A Polygonal Line Algorithm for Constructing Principal Curves

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Balázs Kégl, Adam Krzyzak, Tamás Linder, Kenneth Zeger


Principal curves have been defined as "self consistent" smooth curves which pass through the "middle" of a d-dimensional probability distri(cid:173) bution 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.