Adaptive Constraint K-Segment Principal Curves for Intelligent Transportation Systems

This paper revisits the construction of principal curves. Although they have a solid theoretical foundation as a nonlinear extension to principal components, this paper shows that they are difficult to implement in practice if the data distribution is sparse and uneven or if the data contain outliers. These issues may hamper the application of principal curves to an intelligent transportation system. To address these problems, this paper introduces an adaptive constraint K-segment principal curve (ACKPC) algorithm that can be applied in the presence of uneven and sparse distributions, as well as outliers. The benefits of the ACKPC algorithm are as follows: (1) It utilizes predefined endpoints of the curve to reduce the computational effort, and (2) it shows to be less sensitive to parameter settings and outliers. These benefits are demonstrated using two benchmark studies and experimental data from a freeway traffic stream system as well as recorded data from a Global Positioning System (GPS) data from a low-precision GPS receiver.