# Kernel Sparse Subspace Clustering on Symmetric Positive Definite Manifolds

arXiv: https://arxiv.org/abs/1601.00414 · HTML: https://mlsanity.com/paper/1601.00414/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2016.

## Built on by (most cited first, 10 of 10)

- [Pseudo-supervised Deep Subspace Clustering](https://mlsanity.com/paper/2104.03531/) (2021)
- [Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices](https://mlsanity.com/paper/2110.13475/) (2021)
- [Adaptive Attribute and Structure Subspace Clustering Network](https://mlsanity.com/paper/2109.13742/) (2021)
- [Nonlinear subspace clustering by functional link neural networks](https://mlsanity.com/paper/2402.02051/) (2024)
- [Adaptive Graph Convolutional Subspace Clustering](https://mlsanity.com/paper/2305.03414/) (2023)
- [Geometric Sparse Coding in Wasserstein Space](https://mlsanity.com/paper/2210.12135/) (2022)
- [Learning Log-Determinant Divergences for Positive Definite Matrices](https://mlsanity.com/paper/2104.06461/) (2021)
- [Attentive Multi-View Deep Subspace Clustering Net](https://mlsanity.com/paper/2112.12506/) (2021)
- [Beyond Linear Subspace Clustering: A Comparative Study of Nonlinear Manifold Clustering Algorithms](https://mlsanity.com/paper/2103.10656/) (2021)
- [Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach](https://mlsanity.com/paper/2501.06368/) (2025)

## Abstract (arXiv)

Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. As such, there is still no satisfactory approach to solve subspace clustering by it self-expressive principle for symmetric positive definite (SPD) matrices which is very useful in computer vision. In this paper, by embedding the SPD matrices into a Reproducing Kernel Hilbert Space (RKHS), a kernel subspace clustering method is constructed on the SPD manifold through an appropriate Log-Euclidean kernel, termed as kernel sparse subspace clustering on the SPD Riemannian manifold (KSSCR). By exploiting the intrinsic Riemannian geometry within data, KSSCR can effectively characterize the geodesic distance between SPD matrices to uncover the underlying subspace structure. Experimental results on two famous database demonstrate that the proposed method achieves better clustering results than the state-of-the-art approaches.