A General Framework for Dimensionality-Reducing Data Visualization Mapping

In recent years a wealth of dimension reduction techniques for data visualization and preprocessing has been established. Non-parametric methods require additional effort for out-of-sample extensions, because they just provide a mapping of a given finite set of points. In this contribution we propose a general view on non-parametric dimension reduction based on the concept of cost functions and properties of the data. Based on this general principle we transfer non-parametric dimension reduction to explicit mappings of the data manifold such that direct outof-sample extensions become possible. Furthermore, this concept offers the possibility to investigate the generalization ability of data visualization to new data points. We demonstrate the approach based on a simple global linear mapping as well as prototype-based local linear mappings. In addition, we can bias the functional form according to given auxiliary information. This leads to explicit supervised visualization mappings which discriminative properties are comparable to state-of-the-art approaches.