Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices
Authors: Thibault De Surrel, Fabien Lotte, Sylvain Chevallier, Florian Yger
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on synthetic and real-world datasets demonstrate the robustness and flexibility of this geometry-aware distribution, underscoring its potential to advance manifold-based data analysis. This work lays the groundwork for extending classical machine learning and statistical methods to more complex and structured data. |
| Researcher Affiliation | Academia | 1LAMSADE, CNRS, PSL Univ. Paris-Dauphine, France 2Inria center at the University of Bordeaux / La BRI, France 3TAU, LISN, University Paris-Saclay, France 4LITIS, INSA Rouen-Normandy, France. |
| Pseudocode | Yes | Algorithm 1 Sampling from a Wrapped Gaussian WG(p; µ, Σ) Require: p Pd, µ R d(d+1)/2, Σ Pd(d+1)/2 1: Sample t N(µ, Σ) 2: Compute X Expp(Vect 1 p (t)) 3: Return X WG(p; µ, Σ) |
| Open Source Code | Yes | The codes for the different experiments is available at https://github.com/ thibaultdesurrel/wrapped_gaussians_SPD. |
| Open Datasets | Yes | BNCI2014004 BCI 3 3 720 x 9 subjects 2 (Leeb et al., 2007) Zhou2016 BCI 5 5 320 x 4 subjects 2 (Zhou et al., 2016) Air Quality Atmospheric data 6 6 102 3 (Smith et al., 2022) Indiana Pines Hyperspectral imaging 5 5 14, 641 12 (Baumgardner et al., 2015) Pavia Univ. Hyperspectral imaging 5 5 185, 176 6 Salinas Hyperspectral imaging 5 5 94, 184 17 Textile Image Analysis 10 10 16, 000 2 (Bergmann et al., 2021) Breizh Crops Multispectral imaging 13 13 177, 658 6 (Rußwurm et al., 2020) |
| Dataset Splits | Yes | The experiment we lead was cross-subject: each classifier was trained on all subject except one and tested on this last subject. For the non-BCI datasets (Air Quality, Indiana, Pavia Uni, Salinas, Textile and Breizh Crops), we used a 5-fold cross-validation to evaluate the performance of the classifiers. |
| Hardware Specification | No | The paper does not explicitly mention any specific hardware used for running its experiments, such as GPU models, CPU models, or cloud resources with specifications. |
| Software Dependencies | No | We implemented this MLE in Python using the toolbox Pymanopt (Townsend et al., 2016). We used the library MOABB (Aristimunha et al., 2023) to load and preprocess the data. The TS-LDA uses the Tangent Space class from Py Riemann (Barachant et al., 2024) and the LDA from Scikit-learn (Pedregosa et al., 2011). |
| Experiment Setup | Yes | We chose relatively small values for X and s because otherwise, when the dimension d is large, the generated parameters are very far from identity leading to numerical instability. More details on the experimental setup are given in Appendix I. ... For p , we use the function generate random spd matrix ... We set X = 0.1Id and s = 1. For µ , we generate a random vector of size d(d+1)/2 with values in [0, 0.1]. For Σ , we generate a random SPD matrix using the same function as for p with X = 0.01Id(d+1)/2 and s = 0.02. ... We start by applying a standard band-pass filter with range [7; 35] Hz. Then, we used the Ledoit-Wolf shrunk covariance matrix ... First, we normalize the data by subtracting the image global mean. Then, we apply a PCA to reduce the dimension of the data to 5. A sliding window with no overlap is then used around each pixel for data sampling and then vectorized. In our experiments, we used a window of size 25 25. ... To optimize the MLE, we used in practice the Riemannian Conjugate Gradient method (Boumal, 2023) with a maximum of 1, 000, 000 iterations and a max time set to 2 hours. |