Algorithm Inventory

There are 3 main types of algorithms used in Polislike pipelines:

1. an imputation algorithm, for "filling in" all missing values in the vote matrix due to non-voted statements.
2. a dimensional reduction algorithm, for projecting the high-dimensional structure into a 2D/3D plot.
3. a clustering algorithm, for automatically assigning labels to participants, placing them in groups.

• extended dimensional reduction algos of interest
  • comparison spreadsheet
  • t-SNE
    • 🙁 hyperparams matter a lot, but really hard to set
      • two simple clusters can look like weird objects or random noise if mis-set
    • 🙁 cluster sizes don't mean anything. (big, small, rods, donuts)
    • 🙁 "likes to split data up into false clusters"
    • code docs: https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html
  • UMAP
    • preserves local structure. loses global structure.
    • depends heavily on PCA initialization (not random)
    • code: https://github.com/lmcinnes/umap
  • LargeVis
  • TriMAP
    • works with triplets of points
    • depends heavily on PCA initialization (not random)
    • 🙂 beautiful results for 3D mammoth sample set
  • weighted EMPCA
    • https://github.com/sbailey/empca/
    • https://github.com/jakevdp/wpca
  • PaCMAP
    • non-parameterized
    • alternative to t-SNE
    • preserves both local and global structure, usually when each is important.
      • global structure preservation comparable with TriMAP
      • local structure preservation comparable with UMAP & t-SNE
    • works well with random initialization (no prelim PCA needed)
    • modelled on attractive and repulsive forces. aligns with plurality research.
    • very computationally efficient
    • code: https://github.com/YingfanWang/PaCMAP
    • video: https://www.youtube.com/watch?v=sD-uDZ8zXkc
  • LocalMAP
    • non-parameterized
    • improvement on PaCMAP
    • code: https://github.com/williamsyy/LocalMAP
  • ParamRepulsor
    • parameterized PaCMAP
    • code: https://github.com/hyhuang00/ParamRepulsor

Note: Most dimensional reduction methods don't work on sparse data, and PCA and UMAP have specifically been used because they can accomodate it. There is a possibility that TabPFN, a foundation model for tabular data, could be used to fill in the DNA of missing values, and allow other dimensional reduction algos to be used.

See:

• https://news.ycombinator.com/item?id=42653722
• https://priorlabs.ai/
• https://www.nature.com/articles/s41586-024-08328-6