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 algorithm called LMLIR 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 multiple 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.

Currently, few-shot learning (FSL) is widely used in image classification (HSIC), owing to its exceptional proficiency in achieving good performance with few training samples. Although the FSL has made good progress, there are still some problems to be solved. On the one hand, existing methods rely on linear distance to learn metrics, which cannot capture the subtle similarities and differences between scarce prior samples. On the other hand, many current methods directly superimpose the features of spatial and spectral information, without deeply fusing the internal relationship between these two kinds of information. To address the aforementioned issues, a deep metric learning method based on Brownian distance covariance (DML-BDC) is proposed for few-shot HSIC. A dual-channel Brownian distance covariance feature extraction network is designed, which uses the Brownian covariance representation to model and fuse the spatial and spectral information, and uses two different feature extractors to achieve the effect of information complementarity. Then, a metric loss based on Gaussian kernel distance is proposed to learn the complex nonlinear structure and subtle similarities and differences between support samples. Experiments on three benchmark datasets show that DML-BDC has advantages over the existing mainstream methods in terms of classification accuracy, generalization, and model complexity.