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

arXiv: https://arxiv.org/abs/2512.23766 · HTML: https://mlsanity.com/paper/2512.23766/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 29 Dec 2025.

## Builds on (most cited first, 1 of 1)

- [The Flag Median and FlagIRLS](https://mlsanity.com/paper/2203.04437/) (2022)

## Abstract (arXiv)

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.