Self-organization as an iterative kernel smoothing process
Neural Computation
GTM: the generative topographic mapping
Neural Computation
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Self-Organizing Maps
Probabilistic Principal Surfaces for Yeast Gene Microarray Data Mining
ICDM '04 Proceedings of the Fourth IEEE International Conference on Data Mining
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
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In this paper we propose using manifolds modeled by probabilistic principle surfaces (PPS) to characterize and classify high-D data. The PPS can be thought of as a nonlinear probabilistic generalization of principal components, as it is designed to pass through the “middle” of the data. In fact, the PPS can map a manifold of any simple topology (as long as it can be described by a set of ordered vector co-ordinates) to data in high-dimensional space. In classification problems, each class of data is represented by a PPS manifold of varying complexity. Experiments using various PPS topologies from a 1-D line to 3-D spherical shell were conducted on two toy classification datasets and three UCI Machine Learning datasets. Classification results comparing the PPS to Gaussian Mixture Models and K-nearest neighbours show the PPS classifier to be promising, especially for high-D data.