Abstract Domain adaptation aims to learn an adaptive classifier for target data using the labelled source data from a different distribution. Most proposed works construct cross-domain classifier by exploring one-sided property of the input data, i.e., either geometric or statistical property. Therefore they may ignore the complementarity between the two properties. Moreover, many previous methods implement knowledge transfer with two separated steps: divergence minimization and classifier construction, which degrades the adaptation robustness. In order to address such problems, we propose a u nified c ross-domain classification method via g eometric and s tatistical adaptations (UCGS). UCGS models the divergence minimization and classifier construction in a unified way based on structural risk minimization principle and coupled adaptations theory. Specifically, UCGS constructs an adaptive model by simultaneously minimizing the structural risk on labelled source data, using Maximum Mean Discrepancy (MMD) criterion to implement statistical adaptation, and flexibly employing the Nystrom method to explore the geometric connections between domains. A domain-invariant graph is successfully constructed to link the two domains geometrically. The standard supervised methods can be used to instantiate UCGS to handle inter-domain classification problems. Comprehensive experiments show the superiority of UCGS on several real-world datasets.

中文翻译：

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通过几何和统计适应统一跨域分类

Abstract 域适应旨在使用来自不同分布的标记源数据来学习目标数据的自适应分类器。大多数提出的作品通过探索输入数据的单方面属性，即几何或统计属性来构建跨域分类器。因此，他们可能会忽略这两个属性之间的互补性。此外，许多以前的方法通过两个独立的步骤实现知识转移：散度最小化和分类器构建，这降低了自适应鲁棒性。为了解决这些问题，我们通过几何和统计适应（UCGS）提出了统一的跨域分类方法。UCGS基于结构风险最小化原理和耦合适应理论，以统一的方式对散度最小化和分类器构建进行建模。具体而言，UCGS通过同时最小化标记源数据的结构风险，使用最大平均差异（MMD）准则来实现统计自适应，并灵活地采用Nystrom方法来探索域之间的几何联系来构建自适应模型。成功构建了域不变图以几何连接两个域。标准监督方法可用于实例化 UCGS 以处理域间分类问题。综合实验表明 UCGS 在几个真实世界的数据集上的优越性。并灵活地采用 Nystrom 方法来探索域之间的几何连接。成功构建了域不变图以几何连接两个域。标准监督方法可用于实例化 UCGS 以处理域间分类问题。综合实验表明 UCGS 在几个真实世界的数据集上的优越性。并灵活地采用 Nystrom 方法来探索域之间的几何连接。成功构建了域不变图以几何连接两个域。标准监督方法可用于实例化 UCGS 以处理域间分类问题。综合实验表明 UCGS 在几个真实世界的数据集上的优越性。