Guided Locally Linear Embedding

Authors:
Babak Alipanahi;Ali Ghodsi
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1;Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Venue:
Pattern Recognition Letters
Year:
2011

Citing 14
Cited 1

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Abstract

Nonlinear dimensionality reduction is the problem of retrieving a low-dimensional representation of a manifold that is embedded in a high-dimensional observation space. Locally Linear Embedding (LLE), a prominent dimensionality reduction technique is an unsupervised algorithm; as such, it is not possible to guide it toward modes of variability that may be of particular interest. This paper proposes a supervised variation of LLE. Similar to LLE, it retrieves a low-dimensional global coordinate system that faithfully represents the embedded manifold. Unlike LLE, however, it produces an embedding in which predefined modes of variation are preserved. This can improve several supervised learning tasks including pattern recognition, regression, and data visualization.