# Towards Clustering-friendly Representations: Subspace Clustering via Graph Filtering

arXiv: https://arxiv.org/abs/2106.09874 · HTML: https://mlsanity.com/paper/2106.09874/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Are We Really Making Much Progress? A Worrying Analysis of Recent Neural Recommendation Approaches](https://mlsanity.com/paper/1907.06902/) (2019)
- [Attributed Graph Clustering via Adaptive Graph Convolution](https://mlsanity.com/paper/1906.01210/) (2019)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Deep Comprehensive Correlation Mining for Image Clustering](https://mlsanity.com/paper/1904.06925/) (2019)
- [Large-scale Multi-view Subspace Clustering in Linear Time](https://mlsanity.com/paper/1911.09290/) (2019)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Deep k-Means: Jointly clustering with k-Means and learning representations](https://mlsanity.com/paper/1806.10069/) (2018)
- [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)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Twin Learning for Similarity and Clustering: A Unified Kernel Approach](https://mlsanity.com/paper/1705.00678/) (2017)
- [Structure Learning with Similarity Preserving](https://mlsanity.com/paper/1912.01197/) (2019)
- [Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data](https://mlsanity.com/paper/1509.02649/) (2015)
- [Robust Subspace Clustering with Compressed Data](https://mlsanity.com/paper/1803.11305/) (2018)
- [Relation-Guided Representation Learning](https://mlsanity.com/paper/2007.05742/) (2020)
- [Flexible Auto-weighted Local-coordinate Concept Factorization: A Robust Framework for Unsupervised Clustering](https://mlsanity.com/paper/1909.00523/) (2019)
- [The Effect of Pets on Happiness: A Large-scale Multi-Factor Analysis using Social Multimedia](https://mlsanity.com/paper/1804.03507/) (2018)
- [Robust Unsupervised Flexible Auto-weighted Local-Coordinate Concept Factorization for Image Clustering](https://mlsanity.com/paper/1905.10564/) (2019)

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

- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Unpaired Multi-View Graph Clustering with Cross-View Structure Matching](https://mlsanity.com/paper/2307.03476/) (2023)
- [Graph Data Condensation via Self-expressive Graph Structure Reconstruction](https://mlsanity.com/paper/2403.07294/) (2024)
- [Structure-Preserving Graph Representation Learning](https://mlsanity.com/paper/2209.00793/) (2022)
- [Self-supervised Consensus Representation Learning for Attributed Graph](https://mlsanity.com/paper/2108.04822/) (2021)
- [Adaptive Attribute and Structure Subspace Clustering Network](https://mlsanity.com/paper/2109.13742/) (2021)
- [Spectral Subspace Clustering for Attributed Graphs](https://mlsanity.com/paper/2411.11074/) (2024)
- [Scalable Multi-view Clustering with Graph Filtering](https://mlsanity.com/paper/2205.09228/) (2022)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [Learning idempotent representation for subspace clustering](https://mlsanity.com/paper/2207.14431/) (2022)
- [Learning Structure Aware Deep Spectral Embedding](https://mlsanity.com/paper/2305.08215/) (2023)
- [Multi-view Subspace Clustering via An Adaptive Consensus Graph Filter](https://mlsanity.com/paper/2403.08787/) (2024)
- [An Approach Towards Learning K-means-friendly Deep Latent Representation](https://mlsanity.com/paper/2411.19496/) (2024)
- [Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information](https://mlsanity.com/paper/2608.08418/) (2026)

## Abstract (arXiv)

Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However, this simple assumption does not always hold since the raw data might not be separable into subspaces. To recover the ``clustering-friendly'' representation and facilitate the subsequent clustering, we propose a graph filtering approach by which a smooth representation is achieved. Specifically, it injects graph similarity into data features by applying a low-pass filter to extract useful data representations for clustering. Extensive experiments on image and document clustering datasets demonstrate that our method improves upon state-of-the-art subspace clustering techniques. Especially, its comparable performance with deep learning methods emphasizes the effectiveness of the simple graph filtering scheme for many real-world applications. An ablation study shows that graph filtering can remove noise, preserve structure in the image, and increase the separability of classes.