# Distance Metric Learning with Application to Clustering with Side-Information

- 2002

#### Abstract

Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many " plausible " ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider " similar. " For instance, we may ask them to provide examples. In this paper, we present an algorithm that, given examples of similar (and, if desired, dissimilar) pairs of points in ¢ ¤ £ , learns a distance metric over ¢ ¥ £ that respects these relationships. Our method is based on posing metric learning as a convex optimization problem, which allows us to give efficient, local-optima-free algorithms. We also demonstrate empirically that the learned metrics can be used to significantly improve clustering performance.

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