Principal curve classifier-a nonlinear approach to pattern classification
- 27 November 2002
- proceedings article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 1, 695-700
- https://doi.org/10.1109/ijcnn.1998.682365
Abstract
This paper presents a general nonlinear approach to pattern classification using principal curves. Princi- pal curves(1) are non-parametric, nonlinear generaliza- tions of the first principal component, and may also be regarded as continuous versions of 1-D self-organizing maps (2), (3). The new classification technique, Princi- pal Curve Classifier (PCC), involves a novel way of com- puting a principal curve for each class using the class- labeled training data. An unlabeled test point is given the class-label of the principal curve that is closest to it in Euclidean distance. Preliminary experiments comparing the PCC with established classification methods, using selected datasets (originally from the UCI machine learn- ing repository(4)) from the Elena(5), (6) and Proben1(7) benchmarks , highlight the merits and limitations of this algorithm.Keywords
This publication has 16 references indexed in Scilit:
- Some theoretical results on nonlinear principal components analysisPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Limitations of nonlinear PCA as performed with generic neural networksIEEE Transactions on Neural Networks, 1998
- A class of neural networks for independent component analysisIEEE Transactions on Neural Networks, 1997
- Modeling the manifolds of images of handwritten digitsIEEE Transactions on Neural Networks, 1997
- An approach to non-linear principal components analysis using radially symmetric kernel functionsStatistics and Computing, 1996
- Self-Organization as an Iterative Kernel Smoothing ProcessNeural Computation, 1995
- A nonlinear projection method based on Kohonen's topology preserving mapsIEEE Transactions on Neural Networks, 1995
- Adaptive Principal SurfacesJournal of the American Statistical Association, 1994
- Multivariate Adaptive Regression SplinesThe Annals of Statistics, 1991
- Nonlinear principal component analysis using autoassociative neural networksAIChE Journal, 1991