Discriminative Dimensionality Reduction for the Visualization of Classifiers

Modern nonlinear dimensionality reduction offers powerful techniques to directly inspect high dimensional data in the plane. Since the task of data projection is generally ill-posed and information loss cannot be avoided while projecting, the quality and meaningfulness of the outcome is not clear. In this contribution, we argue that discriminative dimensionality reduction, i. e. the concept to enhance the dimensionality reduction technique by supervised label information, offers a principled way to shape the outcome of a dimensionality reduction technique. We demonstrate the capacity of this approach for benchmark data sets. In addition, based on discriminative dimensionality reduction, we propose a pipeline how to visualize the function of general nonlinear classifiers in the plane. We demonstrate this approach by providing a generic visualization of the function of support vector machine classifiers.