Nearest-Manifold Classification with Gaussian Processes

Manifold models for nonlinear dimensionality reduction provide useful low-dimensional representations of high-dimensional data. Most manifold models are unsupervised algorithms and map the entire data onto a single manifold. Heterogeneous data with multiple classes are often better modeled by multiple manifolds rather than by a single global manifold, but there is no explicit way to compare instances embedded in different subspaces. We propose a novel low-to-high dimensional mapping using Gaussian processes that offers comparisons in the original space. Based on the mapping, we propose a nearest-manifold classification algorithm for high-dimensional data. Experimental results show that the proposed algorithm provides good classification accuracies for problems well-modeled by multiple manifolds.