Stochastic Neighbor Embedding
This project focused on the underlying similarities of the t-SNE and UMAP algorithms for nonlinear dimension reduction. t-SNE (t distributed stochastic neighbor embedding) was first released by van der Marteen et. all in 2008; UMAP was released a decade later in 2018 by McGinnes et. all. Unsurprisingly, UMAP generally performs better, both with global and local embeddings, as well as having far superior performance. What was most interesting to me was the mathematical commonality behind the two algorithms, despite the large differences in how they were framed. In particular, the authors of t-SNE used techniques from probability, stochastics, and information theory to motivate their process, whereas the authors of UMAP appealed to graph theory and topology. In addition to comparing the algorithms’ mathematical underpinnings, I wrote (from the ground up) a basic implementation of stochastic neighbor embedding, the general technique both processes are based on.