Joint Distribution Matters: Deep Brownian Distance Covariance for Few-Shot Classification

Few-shot classification is a challenging problem as only very few training examples are given for each new task. One of the effective research lines to address this challenge focuses on learning deep representations driven by a similarity measure between a query image and few support images of some class. Statistically, this amounts to measure the dependency of image features, viewed as random vectors in a high-dimensional embedding space. Previous methods either only use marginal distributions without considering joint distributions, suffering from limited representation capability, or are computationally expensive though harnessing joint distributions. In this paper, we propose a deep Brownian Distance Covariance (DeepBDC) method for few-shot classification. The central idea of DeepBDC is to learn image representations by measuring the discrepancy between joint characteristic functions of embedded features and product of the marginals. As the BDC metric is decoupled, we formulate it as a highly modular and efficient layer. Furthermore, we instantiate DeepBDC in two different few-shot classification frameworks. We make experiments on six standard few-shot image benchmarks, covering general object recognition, fine-grained categorization and cross-domain classification. Extensive evaluations show our DeepBDC significantly outperforms the counterparts, while establishing new state-of-the-art results. The source code is available at http://www.peihuali.org/DeepBDC