Constrained Metric Learning by Permutation Inducing Isometries


The selection of metric critically affects the performance of classification and clustering algorithms. Metric learning algorithms attempt to boost performance, by learning a additional acceptable metric. Unfortunately, most of the present algorithms learn a distance perform which is not invariant to rigid transformations of pictures. Therefore, the distances between two pictures and their rigidly transformed combine may differ, leading to inconsistent classification or clustering results. We propose to constrain the learned metric to be invariant to the geometry preserving transformations of images that induce permutations within the feature area. The constraint that these transformations are isometries of the metric ensures consistent results and improves accuracy. Our second contribution is a dimension reduction technique that is according to the isometry constraints. Our third contribution is that the formulation of the isometry constrained logistic discriminant metric learning (IC-LDML) algorithm, by incorporating the isometry constraints within the objective operate of the LDML algorithm. The proposed algorithm is compared with the existing techniques on the publicly offered labeled faces within the wild, viewpoint-invariant pedestrian recognition, and Toy Cars information sets. The IC-LDML algorithm has outperformed existing techniques for the tasks of face recognition, person identification, and object classification by a vital margin.

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