Transcription of Dimensionality Reduction by Learning an Invariant Mapping
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Dimensionality Reduction by Learning an Invariant Mapping
Dimensionality Reduction by Learning an Invariant MappingRaia Hadsell, Sumit Chopra, Yann LeCunThe Courant Institute of Mathematical SciencesNew York University, 719 Broadway, New York, NY 1003, yann(November 2005. To appear in CVPR 2006)AbstractDimensionality Reduction involves Mapping a set of highdimensional input points onto a low dimensional mani-fold so that similar points in input space are mapped tonearby points on the manifold. Most existing techniques forsolving the problem suffer from two drawbacks. First, mostof them depend on a meaningful and computable distancemetric in input space. Second, they do not compute a func-tion that can accurately map new input samples whose re-lationship to the training data is unknown.
is not constrained by simple distance measures in the input space. The learning architecture is somewhat similar to the one discussed in [4, 5]. Section 2 describes the generalframework,the loss func-tion, and draws an analogy with a mechanical spring sys-tem. The ideas in this section are made concrete in sec-tion3.
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