Constraint K-Segment Principal Curves

Abstract

To represent the intrinsic regularity of data, one way is to compute the “middle” curves or principal curves (PCs) across the data. However, there are difficulties for current PCs algorithms to discover some known positions that are out of the sampled range of data (Henceforth, out-of-the-samples). Based on principal curves with length constraint proposed by kégl (KPCs), we propose constraint K-segment principal curves (CKPCs) with two refinements. First, out-of-the-samples are introduced as endpoints to improve the performance of the KPCs algorithm. Second, a constraint term is proposed for removing some unexpected vertices and enhancing the stability of the KPCs algorithm. Experiments in three set of practical traffic stream data show that both the stability and the shape of the proposed CKPCs algorithm are better than those of the KPCs algorithm.