Maximum Mean and Covariance Discrepancy for Unsupervised Domain Adaptation

Abstract

A fundamental research topic in domain adaptation is how best to evaluate the distribution discrepancy across domains. The maximum mean discrepancy (MMD) is one of the most commonly used statistical distances in this field. However, information about distributions could be lost when adopting non-characteristic kernels by MMD. To address this issue, we devise a new distribution metric named maximum mean and covariance discrepancy (MMCD) by combining MMD and the proposed maximum covariance discrepancy (MCD). MCD probes the second-order statistics in reproducing kernel Hilbert space, which equips MMCD to capture more information compared to MMD alone. To verify the efficacy of MMCD, an unsupervised learning model based on MMCD abbreviated as McDA was proposed and efficiently optimized to resolve the domain adaptation problem. Experiments on image classification conducted on two benchmark datasets show that McDA outperforms other representative domain adaptation methods, which implies the effectiveness of MMCD in domain adaptation.