# Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering

arXiv: https://arxiv.org/abs/2509.18653 · HTML: https://mlsanity.com/paper/2509.18653/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 80 references that are in the map.
- First posted on arXiv 23 Sep 2025.

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

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [A Survey of Multi-View Representation Learning](https://mlsanity.com/paper/1610.01206/) (2016)
- [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)
- [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)
- [Essential Tensor Learning for Multi-view Spectral Clustering](https://mlsanity.com/paper/1807.03602/) (2018)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Graph Convolutional Subspace Clustering: A Robust Subspace Clustering Framework for Hyperspectral Image](https://mlsanity.com/paper/2004.10476/) (2020)
- [BS-Nets: An End-to-End Framework For Band Selection of Hyperspectral Image](https://mlsanity.com/paper/1904.08269/) (2019)
- [Generalized Canonical Correlation Analysis: A Subspace Intersection Approach](https://mlsanity.com/paper/2003.11205/) (2020)
- [Learning Transformations for Clustering and Classification](https://mlsanity.com/paper/1309.2074/) (2013)
- [Transformed Subspace Clustering](https://mlsanity.com/paper/1912.04734/) (2019)
- [Multisubject Task-Related fMRI Data Processing via a Two-Stage Generalized Canonical Correlation Analysis](https://mlsanity.com/paper/2210.08531/) (2022)

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

- [Provable Subspace Identification of Nonlinear Multi-view CCA](https://mlsanity.com/paper/2602.23785/) (2026)

## Abstract (arXiv)

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data, our formulation directly models each data sample as a matrix and clusters them according to their underlying subspaces. We establish conceptual links to Subspace Clustering and Generalized Canonical Correlation Analysis (GCCA), and clarify key differences that arise in this more general setting. Our approach is based on a Block Term Decomposition (BTD) of a third-order tensor constructed from the input matrices, enabling joint estimation of cluster memberships and partially shared subspaces. We provide the first identifiability results for this formulation and propose scalable optimization algorithms tailored to large datasets. Experiments on real-world hyperspectral imaging datasets demonstrate that our method achieves superior clustering accuracy and robustness, especially under high noise and interference, compared to existing subspace clustering techniques. These results highlight the potential of the proposed framework in challenging high-dimensional applications where structure exists beyond individual data vectors.