# Sparse Subspace Clustering for Concept Discovery (SSCCD)

arXiv: https://arxiv.org/abs/2203.06043 · HTML: https://mlsanity.com/paper/2203.06043/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Explaining by Removing: A Unified Framework for Model Explanation](https://mlsanity.com/paper/2011.14878/) (2020)
- [Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networks](https://mlsanity.com/paper/1801.03454/) (2018)
- [Invertible Concept-based Explanations for CNN Models with Non-negative Concept Activation Vectors](https://mlsanity.com/paper/2006.15417/) (2020)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering](https://mlsanity.com/paper/1605.02633/) (2016)
- [PredDiff: Explanations and Interactions from Conditional Expectations](https://mlsanity.com/paper/2102.13519/) (2021)
- [PACE: Posthoc Architecture-Agnostic Concept Extractor for Explaining CNNs](https://mlsanity.com/paper/2108.13828/) (2021)
- [Instance-wise or Class-wise? A Tale of Neighbor Shapley for Concept-based Explanation](https://mlsanity.com/paper/2109.01369/) (2021)
- [MACE: Model Agnostic Concept Extractor for Explaining Image Classification Networks](https://mlsanity.com/paper/2011.01472/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multi-dimensional concept discovery (MCD): A unifying framework with completeness guarantees](https://mlsanity.com/paper/2301.11911/) (2023)
- [Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces](https://mlsanity.com/paper/2212.14855/) (2022)
- [Revealing Hidden Context Bias in Segmentation and Object Detection through Concept-specific Explanations](https://mlsanity.com/paper/2211.11426/) (2022)
- [Conducting Stylistic Analysis of Paintings through an Art-History Agent](https://mlsanity.com/paper/2608.29644/) (2026)

## Abstract (arXiv)

Concepts are key building blocks of higher level human understanding. Explainable AI (XAI) methods have shown tremendous progress in recent years, however, local attribution methods do not allow to identify coherent model behavior across samples and therefore miss this essential component. In this work, we study concept-based explanations and put forward a new definition of concepts as low-dimensional subspaces of hidden feature layers. We novelly apply sparse subspace clustering to discover these concept subspaces. Moving forward, we derive insights from concept subspaces in terms of localized input (concept) maps, show how to quantify concept relevances and lastly, evaluate similarities and transferability between concepts. We empirically demonstrate the soundness of the proposed Sparse Subspace Clustering for Concept Discovery (SSCCD) method for a variety of different image classification tasks. This approach allows for deeper insights into the actual model behavior that would remain hidden from conventional input-level heatmaps.