Abstract: From 3D point clouds to high-dimensional samples, sparse representations have a key position in the data science toolbox. They complement 2D images and 3D volumes effectively, enabling fast geometric computations for e.g. Gaussian processes and shape analysis.
In this talk, I will present extensions for PyTorch, NumPy, Matlab and R that speed up fundamental computations on (generalized) point clouds by several orders of magnitude, when compared to PyTorch or JAX GPU baselines. These software tools allow researchers to break through major computational bottlenecks in the field and have been downloaded more than 400k times over the last few years.
The presentation may be of interest to all researchers who deal with point clouds, time series and segmentation maps, with a special focus on:
1. Fast and scalable computations with (generalized) distance matrices.
2. Efficient and robust solvers for the optimal transport (= “Earth Mover’s”) problem.
3. Applications to shape analysis and geometric deep learning, with a case study on the “pixel-perfect” registration of lung vessel trees.
References:
- Geometric data analyis - MVA lectures and videos : https://www.jeanfeydy.com/Teaching/index.html
- “Geometric data analysis, beyond convolutions”: https://www.jeanfeydy.com/geometric_data_analysis.pdf
- “Fast geometric learning with symbolic matrices”: http://jeanfeydy.com/Papers/KeOps_NeurIPS_2020.pdf
- KeOps library (geometric computations): http://kernel-operations.io/keops/index.html
- GeomLoss library (optimal transport): https://www.kernel-operations.io/geomloss/
Speaker: Jean Feydy is a research fellow at Inria Paris, working in the joint maths / statistics / public health team HeKA.
His work focuses on scalable geometric data analysis, from 3D anatomy to survival analysis on nationwide drug consumption data.
Affiliation: Inria/Inserm team HeKa
Place of Seminar: Kumpula exactum D122 (in person) & zoom ( Meeting ID: 640 5738 7231 ; Passcode: 825217)