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. We present amethod - called Dimensionality Reduction by Learning anInvariant Mapping (DrLIM) - for Learning a globally co-herent non-linear function that maps the data evenly to theoutput manifold. The Learning relies solely on neighbor-hood relationships and does not require any distance mea-sure in the input space.
A contrastive loss function is employed to learn the param-eters W of a parameterizedfunction GW, in such a way that neighborsare pulled togetherand non-neighborsare pushed apart. Priorknowledgecan beused to identifythe neighbors for each training data point. The method uses an energy based model that uses the
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