Colored Maximum Variance Unfolding

Part of Advances in Neural Information Processing Systems 20 (NIPS 2007)

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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.