Dimensionality Reduction by Learning an Invariant Mapping

Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that "similar" points in input space are mapped to nearby points on the manifold. Most existing techniques for solving the problem suffer from two drawbacks. First, most of them depend on a meaningful and computable distance metric in input space. Second, they do not compute a "function" that can accurately map new input samples whose relationship to the training data is unknown. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent non-linear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distance measure in the input space. The method can learn mappings that are invariant to certain transformations of the inputs, as is demonstrated with a number of experiments. Comparisons are made ...

• Type: Conference
• Year: 2006
• Where: CVPR
• Authors: Raia Hadsell, Sumit Chopra, Yann LeCun
• Keywords: Computable Distance Metric, Computer Vision, CVPR 2006, Dimensional Input Points, Dimensionality Reduction, Input Space, Low Dimensional Manifold