# Log-Euclidean Bag of Words for Human Action Recognition

arXiv: https://arxiv.org/abs/1406.2139 · HTML: https://mlsanity.com/paper/1406.2139/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2014.

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

- [Fusion of Physiological and Behavioural Signals on SPD Manifolds with Application to Stress and Pain Detection](https://mlsanity.com/paper/2207.08811/) (2022)
- [ReL-SAR: Representation Learning for Skeleton Action Recognition with Convolutional Transformers and BYOL](https://mlsanity.com/paper/2409.05749/) (2024)

## Abstract (arXiv)

Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this paper, we tackle the problem of categorising human actions by devising Bag of Words (BoW) models based on covariance matrices of spatio-temporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of Symmetric Positive Definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, we propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison to several state-of-the-art methods.