Discriminative dimensionality reduction for regression problems using the Fisher metric

Discriminative dimensionality reduction refers to the goal of visualizing given high-dimensional data in the plane such that the structure relevant for a specified aspect is displayed. While this framework has been successfully applied to visualize data with auxiliary label information, its extension to real-valued information is lacking. In this contribution, we propose a general way to shape data distances based on auxiliary real-valued information with the Fisher metric which is derived from a Gaussian process model of the data. This can directly be integrated into high quality non-linear dimensionality reduction methods such as t-SNE, as we will demonstrate in artificial as well as real life benchmarks.