A Polygonal Line Algorithm for Constructing Principal Curves
Balázs Kégl, Adam Krzyżak, Tamás Linder, K. Zeger · 1998
Principal curves have been defined as ``self consistent'' smooth curves which pass through the ``middle'' of a $d$-dimensional probability distribution or data cloud. Recently, we \\cite{KeKrLiZe98a} have offered a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution. The new definition made it possible to carry out a theoretical analysis of learning principal curves from training data. In this paper we propose a practical construction based on the new definition. Simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity.