Jenkins - ST-ISOMAP

Jenkins, O.C. and Mataric, M.J. "A spatio-temporal extension to Isomap nonlinear dimension reduction." ICML 2004.

Summary

Jenkins and Mataric present an extension to ISOMAP to take into consideration temporal data when constructing manifolds. ISOMAP is used to find embeddings in a high-dimensional space (manifolds) using geodesic distances and multi-dimensional scaling. ST-ISOMAP is an extension that uses temporal information. Items that are close to each other temporally have their spatial distances reduced.

The idea is that in some domains, like movement of an arm, things that are close together spatially might be quite different. For example, an arm moving one way might be very different than an arm moving the other way. The temporal differences between these gesture would be high because you'd arrive at the same spatial location via different temporal paths (sequences of arm locations). Likewise, seemingly different spatial locations might be very similar, and only 'close' to each other regarding temporal data (arm movements in the same direction but at different heights off the ground). ST-ISOMAP tries to capture these things.

Discussion

ISOMAP is a proven algorithm, and so is this extension for finding the manifold with temporal data. I think this could be useful for clustering of haptic gesture information. The high dimension space of the fingers+hand location could be reduced with ISOMAP into a simpler space where gestures could be segmented or classified more easily.

Maybe. Seems like a neat approach, anyhow. And ISOMAP is used for a /ton/ of stuff in machine learning, so it's not like this is a cheesy hack that no one really uses.

BibTeX

@inproceedings{jenkins2004ste,
title={{A spatio-temporal extension to Isomap nonlinear dimension reduction}},
author={Jenkins, O.C. and Matari{\'c}, M.J.},
journal={International Conference on Machine Learning},
year={2004},
publisher={ACM Press New York, NY, USA}
}