Parametric Distance Metric Learning with Label Information

Abstract

Distance-based methods in pattern recognition and machine learning have to rely on a similarity or dissimilarity measure between patterns in the input space. For many applications, Euclidean distance in the input space is not a good choice and hence more complicated distance metrics have to be used. In this paper, we propose a parametric method for metric learning based on class label information. We first define a dissimilarity measure that can be proved to be metric. It has the favorable property that between-class dissimilarity is always larger than within-class dissimilarity. We then perform parametric learning to find a regression mapping from the input space to a feature space, such that the dissimilarity between patterns in the input space is approximated by the Euclidean distance between points in the feature space. Parametric learning is performed using the iterative majorization algorithm. Experimental results on real-world benchmark data sets show that this approach is promising.