A Granular Grassmannian Clustering Framework via the Schubert Variety of Best Fit

Karim Salta, Michael Kirby, Chris Peterson
12/29/2025
cs.LGcs.CGcs.CV

No official code found. Best implementation: kkarimov/SubspaceClustering (0 stars, last commit 2025-12-02).

Abstract

In many classification and clustering tasks, it is useful to compute a geometric representative for a dataset or a cluster, such as a mean or median. When datasets are represented by subspaces, these representatives become points on the Grassmann or flag manifold, with distances induced by their geometry, often via principal angles. We introduce a subspace clustering algorithm that replaces subspace means with a trainable prototype defined as a Schubert Variety of Best Fit (SVBF) - a subspace that comes as close as possible to intersecting each cluster member in at least one fixed direction. Integrated in the Linde-Buzo-Grey (LBG) pipeline, this SVBF-LBG scheme yields improved cluster purity on synthetic, image, spectral, and video action data, while retaining the mathematical structure required for downstream analysis.

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Code Implementations(1)

kkarimov/SubspaceClusteringCommunity56%

The code for "A Granular Grassmannian Clustering Framework via the Schubert Variety of Best Fit" preprint submitted to arxiv.org in 2025

00Apr 24, 202410 months ago

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Cite this paper

@article{salta2025granular,
  title  = {A Granular Grassmannian Clustering Framework via the Schubert Variety of Best Fit},
  author = {Karim Salta and Michael Kirby and Chris Peterson},
  year   = {2025},
  eprint = {2512.23766},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2512.23766v1}
}

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