We introduce Supervised Variational Relevance Learning (Suvrel), a variational method to determine metric tensors to define distance based similarity in pattern classification, inspired in relevance learning. The variational method is applied to a cost function that penalizes large intraclass distances and favors small interclass distances. We find analytically the metric tensor that minimizes the cost function. Preprocessing the patterns by doing linear transformations using the metric tensor yields a dataset which can be more efficiently classified. We test our methods using publicly available datasets, for some standard classifiers. Among these datasets, two were tested by the MAQC-II project and, even without the use of further preprocessing, our results improve on their performance.Center for the Study of Natural and Artificial Information Processing Systems of the University of Sao Paulo (CNAIPS, Nucleo de Apoio a Pesquisa da Universidade de Sao Paulo)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Instituto de Física, University of Sao Paulo, BrazilIBILCE, Universidade Estadual Paulista, Sao José do Rio Preto, São Paulo,