Generation, data analysis, and machine learning of Grassmannian cluster variables via Young tableaux.
The Data folder contains the respective generated cluster variables, as semi-standard Young tableaux for each Grassmannian (denoted CV), as well as the equivalent non-cluster variable data of tableaux which are not cluster variables (denoted NCV).
...download and unzip the files before running analysis & machine learning.
The python script HPC_Generation.py generates cluster variables as semi-standard Young tableaux stochastically via mutation, saving those of ranks under consideration. The file is set-up for parallelisation on a hpc cluster, saving subfiles intermittently which are later combined (taking the union of all variables).
The scripts ML.py, PCA.py, and KMeans.py perform the respective supervised and unsupervised machine learning used to analyse these datasets. Whilst the script Saliency.py analyses the performance of the neural networks.
...ensure the local filepaths are correct for each of the datasets for importing, instructions are given in each script.
The MiscellaneousAnalysis.py script contains additional analysis used for results in this research.
@article{Cheung:2022itk,
author = "Cheung, Man-Wai and Dechant, Pierre-Philippe and He, Yang-Hui and Heyes, Elli and Hirst, Edward and Li, Jian-Rong",
title = "{Clustering Cluster Algebras with Clusters}",
eprint = "2212.09771",
archivePrefix = "arXiv",
primaryClass = "hep-th",
reportNumber = "LIMS-2022-025",
doi = "10.4310/ATMP.2023.v27.n3.a5",
journal = "Adv. Theor. Math. Phys.",
volume = "27",
number = "3",
pages = "797--828",
year = "2023"
}