# Parametric distance metric learning with label information

### Zhihua Zhang, James T. Kwok and Dit-Yan Yeung

**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.
*Proceedings of the Eighteenth International Joint Conference on Artificial
Intelligence (IJCAI)*, pp.1450-1452, Acapulco, Mexico, August 2003.

Postscript:
http://www.cs.ust.hk/~jamesk/papers/ijcai03.ps.gz

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