Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)
Le Song, Arthur Gretton, Karsten Borgwardt, Alex Smola
Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximiz- ing the variance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distance- preserving constraints. This general view allows us to design “colored” variants of MVU, which produce low-dimensional representations for a given task, e.g. subject to class labels or other side information.