# Fusion Subspace Clustering for Incomplete Data

arXiv: https://arxiv.org/abs/2205.10872 · HTML: https://mlsanity.com/paper/2205.10872/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 76 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 18 of 18)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [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)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Robust subspace clustering](https://mlsanity.com/paper/1301.2603/) (2013)
- [Statistical Properties of Convex Clustering](https://mlsanity.com/paper/1503.08340/) (2015)
- [Noisy Sparse Subspace Clustering](https://mlsanity.com/paper/1309.1233/) (2013)
- [Preference Completion: Large-scale Collaborative Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1507.04457/) (2015)
- [Algebraic Variety Models for High-Rank Matrix Completion](https://mlsanity.com/paper/1703.09631/) (2017)
- [Greedy Subspace Clustering](https://mlsanity.com/paper/1410.8864/) (2014)
- [Theoretical Analysis of Sparse Subspace Clustering with Missing Entries](https://mlsanity.com/paper/1801.00393/) (2018)
- [Innovation Pursuit: A New Approach to Subspace Clustering](https://mlsanity.com/paper/1512.00907/) (2015)
- [Guess Who Rated This Movie: Identifying Users Through Subspace Clustering](https://mlsanity.com/paper/1408.2055/) (2014)
- [Learning task structure via sparsity grouped multitask learning](https://mlsanity.com/paper/1705.04886/) (2017)
- [Clustering of Data with Missing Entries using Non-convex Fusion Penalties](https://mlsanity.com/paper/1709.01870/) (2017)

## Abstract (arXiv)

This paper introduces em fusion subspace clustering, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize the distance between the subspaces of all data, so that subspaces of the same cluster get em fused together. Our method allows low, high, and even full-rank data; it directly accounts for noise, and its sample complexity approaches the information-theoretic limit. In addition, our approach provides a natural model selection em clusterpath, and a direct completion method. We give convergence guarantees, analyze computational complexity, and show through extensive experiments on real and synthetic data that our approach performs comparably to the state-of-the-art with complete data, and dramatically better if data is missing.