Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts, most commonly expressed in the form of cannot-link and must-link constraints. In this setting, distance metric learning algorithms move closer pairs of data points involved in must-link constraints, while pairs of points involved in cannot-link constraints are moved away from each other. For these algorithms to be effective, it is important to use a distance metric that matches the expert knowledge, beliefs, and expectations, and the transformations made to stick to the side-information should preserve geometrical properties of the dataset. Also, it is interesting to filter the constraints provided by the experts to keep only the most useful and reject those that can harm the clustering process. To address these issues, we propose to exploit the dual information associated with the pairwise constraints of the semi-supervised clustering problem. Experiments clearly show that distance metric learning algorithms benefit from integrating this dual information.
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