# Leveraging Union of Subspace Structure to Improve Constrained Clustering

arXiv: https://arxiv.org/abs/1608.02146 · HTML: https://mlsanity.com/paper/1608.02146/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Aug 2016.

## Built on by (most cited first, 5 of 5)

- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)
- [Weighted Sparse Subspace Representation: A Unified Framework for Subspace Clustering, Constrained Clustering, and Active Learning](https://mlsanity.com/paper/2106.04330/) (2021)
- [Semi-Supervised Clustering via Structural Entropy with Different Constraints](https://mlsanity.com/paper/2312.10917/) (2023)
- [Subspace Clustering in Wavelet Packets Domain](https://mlsanity.com/paper/2406.03819/) (2024)
- [Nonlinear mixture model motivated subspace clustering](https://mlsanity.com/paper/2606.29261/) (2026)

## Abstract (arXiv)

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this description, for example with face images or handwritten digits. While it is straightforward to request human input on these datasets, our goal is to reduce this input as much as possible. We present a pairwise-constrained clustering algorithm that actively selects queries based on the union-of-subspaces model. The central step of the algorithm is in querying points of minimum margin between estimated subspaces; analogous to classifier margin, these lie near the decision boundary. We prove that points lying near the intersection of subspaces are points with low margin. Our procedure can be used after any subspace clustering algorithm that outputs an affinity matrix. We demonstrate on several datasets that our algorithm drives the clustering error down considerably faster than the state-of-the-art active query algorithms on datasets with subspace structure and is competitive on other datasets.