Probabilistic Principal Surface Classifier

In this paper we propose using manifolds modeled by probabilistic principle surfaces (PPS) to characterize and classify high-D data. The PPS can be thought of as a nonlinear probabilistic generalization of principal components, as it is designed to pass through the “middle” of the data. In fact, the PPS can map a manifold of any simple topology (as long as it can be described by a set of ordered vector co-ordinates) to data in high-dimensional space. In classification problems, each class of data is represented by a PPS manifold of varying complexity. Experiments using various PPS topologies from a 1-D line to 3-D spherical shell were conducted on two toy classification datasets and three UCI Machine Learning datasets. Classification results comparing the PPS to Gaussian Mixture Models and K-nearest neighbours show the PPS classifier to be promising, especially for high-D data.