In this paper we undergo a theoretical study of supervised distance metric learning, in which we show the mathematical foundations of distance metric learning and its algorithms.

For unsupervised distance metric learning or called manifold learning, the main idea is to learn an underlying low-dimensional manifold where geometric relationships (e.g. distance) between …

Our method is based on posing met-ric learning as a convex optimization problem, which allows us to give efficient, local-optima-free algorithms. We also demonstrate empirically that the …

we will introduce the distance metric learning problem. To begin with, we will remember the concept of distance, with special emphasis on hose distances that will allow us to model our …

The metric learning problem is concerned with learning a distance function tuned to a particular task, and has been shown to be use-ful when used in conjunction with nearest-neighbor …

Given some partial information of constraints, the goal of metric learning is to learn a distance metric which reports small distances for similar examples and large distances for dissimilar …

Global distance metric learning: learns a metric that applies equally over the entire input space; e.g., a metric that satisfies all pairwise constraints simultaneously.