Learning Local Metrics and Influential Regions for Classification

The performance of distance-based classifiers heavily depends on the underlying distance metric, so it is valuable to learn a suitable metric from the data. To address the problem of multimodality, it is desirable to learn local metrics. In this short paper, we define a new intuitive distance with local metrics and influential regions, and subsequently propose a novel local metric learning method for distance-based classification. Our key intuition is to partition the metric space into influential regions and a background region, and then regulate the effectiveness of each local metric to be within the related influential regions. We learn local metrics and influential regions to reduce the empirical hinge loss, and regularize the parameters on the basis of a resultant learning bound. Encouraging experimental results are obtained from various public and popular data sets.