Learning a Combination of Dissimilarities from a Set of Equivalence Constraints

Applications have emerged in the last years in which several dissimilarities and data sources provide complementary information about the problem. Therefore, metric learning algorithms should be developed that integrate all this information in order to reflect better which is similar for the user and the problem at hand. In this paper, we propose a semi-supervised algorithm to learn a linear combination of dissimilarities using the a priori knowledge provided by human experts. A priori knowledge is formulated in the form of equivalence constraints. The minimization of the error function is based on a quadratic optimization algorithm. A L₂ norm regularizer is included that penalizes the complexity of the family of distances and avoids overfitting. The experimental results suggest that the method proposed outperforms a standard metric learning algorithm and improves classification and clustering results based on a single dissimilarity.