By Topic

Nonlinear modeling of scattered multivariate data and its application to shape change

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
B. Chalmond ; Ecole Normale Superieure de Cachan, France ; S. C. Girard

We are given a set of points in a space of high dimension. For instance, this set may represent many visual appearances of an object, a face, or a hand. We address the problem of approximating this set by a manifold in order to have a compact representation of the object appearance. When the scattering of this set is approximately an ellipsoid, then the problem has a well-known solution given by principal components analysis (PCA). However, in some situations like object displacement learning or face learning, this linear technique may be ill-adapted and nonlinear approximation has to be introduced. The method we propose can be seen as a nonlinear PCA (NLPCA), the main difficulty being that the data are not ordered. We propose an index which favors the choice of axes preserving the closest point neighborhoods. These axes determine an order for visiting all the points when smoothing. Finally, a new criterion, called “generalization error”, is introduced to determine the smoothing rate, that is, the knot number for the spline fitting. Experimental results conclude this paper: The method is tested on artificial data and on two databases used in visual learning

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:21 ,  Issue: 5 )