# Weighted Sparse Subspace Representation: A Unified Framework for Subspace Clustering, Constrained Clustering, and Active Learning

arXiv: https://arxiv.org/abs/2106.04330 · HTML: https://mlsanity.com/paper/2106.04330/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Algorithms for Fitting the Constrained Lasso](https://mlsanity.com/paper/1611.01511/) (2016)
- [On Geometric Analysis of Affine Sparse Subspace Clustering](https://mlsanity.com/paper/1808.05965/) (2018)
- [Leveraging Union of Subspace Structure to Improve Constrained Clustering](https://mlsanity.com/paper/1608.02146/) (2016)
- [Subspace Clustering with Active Learning](https://mlsanity.com/paper/1911.03299/) (2019)
- [Constrained Sparse Subspace Clustering with Side-Information](https://mlsanity.com/paper/1805.08183/) (2018)
- [Subspace Clustering of Very Sparse High-Dimensional Data](https://mlsanity.com/paper/1901.09108/) (2019)

## Abstract (arXiv)

Spectral-based subspace clustering methods have proved successful in many challenging applications such as gene sequencing, image recognition, and motion segmentation. In this work, we first propose a novel spectral-based subspace clustering algorithm that seeks to represent each point as a sparse convex combination of a few nearby points. We then extend the algorithm to constrained clustering and active learning settings. Our motivation for developing such a framework stems from the fact that typically either a small amount of labelled data is available in advance; or it is possible to label some points at a cost. The latter scenario is typically encountered in the process of validating a cluster assignment. Extensive experiments on simulated and real data sets show that the proposed approach is effective and competitive with state-of-the-art methods.