Active function Cross-Entropy Clustering

Gaussian Mixture Models (GMM) have many applications in density estimation and data clustering. However, the models do not adapt well to curved and strongly nonlinear data, since many Gaussian components are typically needed to appropriately fit the data that lie around the nonlinear manifold. To solve this problem we constructed the Active Function Cross-Entropy Clustering (afCEC) method, which uses Gaussians in curvilinear coordinate systems. The method has a few advantages in relation to GMM: it enables easy adaptation to clustering of complicated data sets along with a predefined family of functions and does not need external methods to determine the number of clusters, as it automatically (on-line) reduces the number of groups. Experiments on synthetic data, Chinese characters, data from UCI repository and wind turbine monitoring systems show that the proposed nonlinear model typically obtains better results than the classical methods.