Local discriminative distance metrics and their real world applications

The ultimate goal of distance metric learning is to use discriminative information to keep data samples in the same class close, and those in different classes separate. Local distance metric methods can preserve discriminative information by considering neighborhood influence. We propose a discriminative distance metric approach by maximizing local pair wise constraints. Based on the local learning framework, we then extend this approach to a multiple metrics approach, local discriminative distance metrics (LDDM), by learning distance metrics on the local vicinity of each training sample. This extension avoids the global optimization for irrelevant pair wise constraints and can thus maximize the discriminative information in each local area. Theoretical analysis for the error bound of the proposed methods has been provided. In addition, we have studied three challenging real-world problems: crater detection, crime prediction, and accelerometer based activity recognition. We design and apply three local distance learning metrics to achieve the best performance for each particular task.