# PMSSC: Parallelizable multi-subset based self-expressive model for subspace clustering

arXiv: https://arxiv.org/abs/2111.12232 · HTML: https://mlsanity.com/paper/2111.12232/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 57 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [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)
- [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)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [Stochastic Sparse Subspace Clustering](https://mlsanity.com/paper/2005.01449/) (2020)
- [Greedy Feature Selection for Subspace Clustering](https://mlsanity.com/paper/1303.4778/) (2013)
- [Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces](https://mlsanity.com/paper/2006.04246/) (2020)
- [Subspace Clustering using Ensembles of K-Subspaces](https://mlsanity.com/paper/1709.04744/) (2017)
- [Multi-Level Representation Learning for Deep Subspace Clustering](https://mlsanity.com/paper/2001.08533/) (2020)
- [Subspace Clustering via Thresholding and Spectral Clustering](https://mlsanity.com/paper/1303.3716/) (2013)
- [Efficient Sparse Subspace Clustering by Nearest Neighbour Filtering](https://mlsanity.com/paper/1704.03958/) (2017)
- [G2MF-WA: Geometric Multi-Model Fitting with Weakly Annotated Data](https://mlsanity.com/paper/2001.06965/) (2020)

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

- [Subspace-Guided Feature Reconstruction for Unsupervised Anomaly Localization](https://mlsanity.com/paper/2309.13904/) (2023)

## Abstract (arXiv)

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with large datasets, representation of each data point by referring to all data points via a dictionary suffers from high computational complexity. To alleviate this issue, we introduce a parallelizable multi-subset based self-expressive model (PMS) which represents each data point by combining multiple subsets, with each consisting of only a small proportion of the samples. The adoption of PMS in subspace clustering (PMSSC) leads to computational advantages because the optimization problems decomposed over each subset are small, and can be solved efficiently in parallel. Furthermore, PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets, which contributes to an improvement in self-expressiveness. Extensive experiments on synthetic and real-world datasets show the efficiency and effectiveness of our approach in comparison to other methods.