Local Metric Learning on Manifolds with Application to Query-Based Operations

We first investigate the combined effect of data complexity, curse of dimensionality and the definition of the Euclidean distance on the distance measure between points. Then, based on the concepts underlying manifold learning algorithms and the minimum volume ellipsoid metric, we design an algorithm that learns a local metric on the lower dimensional manifold on which the data is lying. Experiments in the context of classification on standard benchmark data sets showed very promising results when compared to state of the art algorithms, and consistent improvements over the Euclidean distance in the context of query–based learning.