# Auto-weighted low-rank representation for clustering

arXiv: https://arxiv.org/abs/2104.12308 · HTML: https://mlsanity.com/paper/2104.12308/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 2 of 2)

- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Linearized Alternating Direction Method with Parallel Splitting and Adaptive Penalty for Separable Convex Programs in Machine Learning](https://mlsanity.com/paper/1310.5035/) (2013)

## Built on by (most cited first, 1 of 1)

- [When Can We Solve the Weighted Low Rank Approximation Problem in Truly Subquadratic Time?](https://mlsanity.com/paper/2502.16912/) (2025)

## Abstract (arXiv)

In this paper, a novel unsupervised low-rank representation model, i.e., Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more favorable similarity graph (SG) for clustering. In particular, ALRR enhances the discriminability of SG by capturing the multi-subspace structure and extracting the salient features simultaneously. Specifically, an auto-weighted penalty is introduced to learn a similarity graph by highlighting the effective features, and meanwhile, overshadowing the disturbed features. Consequently, ALRR obtains a similarity graph that can preserve the intrinsic geometrical structures within the data by enforcing a smaller similarity on two dissimilar samples. Moreover, we employ a block-diagonal regularizer to guarantee the learned graph contains k diagonal blocks. This can facilitate a more discriminative representation learning for clustering tasks. Extensive experimental results on synthetic and real databases demonstrate the superiority of ALRR over other state-of-the-art methods with a margin of 1.8%~10.8%.