tr33hugg3r/knot-crossings

🪢 Knot Crossing Dataset

This dataset contains synthetic and real images of knots labeled by their number of crossings.
It is used to train and evaluate models that classify a knot diagram into its crossing number.

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📂 Dataset Structure

The dataset is organized into two splits:

train/
0/
3/
4/
...
test/
0/
3/
4/
...

• Each folder corresponds to a crossing number class.
• For example, 3/ contains diagrams of prime knots with 3 crossings.

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👩🏻‍🏫 Classes

Each class label is the minimum crossing number of the knot:

Label	Meaning
0	Unknot
3	Trefoil knots
4	Figure-eight knots
...	Higher crossing numbers

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🔢 Dataset Statistics

Split	# Images	Classes
Train	9,051	0, 3, 4, 5, 6, 7, 8, 9, 10
Test	49	0, 3, 4, 5, 6, 7, 8, 9, 10, 11

• The train split covers 9 different crossing-number classes.
• The test split includes a few additional samples of higher crossings (10, 11).

📂 TRAIN SPLIT
  Class   0: 1029 images
  Class  10: 1008 images
  Class   3: 1029 images
  Class   4: 1029 images
  Class   5: 1008 images
  Class   6: 1008 images
  Class   7: 1029 images
  Class   8: 882 images
  Class   9: 1029 images
  ➡ TOTAL: 9051 images


📂 TEST SPLIT
  Class   0: 3 images
  Class  10: 6 images
  Class  11: 2 images
  Class   3: 4 images
  Class   4: 4 images
  Class   5: 6 images
  Class   6: 6 images
  Class   7: 6 images
  Class   8: 6 images
  Class   9: 6 images
  ➡ TOTAL: 49 images

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🛠️ How to Load

Once published, you can load it directly with Hugging Face datasets:

from datasets import load_dataset

dataset = load_dataset("annedranowski/knot-crossings")
dataset["train"][0]

🎯 Intended Use

This dataset is intended for:

• Training and evaluating CNN or Vision Transformer (ViT) models to classify knot diagrams.
• Studying computer vision approaches for topological diagram recognition.
• Exploring ML methods for mathematical objects and low-dimensional topology.

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📜 License

The Unlicense

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✨ Citation

@dataset{dranowski2025knot,
  title     = {Knot Crossing Dataset},
  author    = {Anne Dranowski and Yura Kabkov and Roman Melamud and Daniel Tubbenhauer},
  year      = {2025},
  url       = {https://huggingface.co/datasets/annedranowski/knot-crossings}
}