# Expanding the Family of Grassmannian Kernels: An Embedding Perspective

arXiv: https://arxiv.org/abs/1407.1123 · HTML: https://mlsanity.com/paper/1407.1123/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2014.

## Built on by (most cited first, 6 of 6)

- [Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models](https://mlsanity.com/paper/2107.09814/) (2021)
- [Grassmannian diffusion maps based surrogate modeling via geometric harmonics](https://mlsanity.com/paper/2109.13805/) (2021)
- [Embedding Graphs on Grassmann Manifold](https://mlsanity.com/paper/2205.15068/) (2022)
- [Deep and Shallow Covariance Feature Quantization for 3D Facial Expression Recognition](https://mlsanity.com/paper/2105.05708/) (2021)
- [Random features for Grassmannian kernel approximation with bounded rank-one projections](https://mlsanity.com/paper/2608.04227/) (2026)
- [Soft-Argmax for the Projective Plane via the Veronese Embedding](https://mlsanity.com/paper/2609.00521/) (2026)

## Abstract (arXiv)

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show- is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.