Accelerating $t$ -SNE using Fast Fourier Transforms and the Particle-Mesh Algorithm from Physics

$t$ -Distributed Stochastic Neighbor Embedding ( $t$ -SNE) is a well-known dimensionality reduction technique used for the visualization of high-dimensional data. However, despite several improvements, $t$ -SNE is not well-suited to handle large datasets. Indeed, for large datasets, the computation time required to obtain the visualizations is still too high to incorporate it in an interactive data exploration process. Since $t$ -SNE can be seen as an N -body problem in physics, we present a new variant of $t$ -SNE based on a popular algorithm used to solve the N -body problem in physics called Particle-Mesh (PM). The problem is solved by first computing a potential in space and deriving from it the force exerted on each body. As the potential can be computed efficiently using Fast Fourier Transforms (FFTs), this leads to a significant speed up. The mathematical correspondence between $t$ -SNE and PM presented in this work could also lead to other future improvements since more advanced PM algorithms have been developed in physics for decades.