Relevance Learning for Dimensionality Reduction

Nonlinear dimensionality reduction (NLDR) techniques offer powerful data visualization schemes capturing nonlinear effects of the data at the costs of a decreased interpretability of the projection: Unlike for linear counterparts such as principal component analysis, the relevance of the original feature dimensions for the NLDR projection is not clear. In this contribution we propose relevance learning schemes for NLDR which enable to judge the relevance of a feature dimension for the projection. This technique can be extended to a metric learning scheme which opens a way to imprint the information as provided by a given visualization on the data representation in the original feature space.