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Colored Maximum Variance Unfolding
Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing 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 distancepreserving 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.
@inproceedings{4929, title = {Colored Maximum Variance Unfolding}, journal = {Advances in Neural Information Processing Systems 20: 21st Annual Conference on Neural Information Processing Systems 2007}, booktitle = {Advances in neural information processing systems 20}, abstract = {Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing 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 distancepreserving 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.}, pages = {1385-1392}, editors = {Platt, J. C., D. Koller, Y. Singer, S. Roweis}, publisher = {Curran}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, address = {Red Hook, NY, USA}, month = sep, year = {2008}, slug = {4929}, author = {Song, L. and Smola, AJ. and Borgwardt, K. and Gretton, A.}, month_numeric = {9} }