In this paper, we propose a novel variational approach for supervised classification based on transform learning. Our approach consists of formulating an optimization problem on both the transform matrix and the centroids of the classes in a low-dimensional transformed space. The loss function is based on the distance to the centroids, which can be chosen in a flexible manner. To avoid trivial solutions or highly correlated clusters, our model incorporates a penalty term on the centroids, which encourages them to be separated. The resulting non-convex and non-smooth minimization problem is then solved by a primal-dual alternating minimization strategy. We assess the performance of our method on a bunch of supervised classification problems and compare it to state-of-the-art methods.