# Learning idempotent representation for subspace clustering

arXiv: https://arxiv.org/abs/2207.14431 · HTML: https://mlsanity.com/paper/2207.14431/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering](https://mlsanity.com/paper/1605.02633/) (2016)
- [Subspace Clustering by Block Diagonal Representation](https://mlsanity.com/paper/1805.09243/) (2018)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Doubly Stochastic Subspace Clustering](https://mlsanity.com/paper/2011.14859/) (2020)
- [Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering](https://mlsanity.com/paper/2106.09874/) (2021)
- [Is an Affine Constraint Needed for Affine Subspace Clustering?](https://mlsanity.com/paper/2005.03888/) (2020)
- [Correlation Adaptive Subspace Segmentation by Trace Lasso](https://mlsanity.com/paper/1501.04276/) (2015)
- [Constructing a Non-Negative Low Rank and Sparse Graph with Data-Adaptive Features](https://mlsanity.com/paper/1409.0964/) (2014)

## Built on by (most cited first, 2 of 2)

- [Data-Adaptive Transformed Bilateral Tensor Low-Rank Representation for Clustering](https://mlsanity.com/paper/2510.20077/) (2025)
- [LEA: Label Enumeration Attack in Vertical Federated Learning](https://mlsanity.com/paper/2603.03777/) (2026)

## Abstract (arXiv)

The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block diagonal with each block indicating a subspace; 2) each block is fully connected. Though there are various spectral-type subspace clustering algorithms have been proposed, some defects still exist in the reconstruction coefficient matrices constructed by these algorithms. We find that a normalized membership matrix naturally satisfies the above two conditions. Therefore, in this paper, we devise an idempotent representation (IDR) algorithm to pursue reconstruction coefficient matrices approximating normalized membership matrices. IDR designs a new idempotent constraint for reconstruction coefficient matrices. And by combining the doubly stochastic constraints, the coefficient matrices which are closed to normalized membership matrices could be directly achieved. We present the optimization algorithm for solving IDR problem and analyze its computation burden as well as convergence. The comparisons between IDR and related algorithms show the superiority of IDR. Plentiful experiments conducted on both synthetic and real world datasets prove that IDR is an effective and efficient subspace clustering algorithm.