ClusterAlgebrasML

Supervised machine learning techniques, and general network analysis methods are applied to Cluster Algebras and their exchange graphs.

The ExchangeGraphs.ipynb notebook details the function to generate the exchange graphs; built on the sage ClusterSeed object, please run with a sage kernel (sagemath.org), or via their online cell (CoCalc):
~ As described in the script there is functionality to generate the exchange graphs, perform various network analyses and plot certain cycle embeddings, and also generate data (as seeds in a tensor format) for machine learning.

The ML.py script performs machine learning with dense feed-forward neural networks from the sci-kit learn package:
~ One must first ensure the filepath is correct for the investigation one wishes to perform, then cells can be run sequentially.
~ Sample datasets for the investigations in the paper are available in the TensorData directory (to be unzipped before using).

BibTeX Citation

@article{Dechant:2022ccf,
    author = "Dechant, Pierre-Philippe and He, Yang-Hui and Heyes, Elli and Hirst, Edward",
    title = "{Cluster Algebras: Network Science and Machine Learning}",
    eprint = "2203.13847",
    archivePrefix = "arXiv",
    primaryClass = "math.CO",
    reportNumber = "LIMS-2022-011",
    doi = "10.1016/j.jaca.2023.100008",
    journal = "J. Comput. Algebra",
    volume = "8",
    year = "2023"
}