Local discriminative distance metrics ensemble learning

The ultimate goal of distance metric learning is to incorporate abundant discriminative information to keep all data samples in the same class close and those from different classes separated. Local distance metric methods can preserve discriminative information by considering the neighborhood influence. In this paper, we propose a new local discriminative distance metrics (LDDM) algorithm to learn multiple distance metrics from each training sample (a focal sample) and in the vicinity of that focal sample (focal vicinity), to optimize local compactness and local separability. Those locally learned distance metrics are used to build local classifiers which are aligned in a probabilistic framework via ensemble learning. Theoretical analysis proves the convergence rate bound, the generalization bound of the local distance metrics and the final ensemble classifier. We extensively evaluate LDDM using synthetic datasets and large benchmark UCI datasets.

► Multiple local discriminative distance metrics (LDDM) are learned to model the training space in focal vicinities.
► A new local domain-based VC-dimension is defined.
► The convergence rate bound and the generalization bound of LDDM are studied.
► The proposed LDDM is capable of dealing with multimodal distributions and noisy data.