Tangent Corrected Embedding
- Ali Ghodsi, University of Waterloo
- Jiayuan Huang, University of Waterloo
- Finnegan Southey
- Dale Schuurmans, AICML
Images and other high-dimensional data can frequentlybe characterized by a low dimensional manifold (e.g. onethat corresponds to the degrees of freedom of the camera).Recently, nonlinear manifold learning techniques have beenused to map images to points in a lower dimension space,capturing some of the dynamics of the camera or the subjects.In general, these methods do not take advantage ofany prior understanding of the dynamics we might have, relyinginstead on local Euclidean distances that can be misleadingin image space.In practice, we frequently have some prior knowledgeregarding the transformations that relate images (e.g. rotation,translation, etc). We present a method for augmentingexisting embedding techniques with additional informationderived from known transformations, either in the formof tangent vectors that locally characterize the manifold ordistances derived from reconstruction errors. The extra informationis incorporated directly into the cost function ofthe embedding technique. The techniques we augment arelargely attractive because there is a closed form solution fortheir cost optimization. Our approach likewise produces aclosed form solution for the augmented cost function. Experimentsdemonstrate the effectiveness of the approach ona variety of image data.
Citation
A. Ghodsi, J. Huang, F. Southey, D. Schuurmans. "Tangent Corrected Embedding". Computer Vision and Pattern Recognition (CVPR), June 2005.| Keywords: | tangent-corrected, embedding, machine learning |
| Category: | In Conference |
BibTeX
@incollection{Ghodsi+al:CVPR05,
author = {Ali Ghodsi and Jiayuan Huang and Finnegan Southey and Dale
Schuurmans},
title = {Tangent Corrected Embedding},
booktitle = {Computer Vision and Pattern Recognition (CVPR)},
year = 2005,
}Last Updated: June 01, 2007Submitted by Staurt H. Johnson
