Learning Multiple Local Metrics: Global Consideration Helps

Learning distance metric between objects provides a better measurement for their relative comparisons. Due to the complex properties inside or between heterogeneous objects, multiple local metrics become an essential representation tool to depict various local characteristics of examples. Different from existing methods building more than one local metric directly, however in this paper, we emphasize the effect of the global metric when generating those local ones. Since local metrics can be considered as types of amendments which describe the biases towards localities based on some commonly shared characteristic, it is expected that the performance of every single local metric for a specified locality can be "lifted" when learning with the global jointly. Following this consideration, we propose the Local metrIcs Facilitated Transformation (Lift) framework, where an adaptive number of local transformations are constructed with the help of their global counterpart. Generalization analyses not only reveal the relationship between the global and local metrics but also indicate when and why the framework works theoretically. In the implementation of Lift, locality anchored centers assist the decomposition of multiple local views, and a diversity regularizer is proposed to reduce the redundancy among biases. Empirical classification comparisons reveal the superiority of the Lift idea. Numerical and visualization investigations on different domains validate its adaptability and comprehensibility as well.