A global structure-based algorithm for detecting the principal graph from complex data

Abstract

Principal curves arising as an essential construct in dimensionality reduction and pattern recognition have recently attracted much attention from theoretical as well as practical perspective. Existing methods usually employ the first principal component of the data as an initial estimate of principal curves. However, they may be ineffective when dealing with complex data with self-intersecting characteristics, high curvature, and significant dispersion. In this paper, a new method based on global structure is proposed to detect the principal graph—a set of principal curves from complex data. First, the global structure of the data, called an initial principal graph, is extracted based on a thinning technique, which captures the approximate topological features of the complex data. In terms of the characteristics of the data, vertex-merge step and the improved fitting-and-smoothing phase are then proposed to control the deviation of the principal graph and improve the process of optimizing the principal graph. Finally, the restructuring step introduced by Kégl is used to rectify imperfections of the principal graph. By using synthetic and real-world data sets, the proposed method is compared with other existing algorithms. Experimental results show the effectiveness of the global structure based method.