Dimensionality reduction, categorized

The Canadian mathematician Leland McInnes (@leland_mcinnes), who’s known for his work on designing and popularizing the use of UMAP 1 for dimensionality reduction of single cell data, gave an insightful rundown of the key approaches of dimensionality reduction—finding matrix factorization or neighbor graphs—illustrated by the various algorithms which often feature mesmerizing names. In the talk, he mentioned the nice booklet by Udell et al 2 on low-rank modelling of high-dimensional data, which is also very worth reading.

  1. UMAP stands for uniform manifold approximation and projection and has been described here with example in a Nature Biotechnology publication and implemented in the Python package scanpy

  2. M. Udell, C. Horn, R. Zadeh and S. Boyd, Generalized Low Rank Models, Foundations and Trends in Machine Learning 9, 1–118 (2016). link from a co-author and link from arXiv.