# Learnable Subspace Clustering

arXiv: https://arxiv.org/abs/2004.04520 · HTML: https://mlsanity.com/paper/2004.04520/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2020.

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

- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [An Investigation of Visual Foundation Models Robustness](https://mlsanity.com/paper/2508.16225/) (2025)
- [Robust Multi-Manifold Clustering via Simplex Paths](https://mlsanity.com/paper/2507.10710/) (2025)

## Abstract (arXiv)

This paper studies the large-scale subspace clustering (LSSC) problem with million data points. Many popular subspace clustering methods cannot directly handle the LSSC problem although they have been considered as state-of-the-art methods for small-scale data points. A basic reason is that these methods often choose all data points as a big dictionary to build huge coding models, which results in a high time and space complexity. In this paper, we develop a learnable subspace clustering paradigm to efficiently solve the LSSC problem. The key idea is to learn a parametric function to partition the high-dimensional subspaces into their underlying low-dimensional subspaces instead of the expensive costs of the classical coding models. Moreover, we propose a unified robust predictive coding machine (RPCM) to learn the parametric function, which can be solved by an alternating minimization algorithm. In addition, we provide a bounded contraction analysis of the parametric function. To the best of our knowledge, this paper is the first work to efficiently cluster millions of data points among the subspace clustering methods. Experiments on million-scale datasets verify that our paradigm outperforms the related state-of-the-art methods in both efficiency and effectiveness.