# Large-Scale Subspace Clustering via k-Factorization

arXiv: https://arxiv.org/abs/2012.04345 · HTML: https://mlsanity.com/paper/2012.04345/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Dec 2020.

## Built on by (most cited first, 14 of 14)

- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Online Unsupervised Video Object Segmentation via Contrastive Motion Clustering](https://mlsanity.com/paper/2306.12048/) (2023)
- [Spectral Subspace Clustering for Attributed Graphs](https://mlsanity.com/paper/2411.11074/) (2024)
- [Unsupervised Deep Discriminant Analysis Based Clustering](https://mlsanity.com/paper/2206.04686/) (2022)
- [Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization](https://mlsanity.com/paper/2207.12214/) (2022)
- [Deep Graph-Level Clustering Using Pseudo-Label-Guided Mutual Information Maximization Network](https://mlsanity.com/paper/2302.02369/) (2023)
- [Spectral Clustering for Discrete Distributions](https://mlsanity.com/paper/2401.13913/) (2024)
- [CLUBench: A Clustering Benchmark](https://mlsanity.com/paper/2605.29933/) (2026)
- [One-step Bipartite Graph Cut: A Normalized Formulation and Its Application to Scalable Subspace Clustering](https://mlsanity.com/paper/2305.07386/) (2023)
- [Attention-Guided Deep Adversarial Temporal Subspace Clustering (A-DATSC) Model for multivariate spatiotemporal data](https://mlsanity.com/paper/2510.18004/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [CASC: Causal Adversarial Subspace Clustering for Multivariate Spatiotemporal Data](https://mlsanity.com/paper/2607.21088/) (2026)

## Abstract (arXiv)

Subspace clustering (SC) aims to cluster data lying in a union of low-dimensional subspaces. Usually, SC learns an affinity matrix and then performs spectral clustering. Both steps suffer from high time and space complexity, which leads to difficulty in clustering large datasets. This paper presents a method called k-Factorization Subspace Clustering (k-FSC) for large-scale subspace clustering. K-FSC directly factorizes the data into k groups via pursuing structured sparsity in the matrix factorization model. Thus, k-FSC avoids learning affinity matrix and performing eigenvalue decomposition, and has low (linear) time and space complexity on large datasets. This paper proves the effectiveness of the k-FSC model theoretically. An efficient algorithm with convergence guarantee is proposed to solve the optimization of k-FSC. In addition, k-FSC is able to handle sparse noise, outliers, and missing data, which are pervasive in real applications. This paper also provides online extension and out-of-sample extension for k-FSC to handle streaming data and cluster arbitrarily large datasets. Extensive experiments on large-scale real datasets show that k-FSC and its extensions outperform state-of-the-art methods of subspace clustering.