On UMAP's true loss function release_gfa3ncuqdnc6vaypbw2lcgztrm

by Sebastian Damrich, Fred A. Hamprecht

Released as a article .

2021  

Abstract

UMAP has supplanted t-SNE as state-of-the-art for visualizing high-dimensional datasets in many disciplines, but the reason for its success is not well understood. In this work, we investigate UMAP's sampling based optimization scheme in detail. We derive UMAP's effective loss function in closed form and find that it differs from the published one. As a consequence, we show that UMAP does not aim to reproduce its theoretically motivated high-dimensional UMAP similarities. Instead, it tries to reproduce similarities that only encode the shared k nearest neighbor graph, thereby challenging the previous understanding of UMAP's effectiveness. Instead, we claim that the key to UMAP's success is its implicit balancing of attraction and repulsion resulting from negative sampling. This balancing in turn facilitates optimization via gradient descent. We corroborate our theoretical findings on toy and single cell RNA sequencing data.
In text/plain format

Archived Files and Locations

application/pdf  6.8 MB
file_zaupwb36srffbdzzy2o7gnqrm4
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2021-04-22
Version   v2
Language   en ?
arXiv  2103.14608v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 0ccfd505-45d7-433f-bc91-38b368a4f502
API URL: JSON