A Polygonal Line Algorithm for Constructing Principal Curves

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 [1] 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.

• Type: Conference
• Year: 1998
• Where: NIPS
• Authors: Balázs Kégl, Adam Krzyzak, Tamás Linder, Kenneth Zeger
• Keywords: Continuous Curves, NIPS 1998, NIPS 2007, Principal Curves, Smooth Curves