# Generalized Relevance Learning Grassmann Quantization

arXiv: https://arxiv.org/abs/2403.09183 · HTML: https://mlsanity.com/paper/2403.09183/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 40 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 6 of 6)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Grassmannian Learning: Embedding Geometry Awareness in Shallow and Deep Learning](https://mlsanity.com/paper/1808.02229/) (2018)
- [Dictionary Learning and Sparse Coding on Grassmann Manifolds: An Extrinsic Solution](https://mlsanity.com/paper/1310.4891/) (2013)
- [Visualisation and knowledge discovery from interpretable models](https://mlsanity.com/paper/2005.03632/) (2020)
- [Detection of extragalactic Ultra-Compact Dwarfs and Globular Clusters using Explainable AI techniques](https://mlsanity.com/paper/2201.01604/) (2022)

## Built on by (most cited first, 2 of 2)

- [A prototype-based model for set classification](https://mlsanity.com/paper/2408.13720/) (2024)
- [An explainable approach to detect case law on housing and eviction issues within the HUDOC database](https://mlsanity.com/paper/2410.02978/) (2024)

## Abstract (arXiv)

Due to advancements in digital cameras, it is easy to gather multiple images (or videos) from an object under different conditions. Therefore, image-set classification has attracted more attention, and different solutions were proposed to model them. A popular way to model image sets is subspaces, which form a manifold called the Grassmann manifold. In this contribution, we extend the application of Generalized Relevance Learning Vector Quantization to deal with Grassmann manifold. The proposed model returns a set of prototype subspaces and a relevance vector. While prototypes model typical behaviours within classes, the relevance factors specify the most discriminative principal vectors (or images) for the classification task. They both provide insights into the model's decisions by highlighting influential images and pixels for predictions. Moreover, due to learning prototypes, the model complexity of the new method during inference is independent of dataset size, unlike previous works. We applied it to several recognition tasks including handwritten digit recognition, face recognition, activity recognition, and object recognition. Experiments demonstrate that it outperforms previous works with lower complexity and can successfully model the variation, such as handwritten style or lighting conditions. Moreover, the presence of relevances makes the model robust to the selection of subspaces' dimensionality.