The Minimum Volume Ellipsoid Metric

We propose an unsupervised “local learning” algorithm for learning a metric in the input space. Geometrically, for a given query point, the algorithm finds the minimum volume ellipsoid (MVE) covering its neighborhood which characterizes the correlations and variances of its neighborhood variables. Algebraically, the algorithm maximizes the determinant of the local covariance matrix which amounts to a convex optimization problem. The final matrix parameterizes a Mahalanobis metric yielding the MVE metric (MVEM). The proposed metric was tested in a supervised learning task and showed promising and competitive results when compared with state of the art metrics in the literature.