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arXiv · 1206.6455

Regularizers versus Losses for Nonlinear Dimensionality Reduction: A Factored View with New Convex Relaxations

Yaoliang Yu·James Neufeld·Ryan Kiros·Xinhua Zhang·Dale Schuurmans
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Abstract

We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the current literature. Beyond identifying a useful new loss for manifold unfolding, a key contribution is to derive new convex regularizers that combine distance maximization with rank reduction. These regularizers can be applied to any loss.

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Yaoliang Yu, James Neufeld, Ryan Kiros, Xinhua Zhang, Dale Schuurmans. 2012-06-27. Regularizers versus Losses for Nonlinear Dimensionality Reduction: A Factored View with New Convex Relaxations. https://arxiv.org/abs/1206.6455

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