Dimensionality Reduction by Learning an Invariant Mapping

TLDR

Dimensionality reduction maps high‑dimensional data onto a low‑dimensional manifold, preserving proximity of similar points. The paper introduces DrLIM, a method for learning a globally coherent nonlinear mapping that evenly distributes data onto the output manifold. DrLIM learns a globally coherent nonlinear mapping using only neighborhood relationships, without requiring an input‑space distance metric, and is compared to techniques such as LLE. Experiments show that DrLIM learns mappings invariant to specific input transformations.

Abstract

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. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distancemeasure 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 to other techniques, in particular LLE.