Coordinated Local Metric Learning

Abstract

Mahalanobis metric learning amounts to learning a linear data projection, after which the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> metric is used to compute distances. To allow more flexible metrics, not restricted to linear projections, local metric learning techniques have been developed. Most of these methods partition the data space using clustering, and for each cluster a separate metric is learned. Using local metrics, however, it is not clear how to measure distances between data points assigned to different clusters. In this paper we propose to embed the local metrics in a global low-dimensional representation, in which the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> metric can be used. With each cluster we associate a linear mapping that projects the data to the global representation. This global representation directly allows computing distances between points regardless to which local cluster they belong. Moreover, it also enables data visualization in a single view, and the use of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -based efficient retrieval methods. Experiments on the Labeled Faces in the Wild dataset show that our approach improves over previous global and local metric learning approaches.