Dimension reduction by local principal component analysis
Neural Computation
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Learning and Design of Principal Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A neural implementation of canonical correlation analysis
Neural Networks
Another look at principal curves and surfaces
Journal of Multivariate Analysis
Construction algorithm of principal curves in the sense of limit
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
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Principal Curves are extensions of Principal Component Analysis and are smooth curves, which pass through the middle of a data set. We extend the method so that, on pairs of data sets which have underlying non-linear correlations, we have pairs of curves which go through the 'centre' of data sets in such a way that the non-linear correlations between the data sets are captured. The core of the method is to iteratively average the current local projections of the data points which produces an increasingly sparsified set of nodes. The Twinned Principal Curves are generated in three ways: by joining up the nodes in order, by performing Local Canonical Correlation Analysis and by performing Local Exploratory Correlation Analysis (Koetsier et al., 2002). The latter two are shown to improve the forecasting capability of the method but at an increased computational load. We show that it is crucial to terminate the algorithm after a small number of iterations for the first method and investigate several criteria for doing so.