Regression-based Metric Learning

Existing distance metric learning methods define an objective function and seek a distance metric (or equivalently a projection) that minimizes it. In this paper, we propose a different approach that illustrates how to formulate distance metric learning as a regression problem. First, the objective function is minimized to learn target representations. Then, a regression method is employed to learn a projection that maps the input to the target representations. This global projection function is the single output of the proposed algorithm. Our contribution is a different perspective on how to train a distance metric learning algorithm. The advantages are: (i) this approach has the potential to simplify the optimization process; and (ii) it allows researchers to leverage the power of existing regression methods and those to be invented. Experimental results on several publicly available datasets illustrate that the proposed framework can learn a distance metric with discriminative properties.