An Algorithm for Learning Principal Curves with Explicit Formulation Based on Neural Network

A new algorithm for learning principal curves with explicit formulation is proposed on the basis of artificial neural network (ANN). The algorithm successfully turns an unsupervised learning problem into a supervised one by projecting a data set to the polygonal line learned by existing algorithms of principal curves and identifying the relation between the data points and their corresponding projection indices with ANN. Convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented. Simulation results demonstrate that the new algorithm compares favorably with previous methods for its convenience in applications.