Adaptive Graph Embedding With Consistency and Specificity for Domain Adaptation Shaohua Teng, Member, IEEE, Zefeng Zheng, Naiqi Wu, Fellow, IEEE, Luyao Teng, and Wei Zhang Abstract—Domain adaptation (DA) aims to find a subspace, where the discrepancies between the source and target domains are reduced. Based on this subspace, the classifier trained by the labeled source samples can classify unlabeled target samples well. Existing approaches leverage Graph Embedding Learning to explore such a subspace. Unfortunately, due to 1) the interaction of the consistency and specificity between samples, and 2) the joint impact of the degenerated features and incorrect labels in the samples, the existing approaches might assign unsuitable sim- ilarity, which restricts their performance. In this paper, we pro- pose an approach called adaptive graph embedding with consis- tency and specificity (AGE-CS) to cope with these issues. AGE-CS consists of two methods, i.e., graph embedding with consistency and specificity (GECS), and adaptive graph embedding (AGE). GECS jointly learns the similarity of samples under the geomet- ric distance and semantic similarity metrics, while AGE adap- tively adjusts the relative importance between the geometric dis- tance and semantic similarity during the iterations. By AGE-CS, the neighborhood samples with the same label are rewarded, while the neighborhood samples with different labels are pun- ished. As a result, compact structures are preserved, and advanced performance is achieved. Extensive experiments on five benchmark datasets demonstrate that the proposed method per- forms better than other Graph Embedding methods. Index Terms—Adaptive adjustment, consistency and specificity, do- main adaptation, graph embedding, geometrical and semantic met- rics.    I. Introduction A large amount of data from different domains is required to train a robust classification model. However, in some emerging target domains, only a small amount of labeled data is available, which is insufficient to learn critical classifica- tion knowledge. Moreover, it is time-consuming and costly to manually collect labeled data. In the light of these problems, domain adaptation (DA) is proposed to utilize labeled sam- ples from a well-known domain (the source domain) to tag unlabeled samples from the emerging domain (the target domain) [1]. Up to now, DA has been widely applied to vari- ous fields, e.g., infection detection [2], [3], disease detection [4], anomaly detection [5]–[7], emotion recognition [8], and visual localization [9]. The primary nature of DA is to learn a projected subspace, where the discrepancies between the source and target domains are reduced [1], [10]. Based on a learned subspace, the classifier can properly classify the unlabeled target sam- ples by utilizing the source knowledge. Recently, some researchers adopt local structure preserva- tion to align the distributions [11]–[13]. These methods con- struct a similarity matrix by measuring the geometric distance of samples, so as to preserve a local structure of the domains. However, here are still two issues to be addressed. 1) The Existing Methods Neglect the Interactions of the Consistency and Specificity Between Samples: The consis- tency denotes the common properties between samples, while specificity denotes specific properties of different samples. For example, the same category and common features of two samples might contribute to their consistency, while different categories and specific features of two samples might con- tribute to their specificity. In this case, there exist four possi- ble relationships between two samples: a) a number of com- mon features with the same category; b) a number of com- mon features with different categories; c) a number of spe- cific features with the same category; and d) a number of spe- cific features with different categories. Since most existing works measure similarity by geometric distance, they might connect the samples a) and b) with larger weights, and the samples c) and d) with smaller weight. As a result, the samples b) and c) are weighted inappropriately, and performance is limited. As revealed by [14], the consistency degree of a system reflects whether the projection is reliable or not. The result of having low consistency makes the knowl- edge of a model more unstable, which is not what we want. In order to achieve high consistency, an improved strategy should be used to measure the consistency and specificity between samples appropriately. 2) The Existing Methods Overlook Noise Samples That Con- Manuscript received March 20, 2022; revised May 12, 2022 and July 21, 2022; accepted August 20, 2022. This work was supported in part by the Key- Area Research and Development Program of Guangdong Province (2020B0 10166006), the National Natural Science Foundation of China (61972102), the Guangzhou Science and Technology Plan Project (023A04J1729), and the Science and Technology development fund (FDCT), Macau SAR (015/2020/ AMJ). Recommended by Associate Editor Xin Luo. (Corresponding author: Luyao Teng.) Citation: S. H. Teng, Z. F. Zheng, N. Q. Wu, L. Y. Teng, and W. Zhang, “Adaptive graph embedding with consistency and specificity for domain adaptation,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2094–2107, Nov. 2023. S. H. Teng, Z. F. Zheng, and W. Zhang are with the School of Computer Science and Technology, Guangdong University of Technology, Guangzhou 510006, China (e-mail: shteng@gdut.edu.cn; 2112005001@mail2.gdut.edu. cn; weizhang@gdut.edu.cn). N. Q. Wu is with the Institute of Systems Engineering and Collaborative Laboratory for Intelligent Science and Systems, Macau University of Science and Technology, Macao 999078, China (e-mail: nqwu@must.edu.mo). L. Y. Teng is with the School of Information Engineering, Guangzhou Panyu Polytechic, Guangzhou 511483, China, and also with the Faculty of Information Technology, Monash University, 20 Exhibition Walk Clayton, VIC 3800, Australia (e-mail: tengly@gzpyp.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2023.123318 2094 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 10, NO. 11, NOVEMBER 2023