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Regularizers versus Losses for Nonlinear Dimensionality Reduction

2020-02-28 | |  40 |   47 |   0

Abstract

We demonstrate that almost all nonparametric 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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