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Nonlinear Data Representation for Visual Learning

Bernard Chalmond 1 Stéphane Girard
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : We are given a set of points in a high dimensional space. For instance, this set can 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). Yet, in some situations like object deplacement learning or face learning this linear technique can be ill-adapted and nonlinear approximation must be introduced. The method we propose can be seen as a Non Linear PCA (NLPCA), the main difficulty being that the data points are not ordered. We propose an index to find projection axes encouraging the choice of axes which preserve as well as possible the structure of the closest point neighborhood. 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 spline number of knots in this case. Experimental results conclude this paper: the method is tested on artificial data and on two data sets coming from databases used in visual learning.
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Submitted on : Wednesday, May 24, 2006 - 11:57:13 AM
Last modification on : Friday, February 4, 2022 - 3:29:55 AM
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  • HAL Id : inria-00073133, version 1



Bernard Chalmond, Stéphane Girard. Nonlinear Data Representation for Visual Learning. RR-3550, INRIA. 1998. ⟨inria-00073133⟩



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