A New Principal Curve Algorithm for Nonlinear Principal Component Analysis

This paper summarizes a new concept to determine principal curves for nonlinear principal component analysis (PCA). The concept is explained within the framework of the Hastie and Stuetzle algorithm and utilizes spline functions. The paper proposes a new algorithm and shows that it provides an efficient method to extract underlying information from measured data. The new method is geometrically simple and computationally expedient, as the number of unknown parameters increases linearly with the analyzed variable set. The utility of the algorithm is exemplified in two examples.