Truly Incremental Locally Linear Embedding

Locally Linear Embedding (LLE) has been proposed by Saul and Roweis, and is an algorithm for nonlinear dimensionality reduction, belonging to the family of (unsupervised) manifold learning techniques. Manifold learning is particularly interesting, because of recent findings in neuroscience, where it is believed to be similar to the human brain’s learning process. In The Manifold Ways of Perception Sueng et al. describe this new hypothesis and LLE is suggested as one possible algorithm.
Unfortunately, no accurate incremental formulation of LLE was available to date. This is desired, if one is to use LLE in a robot, where data is coming in continuously (i.e. from a camera) and the believe has to be updated fast and regularly. Our re-formulation of the algorithm makes use of properties of Eigensolvers and achieves up to 100x speed up.

Download the paper here.
(This was joint work with Marko Durkovic, Klaus Diepold, Jürgen Scheurle and Stefan Markward)
Cite as:

@ARTICLE{schuon_ille08,
title={Truly Incremental Locally Linear Embedding},
author={Schuon, Sebastian and Durkovic, Marko and Diepold, Klaus and Scheuerle, Jürgen and Markward, Stefan},
journal={1st International Workshop on Cognition for Technical Systems},
year={2008}}