Computational Statistics & Data Analysis
Probabilistic Visual Learning for Object Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear Modeling of Scattered Multivariate Data and Its Application to Shape Change
IEEE Transactions on Pattern Analysis and Machine Intelligence
Another look at principal curves and surfaces
Journal of Multivariate Analysis
Multispace KL for Pattern Representation and Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-linear dimensionality reduction techniques for classification and visualization
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Neural Processing Letters
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In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatter-plot by a differentiable manifold. In this paper, they are interpreted as Projection pursuit models adapted to the autoassociative case. Their theoretical properties are established and are shown to extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.