---
title: "Continuous nonlinear dimensionality reduction by kernel Eigenmaps"
authors:
  - "Matthew Brand"
doi: ""
url: "https://ijcai.org/proceedings/2003/81"
pdf: "https://ijcai.org/proceedings/2003/0081.pdf"
venue: "Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence"
year: 2003
pages: "547-553"
track: ""
keywords:
---

# Continuous nonlinear dimensionality reduction by kernel Eigenmaps

Matthew Brand

*Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence*, pages 547-553.

## Abstract

We equate nonlinear dimensionality reduction (NLDR) to graph embedding with side information about the vertices, and derive a solution to either problem in the form of a kernel-based mixture of affine maps from the ambient space to the target space. Unlike most spectral NLDR methods, the central eigenproblem can be made relatively small, and the result is a continuous mapping defined over the entire space, not just the datapoints. A demonstration is made to visualizing the distribution of word usages (as a proxy to word meanings) in a sample of the machine learning literature.