Learning principal curves inside divide-and-combine framework

This paper proposes a divide-and-combine learning framework for finding principal curves. The framework is based on the definition of K principal curves. It consists of two phases: divide phase and combine phase. Divide phase finds appropriate division for the distribution under the constraints of two necessary conditions. Then the combine phase combines the representations of the division components into a principal curve according to the neighbor relationship between these components. Through the operations of these two phases, the framework reaches the object of K principal curves and solves the main problems in other methods in learning K principal curves. In practice, a variety of algorithms can be generated by specializing the learning framework for different problem domains. Clustering principal curve algorithm is one of these algorithms specialized from the framework by some simplest definitions and algorithms. Experimental results illustrate the outstanding performance of the clustering principal curve algorithm compared to other existing approaches.