# Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

arXiv: https://arxiv.org/abs/1401.8126 · HTML: https://mlsanity.com/paper/1401.8126/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2014.

## Built on by (most cited first, 5 of 5)

- [Spectral Feature Augmentation for Graph Contrastive Learning and Beyond](https://mlsanity.com/paper/2212.01026/) (2022)
- [High-order Tensor Pooling with Attention for Action Recognition](https://mlsanity.com/paper/2110.05216/) (2021)
- [Subspace Distillation for Continual Learning](https://mlsanity.com/paper/2307.16419/) (2023)
- [Pre-training with Random Orthogonal Projection Image Modeling](https://mlsanity.com/paper/2310.18737/) (2023)
- [On mitigating stability-plasticity dilemma in CLIP-guided image morphing via geodesic distillation loss](https://mlsanity.com/paper/2401.10526/) (2024)

## Abstract (arXiv)

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.