The first linear principal component is the optimal linear 1-d summarization of the data. Principal curves are nonlinear generalizations of the first linear principal component. Principal component analysis is a linear method

but the most data are nonlinear. Sometimes the linear principal component analysis works inadequately when the data are nonlinear. In this paper

a new nonlinear analytic method

principal curve component analysis (PC~2A) is proposed. This method can model nonlinear data effectively

which analyzes the data from its inherence and emphasizes the non-parametric characteristic. And the method uses the advanced neural network to model data. This is an excellent approach for expressing the nonlinear relationship because of its universal approximation property. Experimental results show that principal curve component analysis is excellent for solving nonlinear principal component problem

and it has great applications potentials.