Tangent-Corrected Embedding

Images and other high-dimensional data can frequently be characterized by a low dimensional manifold (e.g. one that corresponds to the degrees of freedom of the camera). Recently, nonlinear manifold learning techniques have been used 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 of any prior understanding of the dynamics we might have, relying instead on local Euclidean distances that can be misleading in image space. In practice, we frequently have some prior knowledge regarding the transformations that relate images (e.g. rotation, translation, etc). We present a method for augmenting existing embedding techniques with additional information derived from known transformations, either in the form of tangent vectors that locally characterize the manifold or distances derived from reconstruction errors. The extra information is incorporated directly into the cost function...

• Type: Conference
• Year: 2005
• Where: CVPR
• Authors: Ali Ghodsi, Jiayuan Huang, Finnegan Southey, Dale Schuurmans
• Keywords: Augmented Cost Function, Closed Form Solution, Computer Vision, CVPR 2005, Local Euclidean Distances, Low Dimensional Manifold, Manifold Learning Techniques