Data clustering based on principal curves

Abstract

In this contribution we present a new method for data clustering based on principal curves. Principal curves consist of a nonlinear generalization of principal component analysis and may also be regarded as continuous versions of 1D self-organizing maps. The proposed method implements the k-segment algorithm for principal curves extraction. Then, the method divides the principal curves into two or more curves, according to the number of clusters defined by the user. Thus, the distance between the data points and the generate curves is calculated and, afterwards, the classification is performed according to the smallest distance found. The method was applied to nine databases with different dimensionality and number of classes. The results were compared with three clustering algorithms: the k-means algorithm and the 1-D and 2-D self-organizing map algorithms. Experiments show that the method is suitable for clusters with elongated and spherical shapes and achieved significantly better results in some data sets than other clustering algorithms used in this work.