bump on the deformed torus. Above, we visualize our synthetic shape space by demonstrating the effect of moving along the individual factors to the final shape. More details on the construction can be found in the appendix of the ICLR 2023 paper Parametrizing Product Shape Manifolds by Composite Networks. Additional to the code, we also include the exact dataset that we used for the results of our paper in the data folder.

Creators

Keywords

shape space, product manifold, low-dimensional data manifolds

Files

Before downloading: Use and redistribution are governed by CC BY-SA 4.0. Review and comply with the license before using the data.
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README.mdtext/markdown3984MD5 80dcd7d85c8b1410c8f02006e7c38df2

Citation

Sassen, Josua; Hildebrandt, Klaus; Rumpf, Martin; Wirth, Benedikt, 2023-06-29, The Freaky Torus, doi:10.60507/FK2/LORXU7, V1.0

Additional Dataverse fields

Id25
Dataset Typedataset
Internal Version Number13
Latest Version Publishing StateRELEASED
Deaccession LinkNot supplied
Release Time2023-06-29T11:09:08Z
Create Time2023-06-28T12:27:31Z
Citation Date2023-06-29
File Access RequestTrue

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Complete Dataverse metadata

Citation Metadata

Title title
The Freaky Torus
Subtitle subtitle
A Synthetic Product Shape Manifold
Alternative URL alternativeURL
https://gitlab.com/jrsassen/freaky-torus
Author author
  1. Author Name
    Sassen, Josua
    Author Affiliation
    University of Bonn
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
    Value
    https://orcid.org/0000-0002-8069-4713
    Expandedvalue
    Person Name
    Sassen, Josua
    @id
    https://orcid.org/0000-0002-8069-4713
    Scheme
    ORCID
    @type
    https://schema.org/Person
  2. Author Name
    Hildebrandt, Klaus
    Author Affiliation
    TU Delft
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
    Value
    https://orcid.org/0000-0002-9196-3923
    Expandedvalue
    Person Name
    Hildebrandt, Klaus
    @id
    https://orcid.org/0000-0002-9196-3923
    Scheme
    ORCID
    @type
    https://schema.org/Person
  3. Author Name
    Rumpf, Martin
    Author Affiliation
    University of Bonn
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
    Value
    https://orcid.org/0000-0001-6049-9390
    Expandedvalue
    Person Name
    Rumpf, Martin
    @id
    https://orcid.org/0000-0001-6049-9390
    Scheme
    ORCID
    @type
    https://schema.org/Person
  4. Author Name
    Wirth, Benedikt
    Author Affiliation
    University of Münster
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
    Value
    https://orcid.org/0000-0003-0393-1938
    Expandedvalue
    Person Name
    Wirth, Benedikt
    @id
    https://orcid.org/0000-0003-0393-1938
    Scheme
    ORCID
    @type
    https://schema.org/Person
Dataset Contact datasetContact
  1. Dataset Contact Name
    Sassen, Josua
    Dataset Contact Affiliation
    University of Bonn
    Dataset Contact Email
    josua.sassen@uni-bonn.de
Ds Description dsDescription
  1. Ds Description Value
    This dataset contains the Python code to compute samples on our shape space Freaky Torus of deformed tori, a synthetic shape space with factors S¹×S¹×T² The first factor, an S¹, controls the deformation of the latitudinal cross-section into a rotated ellipse. The next factor, another S¹, controls the deformation of the longitudinal cross-section into a rotated ellipse. The third factor, a two-dimensional flat torus T², controls the position of a bump on the deformed torus. Above, we visualize our synthetic shape space by demonstrating the effect of moving along the individual factors to the final shape. More details on the construction can be found in the appendix of the ICLR 2023 paper Parametrizing Product Shape Manifolds by Composite Networks. Additional to the code, we also include the exact dataset that we used for the results of our paper in the data folder.
Subject subject
  1. Computer and Information Science
  2. Mathematical Sciences
Free Keyword freeKeyword
  1. Free Keyword Value
    shape space
  2. Free Keyword Value
    product manifold
  3. Free Keyword Value
    low-dimensional data manifolds
Publication publication
  1. Publication Citation
    Parametrizing Product Shape Manifolds by Composite Networks. Josua Sassen, Klaus Hildebrandt, Martin Rumpf, and Benedikt Wirth. In: The Eleventh International Conference on Learning Representations. 2023.
    Publication IDType
    url
    Publication IDNumber
    https://openreview.net/forum?id=F_EhNDSamN
    Publication URL
    https://openreview.net/forum?id=F_EhNDSamN
Depositor depositor
Sassen, Josua
Date Of Deposit dateOfDeposit
2023-06-28
Software software
  1. Software Name
    Python
    Software Version
    3.9

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