SPA: A Graph Spectral Alignment Perspective for Domain Adaptation
Authors: Zhiqing Xiao
Haobo Wang
Ying Jin
Lei Feng
Gang Chen
Fei Huang
Junbo Zhao
Venue: NeurIPS 2023 poster (2023)
Keywords: Domain Adaptation
Self-training
Graph Spectra

Abstract: Unsupervised domain adaptation (UDA) is a pivotal form in machine learning to extend the in-domain model to the distinctive target domains where the data distributions differ. Most prior works focus on capturing the inter-domain transferability but largely overlook rich intra-domain structures, which empirically results in even worse discriminability. In this work, we introduce a novel graph SPectral Alignment (SPA) framework to tackle the tradeoff. The core of our method is briefly condensed as follows: (i)-by casting the DA problem to graph primitives, SPA composes a coarse graph alignment mechanism with a novel spectral regularizer towards aligning the domain graphs in eigenspaces; (ii)-we further develop a fine-grained message propagation module --- upon a novel neighbor-aware self-training mechanism --- in order for enhanced discriminability in the target domain. On standardized benchmarks, the extensive experiments of SPA demonstrate that its performance has surpassed the existing cutting-edge DA methods. Coupled with dense model analysis, we conclude that our approach indeed possesses superior efficacy, robustness, discriminability, and transferability. Code and data are available at: https://github.com/CrownX/SPA.

SPA: A Graph Spectral Alignment Perspective for Domain Adaptation
Zhiqing Xiao Haobo Wang" Ying Jin', Lei Feng", Gang Chen 13 Fei Huang", Junbo Zhao 13+
College of Computer Science and Technology. Zhejiang University
School of Software Technology, Zhejiang University
3 Key Lab of Intelligent Computing based Big Data of Zhejiang Province, Zhejiang University
CUHK-S Sene--SSneeimmn Joint Lab, The Chinese University of Hong Kong
5 School of Computer Science and Engineering, Nanyang Technological University Allibaba Group
{zhiqing xiao, wanghaobo, cg, j. zhao JZjju. @wj..edu..u........... edu. cn, (sherryying003, lfengqaq, feirhuang) Saapnngg@mmall...mmmmm com
Abstract
Unsupervised domain adaptation (UDA) a pivotal form in machine learning to extend the in-domain model to the distinetive target domains where the data distri- butions differ. Most prior works focus on capturing the inter-domain transferability but largely overlook rich intra-domain structures, which empirically results in even worse discriminability. In this work, we introduce a novel graph SPectral Align- ment (SPA) framework to tackle the tradeoff. The core of method is briefly condensed as follows: (i)-by casting the DA problem to graph primitives, SPA composes coarse graph alignment mechanism with novel spectral regularizer towards aligning the domain graphs in eigenspaces; (ii)-we further develop a fine- grained message propagation module upon novel neighbor-aware self-training mechanism - in order for enhanced discriminability in the target domain. On standardized benchmarks, the extensive experiments of SPA demonstrate that its performance has surpassed the existing outting-edge DA methods. Coupled with dense model analysis, we conclude that our approach indeed possesses superior ficacy, robustness, discriminability, and transferability. Code and data are available at: htttps://githtii Com/CroonX//SP
Introduction
Domain adaptation (DA) problem is widely studied area in computer vision field 20
19
73 65 40
which aims to transfer knowledge from label-rich source domains to label-scare target domains where dataset shift [32] domain shift [72] exists. The existing unsupervised domain adaptation (UDA) methods usually explore the idea of learning domain-invariant feature representations based on the theoretical analysis 3 These methods can be generally categorized several types, i.e., moment
matching methods 44
70 and adversarial learning methods [18 66 19 52].
The most essential challenge of domain adaptation is how to find suitable utilization of intra-domain information and inter-domain information to properly align target samples. More specifically, trade-off between discriminating data samples of different categories within domain to the greatest extent possible, and learning transferable features across domains with the existence of domain shift. To achieve this, adversarial learning methods implicitly mitigate the domain shift by driving the feature extractor to extract indistinguishable features and fool the domain classifier.
Cooresponding author.
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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The adversarial DA methods have been increasingly developed and followed by a series of works very unexpected that the remarkable transferability of DANN [8] is
[4 45 [ However, enhanced at the expense of worse discriminability [10 38
To mitigate this problem, there is a promising line of studies that explore graph-based UDA algorithms 87877 54]. The core idea is to establish correlation graphs within domains and leverage the rich topological information connect inter-domain samples and decrease their distances. In this way, self-correlation graphs with intra-domain information are constructed, which exhibits the homophily property whereby nearby samples tend to receive similar predictions [55]. There comes the problem that is how to transfer the inter-domain information with these rich topological information. Graph matching is a direct solution to inter-domai alignment problems. Explicit graph matching methods are usually designed to find sample mapping relations, requiring multiple matching stages for nodes and edges respectively [9, or complicated structure mapping with an attention matrix (54]. Despite the promise, we find that such a point- wiiet matching strategy can be restrictive and inflexible. In effect, UDA does not require an exact mapping plan from one node to another one in different domains. Its expectation is align the entire feature space such that label information of source domains can be transferred and utilized in target domains.
In this work, we introduce a novel graph spectral alignment perspective for UDA, hierarchically solving the aforementioned problem. In a nutshell, our method encapsulates a coarse graph alignment module and fine iine-graind message propagation module, jointly balancing and intra-domain discriminability. Core to our method, we propose a novel spectral regularizer that projects domain graphs into eigenspaces and aligns them based on their eigenvalues. This gives rise to coarse-grained topological structures transfer across domains but in a more intrinsic way than restrictive point-wise matching. Thereafter, we perform the fine- finegrained message passing in the target domain via a neighbor-award self-training mechanism. By then, our algorithm is able to refine the transferred topological structure to produce discriminative domain classifier.
transferability
We conduct extensive evaluations on several benchmark datasets including DomainNet, OfficeHome, Office31, and VisDA2017. The exprimental results show that our method consistently outperforms existing state-of-the-arr art domain adaptation methods, improving the accuracy on 8.6% on original DomainNet dataset and about 2.6% on OfficeHome dataset. Furthermore. the comprehensive model analysis demonstrates the the superiority of our method in efficacy, robustness, discriminability and transferability.
2 Preliminaries
Problem Description. Given source domain data D, = f(x (() of N, labeled samples associated with C2 categories from X, x V/ and target domain data Dj = { of N, unlabeled samples associated with C, categories from X, We assume that the domains share the same feature and label space but follow different marginal data distributions, following the Covariate Shift [67] that is, P (Xx)) * P (X)) but P (),, Xx) P (D: X2). Domain adaptation just occurs when the underlying distributions corresponding to the source and target domains in the shared label space are different but similar enough to make sense the transfer [5]. The goal of unsupervised domain adaptation is to predict the label {uf) )-) in the target domain, where yf E Vr. and the source task is X, + }/, assumed be the same with the target task X, + V,.
Adversarial Domain Adaptation. The family of adversarial domain adaptation methods, egg., Domain Adversarial Neural Network (DANN) (18) have become significantly influential in domain adaptation. The fundamental idea behind is to learn transferable features that explicitly reduce the domain shift. Similar to standard supervised classification methods, these approaches include a feature extractor F(-) and a category classifier C(-). Additionally, a domain classifier D(-) is trained distinguish the source domain from the target domain and meanwhile the feature extractor F(-) is trained to confuse the domain classifier and Iearn domain-invarian invariant features. The supervised classification loss Ldss and domain adversarial loss Lade are presented as bellow:
Less = E (et.vt) Lee (C (F (xt)), vi)
Ladv E =F(())) log [ (F (x:))]
(1)
+ FF((t))D log [1 D (F (x))

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where D, and Dr denote the induced feature distributions of D, and D; respectively, and (ce is the cross-entropy loss function.
Methodology
In this section, we will give specific introduction to our approach. The overall pipeline is shown in Figure Our method is able effectively utilize both intra-domain and inter-domain relations simultaneously for domain adaptation tasks. Specifically, based on our constructed dynamic graphs in Section 3.T we propose novel framework that utilizes graph spectra to align inter-domain relations in Section 3.2 and leverages intra-domain relations via neighbor-aware propagation mechanism in
Section 3.3 Our approach enables us to effectively capture the underlying domain distributions while ensuring that the learned features are transferable across domains.
i ......> L Lgs
Graph Spectral Alignment
Xs
F(-)
D(-)
adv
Xt
Lmap
Ve.Ye
Neighbor- Aware Propagation
Lls
C(-)
Memory
Memory update
Ltotal
cls + Ladv + Lgs + Lnap
Figure I: The overall architecture. The final objective integrates supervised classification loss Leie. domain adversarial loss Ladv. neighbor- aware propagation loss Lnap. and graph spectral alignment loss Lapa-
3.1 Dynamic Graph Construction
Images and text data inherently contain rich sequential or spatial structures that can be effectively represented using graphs. By constructing graphs based on the data, both intra-domain relations and inter-domain relations can be exploited. For instance, semantic and spatial relations among detected objects in image [43), cross-modal relations among images and sentences [Л]. cross- domain relations among images and texts [ 27 have been successfully modeled using graph-based representations. In this paper, leveraging self-correlation graphs enables to model the relations between different samples within domain and capture the underlying data distributions.
Our self-correlation graphs are constructed on source features and target features respectively. A feature extractor F-) can be designed learn source features fs and target features fe from source domain samples and target domain samples respectively, i.e., f. F(x.)) and ft F(x;) Given the extracted features fs. we aim to construct undirected and weighted graph G. (V., E.). Each vertex v; E Ve is represented by feature vector f. Each weighted edge eij È, can be formulated as a relation between a pair of entities 8(f"", fÿ), where ó(-) denotes metric function. With the extracted features ft, another graph 9. = (V,, Eg) can constructed that both fa and keep evolving along with the update of parameter O during the training process. Their adjacency matrices are denoted as A, and A, respectively. As well-known, the adjacency matrix of graph contains all of its topological information. By representing these graphs in domain adaptation tasks, we can directly obtain the intra-domain relations and regard inter-domain alignment graph matching problem 9
same way. Note
3.2 Graph Spectral Alignment
In this section, we will introduce how to align inter-domain relations for source domain graphs and target domain graphs. In domain adaptation scenarios where domain shift exits, if we directly construct graph with source and target domain features together, we can only obtain graph beyond the homophily assumption. In this way, necessary domain alignment comes out.

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As stated in Section 3.1 based on our correlation graphs, the inter-domain alignment can be regard as a graph matching problem. Explicit graph matching methods aim find a one-to-one correspondence between nodes or edges of two graphs and typically involve solving a combinatorial optimization problem for node matching and edge matching respectively [9] Nevertheless, our goal often to align the distributions of the source and target domains and learn of requiring such an complicated matching approach. Therefore, we prefer a implicit graph alignment method, avoiding multiple stages of explicit graph matching.
features, instead
The distance between the spectra of graphs able to measure how far apart the spectrum of graph with n vertices can be from the spectrum of any other graph with n vertices [ [9 22). leading to simplification of measuring the discrepancy of graphs. Inspired by this, we give the definitions of graph laplacians and spectral distances:
Definition 1. (GRAPH LAPLACIANS (77)). Let G (V,E) ) be a finite graph with vertices and weighted edges E. Let Φi V + R be a function of the vertices taking values in a ring and E R. be a weighting function of weighed edges. Then, the graph Laplacian acting on & and 7 is defined by
(A,0)(0) = Σ
Twlld()) - [((w]
w:d(w,r)=1
where d((u (w. v) is the graph distance between vertices w and 0, and "woo is the weight value on the edge we E E.
Definition 2. (SPECTRAL. DISTANCES). Given two simple and nonisomorphic graphs G. and G. on n. vertices with the spectra of Laplacians A, (X{) with X > 2 ... X and
A = (1 with X X₂ 2 X, respectively. Define the spectral distance between G, and G. as
(G,, |A, - Aelpp: p21
For simple undirected graph with a finite number of vertices and edges, the definition is just identical to the Laplacian matrix. With the adjacency matrix A, of source domain graph 9., we can obtain its Laplacian matrix L, and its Laplacian eigenvalues A,. Similarly, we yield Laplacian matrix L, and Laplacian eigenvalues A.. Following the definition Def[2, we can calculate the spectral distances between source domain graph G. and target domain Gr, and thus the graph spectral penalty defined as bellow:
gys = oGs,
(2)
This spectral penalty measures the discrepancy of two graphs on spectrum space. Minimizing this penalty decreases the distance of source domain graphs and target domain graphs. can also be regarded as regularizer and easy to combine with existing domain adaptation methods.
More Insights. Graph Laplacian filters are a type signal processing filter to apply a smoothing operation to the signal on a graph by taking advantage of the local neighborhood structure of the graph represented by the Laplacian matrix [6]. A graph filter can be denoted (f * g)g Ug U f. where f is signal on graph G, and A and U is the eigenvalues and eigenvectors of Laplacian matrix
L UAUT. This filer also the foundation of classic graph neural networks 77 [6] 36) and usually infers the labels of unlabeled nodes with the information from the labeled ones in a graph. Similar to the hypothesis in (91), source features and target features will be aligned into the same eigenspace along with the learning process and finally only differs slightly in the eigenvalues ga-
3.3 Neighbor-aware Propagation Mechanism
In this section, we will introduce how to exploit intra-domain relations within target domain graphs. The well-trained source domain naturally forms tight clusters in the latent space. After aligning via the aforementioned graph spectral penalty, the rich topological information coarsely transferred to the target domain. To perform the fine-grained intra-domain alignment, we take a further step by encouraging message propagation within the target domain graph.
Intuitively, we adopt the weighted N-Nearest-Neighhor (KNN) classification algorithm ate pseudo-label for target domain graph. We focus on unlabelled target samples {x1) and thus
83
to gener-
N;
omit the domain subscript for clarity. Let p; C (F (ax)) denotes the Ca-dimensional prediction of unlabelled target domain sample 2; and p." denotes its mapped probability stored in the memory

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bank. A vote is obtained from the top k nearest labelled samples for each unlabelled sample E x, which is denoted N₁. The vote of each neighbor j E ., weighted by the corresponding predicted probabilities Pj.c that data sample 2j will be identified as category c. Therefore, the voted probability Pi,c of data sample xy corresponding to class c can be defined as qi,e Ljti.JEN, Pje and we yield
the normalized probability 9r. = gt.e/ Emm1 9.m and the pseudo-labed ğ for data sample x; can be calculated as O = arg max, 9i.c. Considering different neighborhoods NV lie in different local density, we should expect larger weight for the target data in higher local density [88] Obviously, a larger qi.e means the data sample lies in a neighborhood of higher density. In this way. we directly utilize the category-normalizn probability Os.c as the confidence value for each pseudo-label and thus the weighted cross-entropy loss based on the pseudo-labels is formulated as:
Lnap -
Ei G..g log Pt.g: N
where is the coefficient term properly designed to grow along with iterations to mitigate the noises in the pseudo-labels early iterations and avoid the error accumulation [39.. Note that our neighbor-aware propagation loss only depends on unlabeled target data samples, just following the classic self-training method 31
Memory Bank. We design the memory bank to store prediction probabilities and their associated feature vectors mapped by their target data indices. Before storing them, we firstly apply the sharpening technique to fix the ambiguity in the predictions of target domain data 5 24
PJ.c = P5.0/ E.e Pj..
where r is the temperature scale the prediction probabilities. As -> O, the probability will collapse to point mass [39]. Then, we utilize L2-norm to normalize feature vectors fú. Finally, we store the sharpened prediction p; and its associated normalized feature [|Se to the memory bank via 3-exponential moving averaging (EMA) strategy, updating them for each iteration. The predictions stored in the memory bank p!th are utilized to approximate real-time probability for pseudo-label generation, and the feature vectors f." stored in the memory bank are employed to construct graphs before neighbor-awand propagation.
The Final Objective. At the end of our approach, let us integrate all of these losses together, i.e, supervised classification loss Lite and domain adversarial loss Cade descried Eq the loss of neighbor-aware propagation mechanism Cnop in Eq 3 and the loss of graph spectral alignment Zgo in Eq 2
Finally, we can obtain the final objective as follows:
Cantal = Lets + Ladd + Lysa + L.aap
(5)
For the sake of simplicity, leave out the loss scale for Ladv and Lysa here. Just as the coefficient term a in Cnep. these two losses are also adjusted with specific scales in the implementation. For more detailed implementation specifics, please refer to our source code. Note that we only describe the problem of unsupervised domain adaptation here our approach can easily to extend to semi-supervised domain adaptation scenario. Concerning the labeled data, we employ the standard cross-entropy loss with label-smoothing regularization [71] in our implementation. We also give different trials of similarity metrics and graph laplacians. More concrete details are in the following section.
4 Experiments
In this section, we present our main empirical results to show the effectiveness of our method. To evaluate the effectiveness of our architecture, we conduct comprehensive experiments under unsupervised domain adaptation, semi-supervised domain adaptation settings. The results of other compared methods are directly reported from the original papers. More experiments can be found in the Appendix.
4.1 Experimental Setups
Datasets. We conduct experiments on benchmark datasets: 1) Office31 6 is widely-used benchmark for visual DA. It contains 4,652 images of 31 office environment categories from three
5

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domains: Amazon (A), DSLR (D), and Webcam (W), which correspond to online website, digital SLR camera and web camera images respectively. 2) OfficeHome (76 is challenging dataset that consists of images of everyday objects from four different domains: Artistic (A), Clipart (C), P Product (P), and Real- Houl-oolld (R). Each domain contains 65 object categories in office and home environments, amounting to 15,500 images around. Following the typical settings [0]], we evaluate methods on one-source to one-target domain adaptation scenario, resulting in 12 adaptation cases total. 3) VisDA2017 [58) is large-scale benekmark that attempts to bridge the significant synthetic-to-ren domain gap with over 280,000 images across 12 categories. The source domain has 152,397 synthetic images generated by rendering from 3D models. The target domain has 55,389 real object images collected from Microsoft COCO [49] Following the typical settings [56]. we evaluate methods on synthetic-ter to-riicct-t----ll---eo task and present test accuracy for each category. 4) DomainNet [57] is large- dataset containing about 600,000 images across 345 categories, which span domains with large domain gap: Clipart (C); Infograph (I), Painting (P), Quickdraw (Q), Real (R), and Sketch (S).
Following the settings in (28), we compare various methods for 12 tasks among C, P. R, S domains on the original DomainNet dataset.
Implementation details. We use PyTTorc and tllib toolbox (8 to implement our method and fine-
tune ResNet pre-trained ImageNet 25 26 Following the standard protocols for unsupervised domain adaptation in previous methods 48 [6]. we use the same backbone networks for fair comparisons. For Office31 and OfficeHome dataset,
use ResNet-50 as the backbone network. For VisDA2017 and DomainNet dataset, we use ResNet-101 as the backbone network. We adopt mini-batch stochastic gradient descent (SGD) with a momentum of 0.9, weight decay of 0.005, and an initial learning rate of 0.01, following the same learning rate schedule in [8]]
4.2 Result Comparisons
In this section, compare SPA with various state- saate-of-the-ar methods for unsupervised domain adaptation (UDA) scenario, and Source Only in UDA task means the model trained only using labeled source data. We also extend SPA semi-suerpervised domain adaptation (SSDA) scenario and conduct experiments on 1-shot and 3-shots setting. With the page limits, see supplementary material for details.
Table 1: Classification Accuracy (%) on DomainNet for unsupervised domain adaptation (inductive), using 01 as backbone. The best accuracy is indicated bold and the second best one is underlined. Note that we compare methods on the original DomainNet dataset with train/test splits in target dataset, leading to an inductive scenario.
Method
C-PP
C-R
C-$
P--
P-R
P-S
R-C
R-P
R-S
S-xC
S-P
S-R
Avg.
Source Only
23
32.7
50.6
39.4
41.1
56.8
35.0
48.6
48.8
36.1
49.0
34.8
46.1
43.3
DAN 5T
38.8
55.2
43.9
45.9
59.0
40.8
50.8
49.8
38.9
56.1
45.9
55.5
48.4
DANN 18
37.9
54.3
44.4
41.7
55.6
36.8
50.7
50.8
40.1
55.0
45.0
54.5
47.2
BCDM
38.5
53.2
43.9
42.5
54.5
51.2
40.6
53.7
46.0
53.4
47.3
MCD 66
37.5
52.9
44.0
44.6
54.5
41.6
52.0
51.5
39.7
55.5
44.6
52.0
47.5
ADDA
73
38.4
54.1
44.1
43.5
56.7
39.2
52.8
51.3
40.9
55.0
45.4
54.5
48.0
CDAN
52
39.9
55.6
45.9
44.8
57.4
40.7
56.3
52.5
44.2
55.1
43.1
53.2
49.1
MCC S1
40.1
56.5
44.9
46.9
57.7
41.4
56.0
53.7
40.6
58.2
45.1
55.9
49.7
JAN
56.7
52.6
56.6
55.5
50.0
MDD 42
42.9
59.5
47.5
48.6
59.4
42.6
58.3
53.7
46.2
58.7
46.5
57.7
51.8
SDAT
62
41.5
57.5
47.2
47.5
58.0
41.8
56.7
53.6
43.9
58.7
48.1
57.1
51.0
1eco
8D
44.1
55.3
48.5
49.4
57.5
45.5
58.8
55.4
46.8
61.3
51.1
57.7
52.6
SPA (Ours)
54.3
70.9
56.1
59.3
71.5
51.8
64.6
89.6
52.1
66.0
57.4
70.6
61.2
Table I (DomainNet) show the results on DomainNet dataset. We compare SPA with the various state-ol- the-ar art methods for inductive UDA scenario on this large-scale dataset. The inductive setting refers that we use the train/test splits of target domain data as the original dataset (57). During the training process, we can use the train split of target domain data and then we use the test split of target domain data for testing. This setting is relatively more difficult than others with the large- scale data amount and inductive learning. Only a few of works follows this setting while we give a result comparison in this setting here. The experiments shows SPA consistently ourperforms than various of DA methods with the average accuracy of 61. .2%% which is 8.6% higher than the recent work Leco 88), demonstrating the superiority of SPA in this inductive setting.

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Table 2: Classification Accuracy (%) OfficeHome for unsupervised domain adaptation, using ResNet50 as backbone. The best accuracy is indicated in bold and the second best one is underlined.
Method
A-=C
A-P
A-R
C-+A
C-P
C-R
P-
P-+C
P-R
R-A
R-+C
R-+P
Avg.
Source Only
34.9
50.0
58.0
37.4
41.9
46.2
38.5
31.2
60.4
53.9
41.2
59.9
46.1
DANN 18
45.6
59.3
70.1
47.0
58.5
60.9
46.1
43.7
68.5
63.2
51.8
76.8
57.6
CDAN
52
50.7
70.6
76.0
57.6
70.0
70.0
57.4
50.9
77.3
70.9
56.7
81.6
63.8
BSP
76.1
70.3
50.2
72.2
59.3
81.9
66.3
NPL
54.1
74.1
78.4
63.3
72.8
74.0
61.7
$1.0
78.9
71.9
56.6
81.9
68.2
GVB 14
64.6
74.1
74.6
84.3
70.4
MCC 31
56.3
77.3
80.3
67.0
77.1
77.0
66.2
55.1
81.2
73.5
57.4
84.1
71.0
71.1
MetaAlign
59.3
76.0
80,2
65.7
74.7
75.1
66.7
56.5
81.6
74.1
61.1
85.2
71.3
ATDOC 13
58.3
78.8
82.3
69.4
78.2
78.2
67.1
56.0
82.7
72.0
58.2
85.5
72.2
FixBi
58.1
77.3
80.4
67.7
79.5
78.1
65.8
57.9
81.7
76.4
62.9
86.7
72.7
SDAT
62
58.2
77.1
82.2
66.3
77.6
76.8
63.3
57.0
K2.2
74,9
64.7
86.0
72.2
NWD
58.1
79.6
83.7
67.7
73.9
60.9
86.1
72.6
SPA (Ours)
60.4
79.7
84,5
73.6
81.3
82.1
72.2
58.0
85.2
77.4
61.0
88.1
75.3
Table Classification Accuracy (%) on (a) Office31 and (b) VisDA2017 for unsupervised domain adaptation, using ResNet50 and ResNet101 as backhone respectively. For VisDA2017, all the results are based on ResNet101 except those with mark 1, which are based ResNet50. The best accuracy is indicated in bold and the second best one is underlined. See supplementary material for more
details.
(a) Office31
(b) VisDA2017
Method
A-+D
A-W
W
D-
D-W
W-+
W-1
Avg.
Method
Avg.
Source Only
78.3
70.4
57.3
93.4
61.5
98.1
76.5
Source Only 25
52.4
DANN 18
79.7
82.0
68.2
96.9
67.4
99.1
82.2
DANN
18
$7.4
CDAN 52
92.9
94.1
71.0
98.6
69.3
100.
87.7
CDAN 52
73.7
MixMatch
5
88.5
84.6
63.3
96.1
65.0
99.6
75.4
MixMarch
5
70.4
BSP 10
93.0
93.3
73.6
98.2
72.6
100.
88.5
BSP
10
75.9
NPL 39
88.7
89.1
65.8
98.1
66.6
99.6
84.7
NPL 39
74.7
GVB 14
95.0
94.8
73.4
98.7
73.7
100.
89.3
GVB
14
75.31
MCC
92.1
94.0
74.9
98.5
75.3
100.
MCC
31
78.8
BNM
74.9
98.5
75.3
BNM 13
79.5
MetaAlign
82
94.5
73.6
98.6
75.0
89.2
ATDOC 48
86.3
ATDOC 48
95.4
94.6
77.5
98.1
77.0
99.7
90.4
FixBi 56
87.2
FixBi 56
95.0
96.1
78.7
99.3
79.4
100.
91.4
SDAT 62
82.1
NWD
8
95.4
95.2
76.4
99.1
76.5
100.
90.4
NWD 8
83.7
SPA (Ours)
95.0
97.2
78.0
99.0
79.4
99.8
91.4
SPA (Ours)
87.7
Table Table 3al and Table 3b show the results OfficeHome, Office31, and VisDA2017 datasets respectively. We compare SPA with the various state-of-the-art methods for transductive UDA scenario on these three public benchmarks. Table 2 (OfficeHome) shows the average accuracy of SPA is 75.3%, %, achieving the best accuracy, which is 2.6% higher than the second highest method FixBi [56] and 2.7% higher than the recent work NWD [8] Note that the average accuracy reported by NWD is based on MCC (31) and SPA is based on DANN [18]. Table 3al (Office31) shows the
results on the small-sized Office31 dataset, the average accuracy SPA is 91.4%. which outperforms
most of domain adaptation methods and comparable with FixBi [56). SPA also shows significant performance improvement over the baseline DANN. Table 3b (VisDA2017) shows the results on VisDA2017. This is large-scale dataset with only 12 classes. SPA based on DANN achieves the accuracy of 83.7%, which have already been superior than lots of methods. However, for fair comparisons, we follow the setting of ATDOC (48 and report the accuracy based MixMatch (5), which achieve best accuracy of 87.7%, 7%, 0.5% better than FixBi, and 1.4% better than ATDOC.
4.3 Model Analysis
Ablation Study. To verify the effectiveness different components of SPA, we design several
variants and compare their classification accuracy. As shown in the first section in Table the w/
Leaas bazsa method is based on CDAN [52]. The difference between these variants is whether utilize the loss of pseudo-labelling and graph spectral penalty not. The results illustrate that both
7

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Table 4: Classification Accuracy (%) on OfficeHome for unsupervised domain adaptation. The table divided into three sections corresponding to the three analysis of ablation study, robustness analysis, and parameter sensitivity, each separated by double horizontal line. More studies other datasets are in supplementary material.
Method
A-C
A-P
A-R
C-+A
C-P
C-R
P-A
P-+
P-+R
R-A
R-C
R-P
Avg.
w/o Cysus Leap
34.6
74.1
78.1
63.0
72.2
74.1
61.6
52.3
79.1
72.3
57.3
82.8
68.5
Cyso
80.1
81.5
71.8
76.7
69.2
57.7
83.0
74.0
64.1
85.8
72.9
wlo Lung
59.0
78.2
81.0
63.5
76.5
76.2
64.7
57.3
82.1
73.6
61.4
85.7
71.6
Ligous Kmua
84.4
61.2
0=0.1
58.3
79.2
83..2
72.8
79.3
80.4
73.3
58.2
84.5
79.0
61.4
87.3
74.7
0.33
83.8
61.3
87.7
75.1
0.5 0.5
59.3
79.5
84.1
73.3
80.66
81.7
73.1
58.0
84.9
78.2
62.2
87.4
75.2
0.7.
59.9
79.4
84.0
73.6
80.5
82.0
72.7
57.3
84.8
77.9
61.9
87.3
75.1
0.9
39.7
79.6
84.7
72.9
78.7
82.2
71.2
57.5
84.5
77.2
61.7
87.5
74.8
Leuk w/ cos
60.6
79.4
84.1
72.5
79.2
81.8
71.9
$7.1
84.8
76.3
61.8
87.4
74.7
byuh grass
60.4
79.7
84.5
73.6
81.3
82.1
72.2
58.0
85.2
77.4
61
88.
75.3
Lage w/ coe
60.7
79.5
83.8
72.7
80.0
81.8
71.5
57.2
84.8
76.3
61.9
87.4
74.8
Leym gasas
59.4
79.5
84.5
73.6
81.0
81.7
72.2
57.6
84.8
61.8
87.8
75.1
Louk w/ k
59.0
80.6
83.9
72.4
79.6
81.7
71.5
56.5
84.7
76.4
62.0
87.7
74.7
Lyuk w/ k: =
60.4
79.7
84.5
73.6
81.3
82.1
72.2
58.0
85.2
77.4
88.1
75.3
Depm
59.2
84.0
81.6
81.5
71.2
57.5
84.7
76.3
61.5
87.4
74.8
L w/ 5
59.4
79.5
84.5
73.6
81.0
81.7
72.2
57.6
84.8
77.5
61.8
87.8
75.1
the loss of pseudo-labelling and graph spectral penalty can improve the performance of baseline, and further combining these two losses together yields better outcomes, which comparable with cutting-edge methods.
Parameter Sensitivity. To analyze the stability SPA, we design experiments on the hyperparameter of exponential moving averaging strategy for memory updates. The experimental results of 3 0.1, 0.3, 0.5, 0.7, 0.9 shown in the second section of Table 4 These results are based on CDAN [52]. From the series of results, can find that in OfficeHome dataset, the choice of B 0.5 outperforms than others. addition, the differences between these results are within 0.5%, which means that SPA insensitive to this hyperparameter.
Robustness Analysis. To further identify the robustness of SPA to different graph structures, we conduct experiments different types of Laplacian matrix, similarity metric of graph relations, and k number of nearest neighbors of KNN classification methods. Here are the two types of commonly-used Laplacian matrix [77]: the random walk laplacian matrix Lrck D- A, and the symmetrically normalized Laplacian matrix Lyym I D D-1/2 AD AD-1/2 where D denotes the degree matrix based on the adjacency matrix A. In addition, the similarity metric are chosen from cosine similarity and Gaussian similarity, and different &o = 3, 5 when applying KNN classification algorithm. The results are shown in the second section of Table[4 We can find that different types of Laplacian matrix still lead comparable results. As for the similarity metric, the Gaussian similarity brings better performance than cosine similarity and the results also presents that 5-NN graphs is superior than 3-NN graphs in OfficeHome dataset. For all these aforementioned experiments results, the differences between them are within 1% around, confirming the robustness of SPA.
Feature Visualization. To demonstrate the learning ability of SPA, we visualize the features of DANN 18], BSP [T0), NPI. (39 and SPA with the 1-SNE embedding [17] under the C - R setting of OfficeHome Dataset. BSP is classic domain adaptation method which also use matrix decomposition and NPL is a classic pscudo-labeling method which also use high-confidence predictions on unlabeled data as true labels. Thus, we choose them as baselines to compare. The results are shown Figure 2 Comparing Figure 2d with Figure 2a Figure 2b and Figure 2c respectively, we make some important observations: (i)-we find that the clusters features Figure 2d are more compact, or say less diffuse than others, which suggests that the features learned by SPA are able to attain more desirable discriminative property; (ii)-we observe that red markers are more closer and overlapping with blue markers in Figure 2d which suggests that the source features and target features learned by SPA are transferred better. These observations imply the superiority of SPA over discriminability and transferability in unsupervised domain adaptation scenario.

---

(a) DANN
(b) BSP
(c) NPL
(d) SPA
Figure Feature Visualization. the t-SNE plot of DANN [88, BSP [T]. NPL [39. and SPA features
on OfficeHome dataset in the C R setting, We use red markers for source domain features and blue markers for target domain features.
Related Work
Domain Adaptation. Domain adaptation (DA) problem is specific subject of transfer learning
90 29 and also widely studied area in computer vision field [18, 20
19
73
52
65
66
40)
44]
70 1.
By the label amount target domain, domain adaptation can be divided into unsupervised
domain adaptation, and semi-supervised domain adaptation etc. Unsupervised domain adaptation methods are very effective at aligning feature distributions of source and target domains without any target supervision but perform poorly when target. Our approach mainly focus on unsupervised domain adaptation. achieving the cutting-edge performance. It can also be extended to semi-supervised domain adaptation with comparable results.
few labeled examples available in the
There are more specifies of our baselines. Inspired by random walk 777 in graph theory, MCC Bi proposes a self-training method by optimizing the class confusion matrix. BNM [I3] formulates the loss nuclear norm, i.e, the sum of singular values based on the prediction outputs. NWD calculates the difference between the nuclear norm of source prediction matrix and target prediction matrix. The aforementioned three methods all focus on the prediction outputs and establish class-to- class relations. Besides, there are two works focusing on the features, CORAL [70], measuring the difference of covariance, and BSP [00,, directly performing singular value decomposition on features and calculate top A singular values. BNM, NWD and BSP are similar to method with the use of singular values. However, our eigenvalues comes out from the graph laplacians, which contains graph topology information [12. For example, the second-smallest non-zero laplacian eigenvalue is called as the algebraic connectivity, and its magnitude just reflects how connected graph is [2]. As we know, are the first to propose graph spectral alignment perspective for domain adaptation scenarios.
Self-training. Self-training is sumi-super learning method that enhances supervised models by generating pseudo-labed for unlabeled data based on model predictions, which has been explored 84 68). These methods pick up the class with the maximum predicted probability as true labels each time the weights are updated. With filtering strategies and iterative approaches employed to improve the quality of pseudo labels, this self-training technique has also been applied to some domain adaptation methods [48 88 81 37]. This kind of methods proves beneficial when the labeled data is limited. However, relies on an assumption of the unlabeled data following the same distribution with the labeled data and requires accurate initial model predictions for precise results 55 2 The intra-domain alignment in our approach helps the neighbor-ave aware self-training mechanism generate more precise labels. The interaction between components of our approach brings our impressive results in DA scenarios.
in lots of works (27 39 50 83
Graph Data Mining. Graphs are widely applied in real-world applications to model pairwise interactions between objects in numerous domains such as biology 78). social media [60] and finance Because of their rich value, graph data mining has long been an important research direction also plays a significant role in computer vision tasks such as image retrieval object detection [46), and image classification (74). Bruna et |l.[7] first introduce the graph convolution operation based on spectral graph theory. The graph filter and the agen-decomposition of the graph Laplacian matrix inspire to propose graph spectral alignment.
86
16
36
75

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6 Conclusion
In this paper, we present novel spectral alignment perspective for balancing inter-domain transfer- ability and intra-domain discriminability in UDA. We first leveraged graph structure to model the topological information of domain graphs. Next, we aligned domain graphs in their eigenspaces and propagated neighborhood information to generate pseudo-labels. The comprehensive model analysis demonstrates the superiority of our method. The current method for constructing graph spectra is only a starting point and may be inadequate for more difficult scenarios such universal domain adaptation. Additionally, this method is currently limited to visual classification tasks and more sophisticated and generic methods to object detection semantic segmentation are expected in the future. Furthermore, we believe that graph data mining methods and the well-formulated properties of graph spectra should have more discussion in both domain adaptation and computer vision field.
7 Acknowledgement
This work is majorly supported in part by the National Key Research and Development Program of China (No. 2022YFB3304100 the NSFC under Grants (No. 62206247), and by the Fundamental Research Funds for the Central Universities (No. 226-2022-00028). JZ also thanks the sponsorship by CAAI-Huawei Open Fund.
References
[1] Mustapha Aouchiche and Pierre Hansen. Distance spectra of graphs: survey, Linear algebra and its applications, 458:301-386 2014.
[2] Eric Arazo, Diego Ortego, Paul Albert, Noel E O' O'Connor, and Kevin McGuinness. Pseudo- labeling and confirmation bias in deep supervisd learning. In International Joint Confer- ence on Neural Networks (JJCNN). IEEE, 2020.
[3] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representations for domain adaptation. In Advances in Neural Information Processing Systems (NeurIPS), volume 19, 2006.
[4] Shai Ben-David, John Blitzer, Koby Crammer, and Fernando Pereira. Analysis of representa- tionsfor domain adaptation. In Advances in Neural Information Processing Systems (NeurIPS), page 137-144, 2007.
[5] David Berthelot, Nicholas Carlini, Ian J. Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: holistic approach to semi-supervised learning. In Advances in Neural Information Processing Systems (NeurIPS), volume 32, pages 5050-5060, 2019.
[6] Andries E. Brouwer and Willem H. Haemers. Spectra of graphs. Springer Science and Business Media, 2011.
[7] Joan Bruna, Wojeiech Zaremba, Arthur Szlam, and Yann LeCun. Spectral networks and locally connected networks on graphs. In International Conference on Learning Representations (ICLR), 2014.
[8] Lin Chen, Huaian Chen, Zhixiang Wei, Xin Jin, Xiao Tan, Yi Jin, and Enhong Chen. Reusing the task-specific classifier discriminator: Discriminator-frer adversarial domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 7181-7190. IEEE, 2022.
[9] Liqun Chen, Zhe Gan, Yu Cheng, Linjie Li, Lawrence Carin, and Jingjing Liu. Graph optimal transport for cross-domain alignment. In Proceedings of the 37th International Conference Machine Learning (ICML), pages 1542-1553. PMLR, 2020.
[10] Xinyang Chen, Sinan Wang, Mingsheng Long, and Jianmin Wang- Transferability vs. discrim- inability: Batch spectral penalization for adversarial domain adaptation. In Proceedings of the 36th International Conference Machine Learning (ICML), pages 1081-1090, PMLR, 2019.
10

---

[11] Yuhao Cheng, Xiaoguang Zhu, Jiuchao Qian, Fei Wen, and Peilin Liu. Cross-modal graph matching network for image-text retrieval. ACM Transactions on Multimedia Computing. Communications, and Applications, 18(4):1-23, 2022.
[12] Fan RK Chung. Spectral graph theory. American Mathematical Society, 92, 1997.
[13] Shuhao Cui, Shuhui Wang. Junbao Zhuo, Liang Li, Qingming Huang, and Qi Tian. Towards discriminability and diversity: Batch nuclear-norm maximization under label insufficient situa- tions. Proceedings of the IEEE Conference on Computer Vision and Puttern Recognition (CVPR), pages 3941-3950. IEEE, 2020.
[14] Shuhao Cui, Shuhui Wang. Junbao Zhuo, Chi Su, Qingming Huang, and Qi Tian. Gradually vanishing bridge for adversarial domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 12452-12461. IEEE, 2020.
[15] Shai Ben David, Tyler Lu, Teresa Luu, and David Pal. Impossibility theorems for domain adaptation. In Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS), pages 129-136. PMLR, 2010.
[16] Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural networks on graphs with fast localized spectral filtering. In Advances in Neural Information Processing Systems (NeurIPS), volume 29, pages 3837-3845, 2016.
[17] Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. The Journal of Machine Learning Research (JMLR), 9(11), 2008.
[18] Yaroslav Ganin and Victor Lempitsky. Unsupervised domain adaptation by back propagation. In Proceedings of the 32th International Conference on Machine Learning (ICML), pages 1180-113 1180-119..10 PMLR, 2015.
[19] Yaroslav Ganin, Evgeniya Ustinova, Hana Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario Marchand, and Victor S. Lempitsky. Domain-adversen training of neural networks. The Journal of Machine Learning Research (JMLR), 17:59:1-5::35, 2016.
[20] Boqing Gong, Yuan Shi, Fei Sha, and Kristen Grauman. Geodesic flow kernel for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2066-2073. IEEE, 2012.
[21] Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. In Advances in Neural Information Processing Systems (NeurIPS), 2004.
[22] Jiao Gu, Bobo Hua, and Shiping Liu. Spectral distances on graphs. Discrete Applied Mathemat- ics, 190:56-74, 2015.
[23] Xiang Gu, Jian Sun, and Zongben Xu. Spherical space domain adaptation with robust pseudo- label loss. In Proceedings of the IEFE Conference Computer Vision and Pattern Recognition (CVPR), pages 9101-91 10. IEEF, 2020.
[24] Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger. On calibration of modern neural networks. In Proceedings of the 34th International Conference on Machine Learning (ICML), pages 1321-1330. PMLR, 2017.
[25] Kaiming He. Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for im- age recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 770-778. IEEE, 2016.
[26] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Identity mappings in deep residual networks. In the 14th European Conference on Computer Vision (ECCV), volume 9908, pages 630-645. Springer, 2016.
[27] Ahmet Iscen, Giorgos Tolias, Yannis Avrithis, and Ondrej Chum. Label propagation for deep semi-supervised learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5070-5077 IEEE, 2019.

---

[28] Junguang Jiang, Baixu Chen, Bo Fu, and Mingsheng Long. Transfer-lcaring-iibee https //github. Satm/thtmm/raannfeeee wtwp://rrrasee-eerrninn
2020.
[29] Junguang Jiang, Yang Shu, Jianmin Wang, and Mingsheng Long. Transferability in deep learning: A survey. CoRR, abs/2201 10056677 2022.
[30] Pin Jiang, Aming Wu, Yahong Han, Yunfeng Shao, Meiyu Qi, and Bingshuai Li. Bidirec- tional adversarial training for semi-supervised domain adaptation. In Proceedings of the 29th International Joint Conference Artificial Intelligence (IJCAI), page 934 9440 2020.
[31] Ying Jin, Ximei Wang, Mingsheng Long, and Jianmin Wang- Minimum class confusion for versatile domain adaptation. In the 16th European Conference on Computer Vision (ECCV), volume 12366, pages 464 480. Springer, 2020.
[32]
Quinonero-Canded Joaquin, Masashi Sugiyama, Anton Schwaighofer, and Neil D. Lawrence. Dataset shift in machine learning. Mit Press, 2008
[33] Tarun Kalluri, Astuti Sharma, and Manmohan Chandraker. Memsac: Memory augmented sample consistency for large scale domain adaptation. In the 17th European Conference on Computer Vision (ECCV), pages 550-568. Springer. 2022.
[34] Andrej Karpathy and Fei-Fei Li. Deep visual-semantic alignments for generating image descrip- tions. Proceedings of the IEEE Conference on Computer Vision and Puttern Recognition (CVPR), pages 31 3128-3137. IEEE, 2015.
[35] Taekyung Kim and Changick Kim. Attract, perturb, and explore: Learning feature alignment network for semisupervised domain adaptation. In the 16th European Conference on Computer Vision (ECCV), pages 591-607. Springer, 2020.
[36] Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations (ICLR), 2017.
[37] Jogendra Nath Kundu, Suvaansh Bhambri, Akshay Kulkarni, Hiran Sarkar, Varun Jampani, and R. Venkatesh Babu. Subsidiary prototype alignment for universal domain adaptation. In Advances in Neural Information Processing Systems (NeurIPS), volume 35, 2022.
[38] Jogendra Nath Kundu, Akshay R Kulkarni, Suvaansh Bhambri, Deepesh Mehta, Shreyas Anand Kulkarni, Varun Jampani, and Venkatesh Babu Radhakrishnan. Balancing discriminability and transferability for source-free domain adaptation. In Proceedings of the 39th International Conference on Machine Learning (ICMI., volume 162, pages 11710-11728, PMIR, 2022.
[39] Dong-Hyur Lee, Pseudo-label: The simple and efficient semi-supervised learning method for deep neural networks. In Workshop on challenges in representation learning, ICML, page 896, 2013.
[40] Seungmin Lee, Dongwan Kim, Namil Kim, and Seong-Gyun Jeong. Drop to adapt: Learning discriminative features for unsupervised domain adaptation. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 91-100. IEEE, 2019.
[41] Jichang Li, Guanbin Li, Yemin Shi, and Yizhou Yu. Cross-domain adaptive clustering for sumi-supervised domain adaptation. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (CVPR), pages 2505-2514, 2021.
[42] Jingjing Li, Erpeng Chen, Dingm Zhengming. Lei Zhy, Ke Lu, and Heng Tao Shen. Maximum density divergence for domain adaptation. IEEE transactions on pattern analysis and machine intelligence (TPAMI), (1(4))3318839933 2020.
[43] Linjie Li. Zhe Gan, Yu Cheng, and Jingjing Liu. Relation-aware graph attention network for visual question answering. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 10312-10321. IEEF, 2019.
[44] Mengxue Li, Yi-Ming Zhai, Yei Luo, Peng-Fei Ge, and Chuan-Xian Ren. Enhanced transport distance for unsupervised domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pages 13936-13944, IEEE, 2020.
12

---

[45] Shuang Li, Fangrui Lv, Binhui Xie, Chi Harold Liu, Jian Liang, and Chen Qin. Bi-classifier determinacy maximization for unsupervised domain adaptation. In Proceedings of 35th AAAI Conference Artificial Intelligence, pages 8455-8466 AAAI Press, 2021.
[46] Wuyang Li, Xinyu Liu, and Yixuan Yuan. SIGMA: semantic- graph matching for domain adaptive object detection. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5281-5290. IEEE, 2022.
[47] Jian Liang, Ran He, Zhenan Sun, and Tieniu Tan. Exploring uncertainty in pseudo-label guided unsupervised domain adaptation. Pattern Recognition, 96, 2019.
[48] Jian Liang, Dapeng Hu, and Jiashi Feng. Domain adaptation with auxiliary target domain- oriented classifier. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 16632-16642. IEEE, 2021.
[49] Tsung-Y- Yi Lin, Michael Maire, Serge Belongie, Lubomir Bourdev, Ross Girshick, James Hays, Pietro Perona, Deva Ramanan, C. Lawrence Zitnick, and Piotr Dollár. Microsoft coco: Common objects in context. In the 13th European Conference on Computer Vision (ECCV), pages 740-755. Springer, 2014.
[50] Yanbin Liu, Juho Lee, Minseop Park, Saehoon Kim, Eunho Yang, Sungju Hwang, and Yi Yang. Learning to propagate labels: Transductive propagation network for few-shot learning. In International Conference on Learning Representations (ICLR), 2019.
[51] Mingsheng Long, Yue Cao, Jianmin Wang, and Michael I. Jordan. Learning transferable features with deep adaptation networks. In Proceedings of the 32th International Conference on Machine Learning (ICML), pages 97-105. PMLR, 2015.
[52] Mingsheng Long, Zhangjie Cao, Jianmin Wang, and Michael I. Jordan. Conditional adver- sarial domain adaptation. In Advances in Neural Information Processing Systems (NeurIPS), volume 31, pages 1647-1657, 2018.
[53] Mingsheng Long, Han Zhu, Jianmin Wang, and Michael I. Jordan. Deep transfer learning with joint adaptation networks. In Proceedings of the 34th International Conference on Machine Learning (ICML), pages 2208 22177. PMLR, 2017.
[54] Lingkun Luo, Liming Chen, and Shiqiang Hu. Attention regularized laplace graphfor domain adaptation. In Proceedings of 31th IEEE International Conference on Image Processing (ICIP), pages 7322-7337. IEEE, 2022.
[55] Miller McPherson, Lynn SmithLovin, and James M Cook. Birds of a feather: Homophily in social networks. Annual review of socialogy, 27(1):415 444, 2001.
[56] Jaemin Na. Heechul Jung, Hyung Jin Chang, and Wonjun Hwang. Fixbi: Bridging domain spaces for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Com- puter Vision and Pattern Recognition (CVPR), pages 1094-1103. IEEE, 2021.
[57] Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. In Proceedings of the IEFE International Conference on Computer Vision (ICCV), pages 1406-1415. IEFE, 2019.
[58] Xingchao Peng, Ben Usman, Neela Kaushik, Dequan Wang. Judy Hoffman, and Kate Saenko. Visda: synthetic-to-reat benchmark for visual domain adaptation. In Proceedings of the IEFE Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), pages 2021 IEFE, 2018
[59] Hieu Pham, Zihang Dai, Qizhe Xie, and Quoe V. Le. Meta pseudo labels. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (CVPR), pages 11557-11568. IEEF, 2021.
[60] Zhenyu Qiu, Wenbin Hu, Jia Wu, ZhongZheng Tang, and Xiaohua Jía. Noise-resilient similarity preserving network embedding for social networks. In Proceedings of the 28nd International Joint Conference Artificial Intelligence (IJCAI), pages 3282-3288, 2019.
13

---

[61] Md Mahmudur Rahman, Rameswar Panda, and Mohammad Arif U1 Alam. Semi-supervised domain adaptation with auto- encoder via simultaneous learning. Proceedings of the IEEE Winter Conference on Applications of Computer Vision, 2023.
[62] Harsh Rangwani, Sumukh K Aithal, Mayank Mishra, Arihant Jain, and Venkatesh Babu. A closer look at smoothness in domain adversarial training. In Proceedings of the 39th International Conference on Machine Learning (ICMI.). PMLR, 2022.
[63] Kate Saenko, Brian Kulis, Mario Fritz, and Trevor Darrell. Adapting visual category models to new domains. In the 11th European Conference on Computer Vision (ECCV), pages 213-226. Springer, 2010.
[64] Kuniaki Saito, Donghyun Kim, Stan Sclaroff, Trevor Darrell, and Kate Saenko. Semi-supervised domain adaptation via minimax entropy. Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 8050-8058, 2019.
[65] Kuniaki Saito, Donghyun Kim, Stan Sclaroff, and Kate Saenko. Universal domain adaptation through self supervision. In Advances Neural Information Processing Systems (NeurIPS), volume 33, 2020.
[66] Kuniaki Saito, Kohei Watanabe, Yoshitaka Ushiku, and Tatsuya Harada. Maximum classifier discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3723-3732. IEEE, 2018.
[67] Hidetoshi Shimodaira. Improving predictive inference under covariate shift by weighting the log-likelihhn likelihood function. Journal of Statistical Planning and Inference, 90(2):227 244, 2000.
[68] Tiberiu Sosea and Cornelia Caragea. Leveraging training dynamics and self-training for text classification. In Findings of the Association for Computational Linguistics: EMNLP, pages 4750-4762. ACL, 2022.
[69] Dragan Stevanović. Research problems from the aveiro workshop on graph spectra. Linear Algebra and its Applications, 423(1):172-181. 2007. Special Issue devoted to papers presented at the Aveiro Workshop on Graph Spectra.
[70] Baochen Sun and Kate Saenko. Deep coral: Correlation alignment for deep domain adaptation. In ECCV 2016 Workshops, 2016.
[71] Christian Szegedy, Vincent Vanhoucke, Sergey loffe, Jonathon Shlens, and Zbigniew Wojna. Re- thinking the inception architecture for computer vision. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2818-2826. IEEE, 2016.
[72] Tatiana Tommasi, Martina Lanzi, Paolo Russo, and Barbara Caputo. Learning the roots of visual domain shift. In Gang Hua and Hervé Jégou, editors, ECCV 2016 Workshops, volume 9915 of Lecture Notes in Computer Science, pages 475-482, 2016.
[73] Eric Tzeng, Judy Hoffman, Kate Saenko, and Trevor Darrell. Adversarial discriminative domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2962-2971. IEEE, 2017.
[74] Varun Vasudevan, Maxime Bassenne, Md Tauhidul Islam, and Lei Xing. Image classification using graph neural network and multiscale wavelet superpixels. Puttern Recognition Letters, 166:89-96, 2023.
[75] Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. International Conference on Learning Representations (ICLR), 2018.
(76) Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 5018-5027. IEEF, 2017.
14

---

[77] Ulrike von Luxburg. A tutorial on spectral clustering. Statistics and Computing, 17(():395-44 416, 2007.
[78] Bo Wang, Armin Pourshafeie, Marinka Zitnik, Junjie Zhu, Carlos Bustamante, Serafim Batzoglou, and Jure Leskovec. Network enhancement as a general method to denoise weighted biological networks. Nature communications, 9(1):1-8, 2018.
[79] Sinan Wang, Xinyang Chen, Yunbo Wang, Mingsheng Long, and Jianmin Wang. Progressive adversarial networks for fine-grained domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pages 9213-9222, 2020.
[80] Xiaodong Wang, Junbao Zhuo, Mengru Zhang, Shuhui Wang, and Yuejian Fang. Revisiting unsupervised domain adaptation models: smoothness perspective. In Proceedings of the Asian Conference on Computer Vision (ACCV), pages 1504-1521, 1521, 2022.
[81] Yuxi Wang, Junran Peng, and Ziaog Zhang. Uncertainty- pseudo label refinery for domain adaptive semantic segmentation. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 9092-9101. IEEE, 2021.
[82] Guoqiang Wei, Cuiling Lan, Wenjun Zeng, and Zhibo Chen. Metaalign: Coordinating domain alignment and classification for unsupervised domain adaptation. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition (CVPR), pages 16643-16653 IEEE, 2021.
[83] Zhirong Wu, Yuanjun Xiong, Stella Yu, and Dahua Lin. Unsupervised feature learning via non parammamtttric instanedissrimination. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 3733-3742. 2018.
[84] Sang Michael Xie, Ananya Kumar, Robbie Jones, Fereshte Khani, Tengyu Ma, and Percy Liang. In-n-out: Pre-training and self-training using auxiliary information for out-o--distribution robustness. In International Conference on Learning Representations (ICiaaiiioon((RR)) (ICI.R, 2021.
[85] Ruijia Xu. Guanbin Li, Jihan Yang, and Liang Lin. Larger more transferable: An adaptive feature norm approach for unsupervised domain adaptation. In Proceedings of the IEEE International Conference on Computer Vision (ICCV), pages 1426-1435, 2019.
[86] Rex Ying, Ruining He, Kaifeng Chen, Pong Eksombatchai, William Hamilton, and Jure Leskovec. Graph convolutional neural networks for web-scale recommender systems. In Proceedings of the 24th ACM SIGKDD International Conference Knowledge Discovery and Data Mining., pages 974-983. ACM, 2018.
[87] Yue Zhang, Shun Miao, and Rui Liao. Structural domain adaptation with latent graph alignment. In Proceedings of 25th IEEE International Conference on Image Processing (ICIP), pages 3753-3757. IEEE, 2018
[88] Zijun Zhang, Xiao Cao, Yuan Liu, and Mingsheng Long. Progressive graph learning for open-set domain adaptation. In Proceedings of the 37th International Conference on Machine Learning (ICML), pages
PMLR, 2020.
[89] Erheng Zhong, Wei Fan, Qiang Yang, Olivier Verscheure, and Jiangtao Ren. Cross validation framework to choose amongst models and datasets for transfer learning. In Machine Learning and Knowledge Discovery in Databases, European Conference, ECML PKDD, volume 6323 of Lecture Notes in Computer Science, pages 547-562. Springer, 2010.
[90] Fuzhen Zhuang, Zhiyuan Qi, Keyu Duan, Dongbo Xi, Yongchun Zhu, Hengshu Zhu, Hui Xiong. and Qing He. A comprehensive survey on transfer learning. Proceedings of the IEEE, 109(1):43-76, 2021.
[91] Zhijian Zhuo, Yifei Wang, Jinwen Ma, and Yisen Wang. Towards a unified theoretical un- derstanding of non-contrastive learning via rank differential mechanism. International Conference Learning Representations (ICLR), 2023.
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A More Setups
Hardware and Software Configurations. All experiments are conducted on a server with the following configurations:
Operating System: Ubuntu 20.04.4 LTS
CPU: Intel(R) Xeon(R) Platinum 8358P CPU @ 2.60GHz, 32 cores, 128 processors
GPU: NVIDIA GeForce RTX 3090
More Implementation Details. We use PyTorch and tllib toolbox [28 implement method and fine-tune ResNet pre-trained on ImageNet [25] 26]. Following the standard protocols for unsupervised domain adaptation in previous methods 48 56
the same backbone networks for fair comparisons. For Office31 and OfficeHome dataset, we use ResNet-50 as the backbone network. For VisDA2017 and DomainNet dataset, Following previous work 48 we adopt mini-batch stochastic gradient descent (SGD) to learn the feature encoder by fine-tuning from the ImageNet pre-trained model with the learning rate 0.001, and new layers, as bottleneck layer and classification layer. The learning rates of the layers trained from scratch
ResNet-101 the backbone network.
to be 0.01. We use the the same learning rate schedule in 48 [22. including learning rate scheduler with a momentum of 0.9, a weight decay of 0.005, the bottleneck size of 256, and batch size of 32.
We report main experimental results with the average accuracy over 5 random trials with the initial seed O. For transductive unsupervised domain adaptation, the reported accuracy is computed
the complete unlabeled target data, following established protocol for UDA 18 52 For inductive unsupervised domain adaptation on the provided test dataset.. We use a standard batch size of 32 for both source and target in all experiments and for all variants of our method. The reverse validation 47 hyper-parameters. For both unsupervised domain adaptation (UDA) and semi-supervised domain adaptation (SSDA) scenarios, 1.0, while we will offer a sensitivity analysis for this two coefficients in the following section. More details refer to our code in the supplemental materials.
31 10 48)
DomainNet, the reported accuracy computed
89 is conducted to select
fix the coefficient of Lepp as 0.2 and the coefficient of Lasa as
B
More Experiments
B.1 Unsupervised Domain Adaptation
In the main paper, present the classification accuracy results on VisDA2017 dataset for unsuper- vised domain adaptation and leave out per-category accuracy details. In the appendix, Table we give the full table on VisDA2017, using ResNet101 backbone. Looking into this table, we can find that our SPA model consistently outperforms most of domain adaptation methods. For classic baselines, improve DANN [8] by 30.3%, and CDAN 52 by 14 %. For recent and state-of-the-an baselines, our results is 4% higher than NWD g and 0.5 % better than FixBi [56]. Our SPA model ranks top in out of 12 categories, ranks top 2 in 9 out of 12 categories, and SPA also achieves the best classification accuracy in total.
Furthermore, in the main paper, present the classification accuracy results original NomainNet with 365 categories. While the original DomainNet dataset has noisy labels, the previous work [64] use subset of it that contains 126 categories from C, P, R and S, 4 domains in total, which we refer to as Net In the appendix, Table we show the results on DomainNet Our SPA model consistently ranks top among 12 tasks across 4 domains and achieves the best accuracy of 77.1 %, which is 12.3 % better than the second one. For classic basclines, we improve DANN [8 by 20.2 %, and CDAN 552 by 16 %o.
B.2 Semi-supervised Domain Adaptation
We also extend our SPA model to semi-superivsed domain adaptation (SSDA) scenario and conduct experiments on I-shot and 3-shot setting, and in SSDA task means the model trained only by the labeled source and target data.
16

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Table 5: Per-category Accuracy (%) VisDA2017 for unsupervised domain adaptation, using ResNet101 as backbone. All the results are based on ResNet101 except those with mark 1, which are based ResNet50. The best accuracy is indicated in bold and the second best one is underlined.
Method
Bero
bike
bus
car
horse
knife
motor
person
plant
skute
train
truck
Avg.
Source Only
55.1
53.3
61.9
59.1
80.6
17.9
31.2
26.5
73.5
8.5
52.4
DANN 18
81.9
77.7
82.8
44.3
81.2
29.5
65.1
28.6
51.9
54.6
82.8
7.8
57.4
CDAN
52
85,2
66.9
83.0
50.8
84,2
74,9
88.1
74.5
83.4
76.0
81.9
38.0
73.7
Mixcaach
93.9
71.8
93.5
82.1
95.3
0.7
90.8
38.1
94.5
96.0
86.3
2.2
70.4
RSP 10
92.4
61.0
57.5
89.0
80.6
82.1
38,4
75.9
NPL 39
90.9
74.6
73.2
55.8
89.6
64.6
86.8
68.7
90.7
64.8
89.5
47.7
74.7
GVB 14
75.31
MCC 31
92.2
82.9
76.8
66.6
90.9
78.5
87.9
73.8
90.1
76.1
87.1
41.0
78.8
BNM 1K
93.6
70.3
91.1
$2.8
78.7
89.1
40.9
79.5
ATDOC 48
95.3
84.7
82.4
75.6
95.8
97.7
88.7
76.6
94.0
91.7
91.5
61.9
86.3
FixBi 56
96.1
87.8
90.5
90.3
96.8
95.3
92.8
88.7
97.2
94.2
90.9
25.7
87.2
SDAT
94.8
77.1
82.8
60.9
92.3
95.2
91.7
79.9
89.9
91.2
88.5
41.2
82.1
NWD
8
96.1
82.7
76.8
71.4
92.5
96.8
88.2
81.3
92.2
88.7
84.1
53.7
83.7
SPA (Ours)
98.5
86.3
63.0
97.5
95.4
93.5
80.7
97.2
91.1
61.4
87.7
Table 6: Classification Accuracy (%) 2 for unsupervised domain adaptation, using ResNet101 as backbone. The best accuracy is indicated in bold and the second best one is underlined.
Method
C-P
C-R
C-$
P-+C
P--R
P-4S
R-CC
R-P
R-$
S-*C
S-P
S-R
Avg.
Source Only
25
38.4
50.9
43.9
50.3
66.7
39.9
54.6
57.9
43.7
52,5
43.5
48.3
49.2
DANN [8
46.5
58.2
51.6
52.7
64.2
52.9
60.3
53.9
62.7
56.7
61.6
56,9
MCD 66
43.7
55.7
47.6
51.9
67.8
45.0
52.9
57.3
40.4
56.3
50.8
56,8
52.3
BSP
45.7
58.7
55.5
48.6
65.2
48.6
55.2
60.8
48.6
56.8
55.8
61.4
55.1
CDAN 52
50.9
61.6
54.8
59.4
68.5
55.5
70.4
66.9
57.7
64.2
59.1
64.3
61.1
SAFN 85
50.0
58.7
52.4
56,3
73.7
53.5
55.8
64.8
48.5
60.7
59.5
64.3
58.2
RSDA
56.6
46.6
45.7
61.5
50.9
56.1
54.0
58.6
53.4
PAN 79
58.8
65.2
54.6
57.5
70.5
53.1
67.6
66.7
55.9
64.4
60.2
66.6
61.8
MemSAC
33
53.6
66.5
58.8
63.2
71.2
58.1
23.2
20.5
61.5
68.8
64.1
67.6
64.8
(Ours)
76.8
Table 7: Classification Accuracy (%) 2em1 for 1-shot and 3-shot semi-supervised domain adaptation, using ResNet34 as backbone. The best accuracy is indicated in bold and the second best one is underlined.
Method
C-S
P-R
S-P
Avg.
3.
1-
3.
3.
1.
3.
1.
3.
1.
3.
1-
3.
3.
S+
25
54.8
57.9
59.2
63.0
73.7
75.6
61.2
63.9
64.5
66.3
52.0
56.0
60.4
62.2
60.8
63.6
DANN
18
52.8
55.4
70.3
72.2
56.3
59.6
58.2
59.8
61.4
62.8
52.2
54,9
57.4
59.9
58.4
60.7
ENT
54.6
60.0
65.4
71.1
75.0
78.6
65.2
71.0
65.9
69.2
52.1
61.1
59.7
62.1
62.6
67.6
MME
64
56.3
61.8
69.0
71.7
76.1
78.5
70,0
72.2
67.7
69.7
61.0
61.9
64.8
66.8
66.4
68.9
APE
56.7
63.1
72.9
76.7
76.6
79.4
70.4
76.6
70.8
72.1
63.0
67.8
64.5
66.1
67.6
71.7
BiAT 30
57.9
61.5
71.6
74.6
77.0
78.6
73.0
74.9
68.0
68.8
58.5
62.1
63.9
67.5
67.1
69.7
MixMalch
59.3
62.7
66.7
68.7
74.8
78.8
69.4
72.6
67.8
68.8
62.5
65.6
66.3
67.1
66.7
69.2
NPI. 39
62.5
64.5
67.6
70.7
78.3
79.3
70.9
72.9
69.2
62.0
64.8
67.0
68.6
68.2
70.2
BNM
13
5844
62.6
69.4
72.7
77.0
79.5
69.8
73.7
69.8
71.2
61.4
65.1
64.1
67.6
67.1
70.3
MCC
31
56.8
60.5
62.8
66.5
75.3
76.5
65.5
67.2
66.9
68.1
57.6
59.8
63.4
65.0
64.0
66.2
ATDOC
48
65.6
66.7
72.8
74.2
81.2
81.2
74.9
76.9
71.3
72.5
65.2
64.6
68.7
70.8
71.4
72.4
AFSI.
59.5
65.2
74.6
76.2
72.4
74.1
74.8
77.3
79.4
80.5
66.2
69.5
66.6
69.6
70.5
73.2
SPA (Ours)
65.9
67.0
74.8
76.5
81.1
82.3
75.3
76.0
71.8
72.2
65.8
67.2
69.8
71.1
72.1
73.2
We present the classificaition accuracy results on DomainNet1 26 and OfficeHome datasets for SSDA scenario in the Table and Table respeciespe Looking at the details, Table the classification results for 1-shot and 3-shot SSDA setting on DomainNet 126 dataset. For the 1-shot setting, SPA model can improve DANN [8] by 13.7 % and ENT 21 by 9.5 %. our SPA consistently ranks top among 4 out of 7 tasks and ranks top 2 among all tasks, achieving the best accuracy of 72.1 %, which is better 1.6 % then the second one. For the 3-shot setting, our SPA model can improve DANN [8 by 12.5 % and ENT 21 by 5.6 %. SPA achieves the best accuracy of 73.2 %, comparable with recent work AESL 61
Furthermore, Table 8 shows the classification results for 1-shot and 3-shot SSDA setting on Office- Home dataset. To verify that our SPA model can also generalize to SSDA scenario, we compare SPA with several classic and recent baselines. The first section of the table shows our SPA model can
17

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Table 8: Classification Aceuracy (%) OfficeHome for 1-shot and 3-shot semi-supervised domain adaptation, using ResNet34 as backbone. The best accuracy is indicated bold and the second best one is underlined.
Method (1-shot)
A-C
A-P
C-
C-RR
P-AA
P--R
R-CC
Avg.
S
225
52.1
78.6
66.2
74.4
48.3
57.2
69.8
50.9
73.8
70.0
56.3
68.1
63.8
DANN
18
53.1
74.8
64.5
68.4
51.9
53.7
67.9
$2.3
73.9
69.2
54.1
66.
62.7
ENT
21
53.6
81.9
70.4
79.9
51.9
63.0
75.0
52.9
76.7
73.2
63.2
73.6
67.9
MMF
64
61.9
82.8
71.2
79.2
57.4
64.7
75.5
59.6
77.8
74.8
65.7
74.5
70.4
APE
60.7
81,6
72.5
78.6
58.3
63.6
76.1
72.3
63.6
68.9
CDAC
41
61.9
83.1
72.7
80.0
59.3
64.6
75.9
61.2
78.5
75.3
64.5
75.1
71.0
SPA (Ours)
62.3
76.7
79.0
66.6
77.3
76.4
65.7
59.1
80.7
71.4
65.2
84.1
72.0
Method (3-shot)
A-+C
A-+P
A-+R
C-+A
C-+P
C-+R
P-+A
P-+C
P-
R-+A
R-CC
R-PP
Avg.
S
251
55.7
80.8
67.8
73.1
53.8
63.5
73.1
54.0
74.2
68.3
57.6
72.3
66.2
DANN 18
57.3
75.5
65.2
69.2
51.8
56.6
68.3
54.7
73.8
67.1
55.1
67.5
63.5
ENT 21
62.6
85.7
70.2
79.9
60.5
63.9
79.5
61.3
79.1
76.4
64.7
79.1
71.9
MME
664
64.6
85.5
71.3
80.1
64.6
65.5
79.0
63.6
79.7
76.6
67.2
79.3
73.1
APE
66.4
86.2
73.4
82.0
65.2
66.1
81.1
63.9
66.6
79.9
74.0
CDAC
[4
67.8
85.6
72.2
81.9
67.0
62.5
80.3
65.9
80.6
80.2
67.4
81.4
74.2
SPA (Ours)
63.1
81.0
80.2
68.5
81.7
77.5
69.5
65.2
82.0
73.9
67.2
87.0
74.7
improve DANN [8] by 9.3 % and ENT 21 by 4.1 % in the 1-shot setting. The second section shows our SPA model can improve DANN 18 by 11.2 and ENT (21 by 2.8 in the 3-shot setting. This shows that our SPA model can greatly improve the classic baselines and achieve comparable results with CDAC 41
B.3 Model Analysis
Robustness Analysis. In the main paper, we have already verified the robustness of SPA different graph structures on OfficeHome dataset. In the appendix, we further show the experimental results on Office31 dataset in Table Similarly, we conduct experiments on different types of Laplacian matrix, similarity metric of graph relations, and & number of nearest neighbors of KNN classification methods. The Laplacian matrices are chosen from the random walk laplacian matrix Lrwk D AA
and the symmetrically normalized Laplacian matrix Lagm the degree matrix based on the adjacency matrix A. In addition, the similarity metrics are chosen from cosine similarity and Gaussian similarity, and different & 5 when applying KNN classification algorithm. From Table We can find that different types of Laplacian matrix still lead to comparable results. As for the similarity metric, the Gaussian similarity brings better performance than cosine similarity. On Office31 dataset, 5-NN graphs is superior than 3-NN graphs when combining with Lrok. and comparable when combining with L Lym. For all these aforementioned experiments results, the differences between them are within 1% around, confirming the robustness of SPA.
D - AD- AD-1/2 where denotes
Table Classification Accuracy (%) on OfficeHome for unsupervised domain adaptation. The table is divided into three sections corresponding to robustness analysis, and parameter sensitivity, each separated by a double horizontal line.
Method
A >D
A
W
D-A
D-W
W >A
W WD
Avg.
3 0.1
94.2
95.1
76.6
98.9
78.6
99.6
90.5
3 0.3
94.0
96.2
76.9
98.9
79.3
99.8
90.8
3 0.5
94.0
96,4
77.9
99.0
78.0
99.8
90.8
#= 0.7
94.4
96.0
79.0
98.6
80.3
100.
91.4
= 0.8
94.2
95.7
76.1
98.6
78.3
99.8
90.5
Lruk w/ cos
93.8
95.0
76.3
98.6
79.7
100.
90.6
Lrun w/ gauss
95.0
95.6
78.2
98.6
80.0
99.8
91.2
L Lagmn w/ cos
93.8
93.8
78.5
98.6
79.9
100.
90.8
Lagon w/ gauss
93.8
95.6
79.4
98.6
78.8
99.8
91.0
Lonk w/ k 3
93.8
95.2
78.3
98.9
80.4
99.8
91.1
L Lywk w/ b=
93.8
95.0
76.3
98.6
79.7
100.
90.6
w/ l =
94.0
95.8
75.2
99.0
80.5
100.
90.7
w/ A 93.8
93.8
78.5
98.6
79.9
100.
90.8
18

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Parameter Sensitivity. In the main paper, we have already analyzed the experiments on the hyperparameter B of exponential moving averaging strategy for memory updates and verify that SPA is insensitive to this hyperparameter. Here, we show the experimental results on Office31 dataset in Table 9 Similarly, we design experiments on the hyperparameter 3 of exponential moving averaging strategy for memory updates, choosing 3 = 0.1, 0.3, 0.5, 0.7, 0.9 respectively. These results are based on DANN [88. From the series of results, we can find that Office31 dataset, the choice of 3 = 0.7 outperforms than others. In addition, the differences between these results are within 1.0%, which means that SPA relatively stable to this hyperparameter.
Furthermore, we design experiments for the coefficient of Cnap and the coefficient of Lysa to analyze the stability of SPA. The experimental results are shown in the Figure These results are based on DANN [8]. Fixing the coefficient of Lnap = 0.2, the coefficient of gaa changes from 0.1 to 0.9, Fixing the coefficient of Lasaa = 1.O, the coefficient of Lnap changes from 0. to 0.9. From the series of results, we can find that in OfficeHome dataset, the choice of different coefficients result in similar results, which means that SPA is insensitive to these coefficients.
80
60
Acsiney (%)
Accuracy
70
50
coefficient Eass coefficient of faus
Eyos coefficient of Luss
0.1
0.3
0.5
0.7
0.9
0.1
0.3
0.5
0.7
0.9
aa) A
+
(b) C-R
Figure 3: Parameter Sensitivity. The line plot of the coefficient of Lnap and the coefficient of Lase change from 0.1 to 0.9, leading to different accuracy results. The experiments are conducted on OfficeHome dataset, where (a) is A + C setting and (b) is R setting.
Transferability and Discriminability. The A-distance [ measures the distribution discrepancy that is defined d = 21 - 2c), where is the classifier loss discriminate the souce and target domains. Smaller A-distance indicates better domain-invarian features. Figure 4a shows that SPA achieve lower d.a, implying lower generalization error. Furthermore, following previous work [10]. we further offer the source accuracy and target accuracy specifically, in Figure 44 and Figure 4c We find that various methods achieve similar results of source accuracy, and SPA can always achieve higher target accuracy. Combined with the experimental results in Figure 4al this reveals that SPA enhances transferability while still keep a strong discriminability. Back our Introduction, this means that SPA can find a more suitable utilization of intra-domain information and inter-domain information properly align target samples.
DANS
DASS
DAAN
Dom
Scare Ascas
Tarpet Acoeecy
Scurce Racur
TapetArcuv
Owvil Naanyyy
(a) A-distance
(b) AC
C-R
Figure 4: Transferability and Discriminability. We compare SPA with DANN 18 BSP 10 and NPL 39 on OfficeHome dataset, where (a) is A-distance in - Cnd C R setting, (b) is accuracy
results in A + C setting and (c) is accuracy results in C R setting.
19

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Feature Visualization. To demonstrate the learning ability of SPA, we visualize the features of DANN [8] BSP [3]. NPL 399 and SPA with the t-SNE embedding [T7] under the C - R setting of OfficeHome Dataset in the main paper, referred as Figure 2 In the appendix, we offer more visualization figures, including Figure 5 in - setting and Figure in - W setting on Office31 dataset, Figure in A - C setting observations are consistent that the source features and target features learned by SPA are transferred better. These observations imply the superiority of SPA over discriminability and transferability in unsupervised domain adaptation scenario.
OfficeHome dataset. According to all the figures, the
(a) DANN
(b) BSP
(c) NPL
(d) SPA
Figure Feature Visualization. i-SNE plot of DANN 18 BSP 13 NPL 39 and SPA features
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Figure 6: Feature Visualization. the t-SNE plot of DANN [8), BSP [3). NPL [39], and SPA features on Office31 I dataset in the A - W setting. We use red markers for source domain features and blue markers for target domain features.
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Figure 7: Feature Visualization. the SNE plot of DANN 18) BSP 13 on OfficeHome dataset in the A C setting. We use red markers for source domain features and blue markers for target domain features.
NPL 39 and SPA features
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Convergence Analysis. To demonstrate the convergence of SPA, we visualize the changes of accuracy and training loss respectively during the training process. As shown in Figure the red curve is the changes of accuracy and the blue curve is the changes of training loss. The experiments are conducted on OfficeHome dataset, where Jare in A setting, (dd setting. Based on our experiments, it is evident that the model demonstrates satisfactory convergence properties. Through multiple iterations and varied initial settings, the model consistently approached and reached stable state,
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Figure 8: Convergence. The red curve is the changes of accuracy during the training process and the blue curve is the changes of training loss. The experiments are conducted on OfficeHome dataset, where (a) and (b) are in A + P setting, (c) and (d) are in R + A setting.
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Reviews:
[{"review_id": "Yto73nRiaS", "reviewer": "Reviewer_54MB", "summary": "This work proposed a graph spectral alignment model for unsupervised domain adaptation. They evaluated on several benchmarks and show good performance, especially in DomainNet and Office-Home, compared with existing UDA methods. Generally, the paper is easy to follow. ", "questions": "What are the cross-domain graphs? How are they aligned? \n\nWhat is key difference in terms of the proposed two terms?\n\n", "limitations": "The experimntal results are not diverse, mainly on classification performance.\n\nThe model is incremental over existing methods. ", "rating": 3, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper is generally easy to follow and the experimental results on DomainNet and Office-Home are pretty good. ", "weaknesses": "The novelty of this work is limited. The graph alignment is simply extended from BSP [12] and Graph Matching like SIGMA [39]. The Neighbor-aware Self-training Mechanism is similar to embedding propagation. In this sense, there is limited novelty in terms of the methodology contribution. \n\nThe performance on other benchmarks like Office-31 and VisDA seem not better than others. The visualization of feature embedding is not informative enough to validate the graph alignment. It is essential to visualize the domain-wise graphs, and how are they aligned? This can show more insights. For example, in Office-Home, their model performs better when A is target domain. Then what is the key reason?\n\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable time and review, and we have made great efforts to address all these concerns below:\n> **[Weakness 1]** \"The novelty of this work is limited. The graph alignment is simply extended from BSP [12] and Graph Matching like SIGMA [39]. The Neighbor-aware Self-training Mechanism is similar to embedding propagation. In this sense, there is limited novelty in terms of the methodology contribution.\"\n\n**[Answer]** Thanks for the feedback. \nAs we stated in the (Line 295-297 and Line 316), both work ([9] and [39]) are indeed related to our work.\nThe key finding of BSP [9] is that the eigenvectors with the largest singular values will dominate the feature transferability and thus, BSP penalizes the largest singular values for improving transferability.\nSIGMA [39] focuses on the category-level adaptation of object detection. Technically, their bipartite graph matching is a type of exact graph matching, requiring multiple matching stages for nodes and edges respectively.\n\nDespite that, as is stated by multiple previously published papers [9, 12, 32], the very core and crucial challenge of DA (and UDA) attributes to a balancing between inter-domain transferability and intra-domain discriminability (in our paper: Line 23-27).\nTo approach this balancing problem is not trivial since the remarkable transferability is usually enhanced at the expense of worse discriminability (in our paper: Line 30-31).\n\nOur work's major finding centers at this core problem as we develop a joint adjusting mechanism of graph spectral alignment and message propagation module.\nTo make the graph propagation feasible in UDA, we present a novel batch-wise propagation operator and develop the self-training propagation method, which is not a direct application of existing method. \n\nIn comparison with the two works the reviewer mentioned, while we do believe they make substantial contributions to the community, we believe neither work concerns this essential balancing problem.\n\n\n\n> **[Weakness 2]** \"The performance on other benchmarks like Office-31 and VisDA seem not better than others. \"\n\n**[Answer]** \nFirst, while the reviewer (rightfully) point this out, we may still want to list the performance gain of our approach overall: +2.6% on OfficeHome, +0.5% on VisDA, neck-to-neck performance with current SOTA[48] on Office-31, and **most notably*** the large-scale DomainNet with +8.6%.\nPartially, the reviewer also gave us credits on the empirical performances as is written in Strength section of th review :)\n\nUpon that, we pledge the reviewer to reconsider the empirical aspect of our approach, especially crediting the significant performance plus on the large-scaled one (DomainNet).\nTo have this result was somewhat rare, as we posit that a certain amount of prior papers did not report original DomainNet in the experiments.\n\n\n\n> **[Weakness 3 + Questions]** \"The visualization of feature embedding is not informative enough to validate the graph alignment. It is essential to visualize the domain-wise graphs. What are the cross-domain graphs? How are they aligned? What is key difference in terms of the proposed two terms?\"\n\n**[Answer]** \nThere seems some misunderstanding here. The graphs we built in our approach always attribute to each individual domain. As such, we do not have the domain-wise or the cross-domain graphs in that sense.\nWe kindly ask the reviewer to reiterate Line 96-104 for the graph definition, as well as the visualization plots in both experiments and the appendix.\n\n\n\n> **[Weakness 4]** \"For example, in Office-Home, their model performs better when A is target domain. Then what is the key reason?\"\n\n**[Answer]** \nThis is a good observation. As we can see from Table 2, the performances across different setups do have exhibited some patterns: C2A > A2C, A2P > P2A, A2R > R2A, as is rightfully pointed out by the reviewer.\nHowever, all the baselines in Table 2 also exhibit the same pattern --- not just our approach.\nWe postulate that this very much aligned results reveal a intrinsic properties in these public datasets --- and perhaps more importantly --- a difference of difficulty-level for these different pair of domain transfer.\n \n\n\n> **[Limitations]** \"The experimental results are not diverse, mainly on classification performance.\"\n\n**[Answer]**\nAs we dive into the literature, most papers published in the past ML venues (such as ICML, ICLR and NeurIPS) on DA, DG or UDA [9, 12, 17, 18, 31, 32, 44, 48], have commonly stuck with the benchmarks we report in our paper. We believe this is due to that this line of work mostly focuses on the fundamental ML problem behind UDA, rather than specific task.\nOn the other line, we do acknowledge that there are papers covering other diversified tasks such as object detection [39], semantic segmentation [36], or NLP [8, 10]. Different from the ML line of work, these papers were dedicated at specific task rather than promoting the generality of the method. \n\nThat said, given the terrain of the normal empirical proxy of UDA, we believe our experiments suffice to establish our contribution.\n\n"}, {"review_id": "PR8EtLCfvl", "reviewer": "Reviewer_AnYf", "summary": "This paper proposes a novel graph spectral alignment framework for unsupervised domain adaptation, jointly balancing the inter-domain transferability and the intra-domain discriminability. First, they cast the domain adaptation problem to graph primitives by composing a coarse graph alignment and aligning domain graphs in eigenspaces. Second, they perform a fine-grained message passing in the target domain via a neighbor-aware self-training mechanism. The first alignment method gives rise to coarse-grained topological structures transfer across domains but in a more intrinsic way than restrictive point-wise matching. With the help of fine-grained neighbor-aware propagation, the whole framework is able to refine the transferred topological structure to produce a discriminative domain classifier.", "questions": "1.\tThe questions are mentioned in weakness. More ablation studies can be offered. More information can be added to introduction. \n2.\tFor related work part, more latest references about graph methods can be added.\n3.\tFor the Laplacian metrices, you report the results based on two normalized types. Did you try any other types? \n4.\tThe authors mentioned the relation between kNN pseudo-labeling and graph propagation, which is confusing for me. Can you explain more on this?\n", "limitations": "Yes, the authors have addressed the limitations of their work at the end of the paper.", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1.\tThis paper is easy to follow with clear writing, concise figures, and well-structured formulation in problem definition and methods. \n2.\tThe research problem is essential and motivation is clear. This paper gives a new perspective for the essential problem of how to find a suitable utilization of intra-domain information and inter-domain information in unsupervised domain adaptation. \n3.\tThe proposed graph spectral alignment method is an attractive method in domain adaptation, which works well and inspires follow-up research.\n4.\tThe experiment part is comprehensive, including 4 commonly used datasets in domain adaptation.\n", "weaknesses": "1.\tTo support the claim of balancing transferability and discriminability, the authors offer the figures of visualized features. More ablation studies to express the balance can be offered.\n2.\tThe introduction of this paper is less informative. More technical details of the proposed method can be provided there to improve legibility, as well as more comparative description of previous works.\n3.\tSome grammars need to be improved. Line 120-122, the long sentence with two predicates. Line 241, ‘achieve’ should add ‘s’. Line 265, ‘presents’ should remove ‘s’. Line 270, ‘also use’ should add ‘s’. Line 283, ‘, By’ should use period. Line 289-292, ‘propose’, ‘formulate’, ‘calculate’ should add ‘s’. Line 297, ‘comes out’ should remove ‘s’.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for these thoughtful comments, and we would like to address your concerns in detail below:\n> **[Weakness 1 + Question 1]** \"To support the claim of balancing transferability and discriminability, the authors offer the figures of visualized features. More ablation studies to express the balance can be offered.\"\n\n**[Answer]** Thank you for expressing your concern regarding the balance between transferability and discriminability of our method. We offer feature visualizations of C->R setting of OfficeHome dataset in the main paper. More visualized features of A->D, A->W setting of Office31 dataset and A->C setting of OfficeHome dataset in the appendix. \n\nBesides, we offer a Transferability and Discriminability section in appendix. We use A-distance [27] measures the distribution discrepancy, which shows our SPA model achieves a lower generalization error. \n\nFurthermore, following previous work [3], we also offer the source accuracy and target accuracy specifically in Figure 2b and Figure 2c in appendix, which illustrates our SPA can always achieve higher target accuracy. Combined with all of these experimental results, it reveals that our SPA enhances transferability while still keep a strong discriminability. \nHope this can address your concern.\n\n\n> **[Weakness 2 + Questions 1]** \"The introduction of this paper is less informative. More technical details of the proposed method can be provided there to improve legibility, as well as more comparative description of previous works. [...] More information can be added to introduction.\"\n\n**[Answer]** Thanks for your suggestion. We leave out some information because of page limits. More comparisons with previous works are in related work. We will add more details and highlights to the introduction in the revised revision as the reviewer suggests.\n\n\n> **[Weakness 3]** \"Some grammars need to be improved. Line 120-122, [...]\"\n\n**[Answer]** Thank you for pointing out these grammar problems. We will fix these grammars for more clear presentation in the revised revision.\n\n\n> **[Question 2]** For related work part, more latest references about graph methods can be added.\n\n**[Answer]** Thank you for your suggestion. Although our method focuses mainly on graph matching and alignment methods for domain adaptation, we will improve our reference with more papers about graph data mining methods or graph neural networks for domain adaptation as suggested by the reviewer.\n\n\n> **[Qeustion 3]** For the Laplacian matrices, you report the results based on two normalized types. Did you try any other types?\n\n**[Answer]** Thanks for your question. We choose random walk Laplacian matrix and symmetrically normalized Laplacian matrix for robustness analysis in experiment section. These two types of graph laplacians are commonly-used among graph methods, because they have very good properties such as being symmetric, positive semi-definite, and having non-negative eigenvalues, which is an important basis for following spectral alignment. \n\nFurthermore, here we offer some extra experimental results for a type of unnormalized laplacian matrix $L = D - A$ with cosine similarity and Guassian similarity respectively in the following:\n| OfficeHome       | A2C  | A2P  | A2R  | C2A  | C2P  | C2R  | P2A  | P2C  | P2R  | R2A  | R2C  | R2P  | avg  |\n| ---------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| w/ $cos$  | 42.1 | 67.9 | 71.9 | 38.8 | 51.2 | 55.7 | 55.8 | 32.4 | 71.9 | 66.1 | 48.7 | 80.2 | 56.9 |\n| w/ $gas$  | 50.2 | 65.7 | 75.4 | 56.3 | 53.3 | 61.1 | 63.2 | 44.7 | 66.8 | 64.2 | 47.5 | 72.1 | 60.1 |\n\nFrom these experimental results, it also illustrates that the normalized graph laplacians with good properties perform better than the unnormalized one. \n\n\n> **[Question 4]** The authors mentioned the relation between kNN pseudo-labeling and graph propagation, which is confusing for me. Can you explain more on this?\n\n**[Answer]** Thanks for your thoughtful review. \nFor graph propagation methods, it can be represented as $\\mathbf{Z} = (\\mathbf{I} - \\alpha \\mathbf{A})^{-1}$ $\\mathbf{Y}$. The rows of $\\mathbf{Y}$ corresponding to labeled examples are one-hot encoded labels and the rest are zeros. The $\\alpha \\in [0,1)$ is a parameter. The class prediction for an unlabeled example $x_i$ is $\\hat{y} = \\arg \\max_{j} z_{i, j}$, where $z_{i, j}$ is the $(i, j)$ element of matrix $\\mathbf{Z}$.\nBased on our constructed graphs, it is intuitive for us to adopt graph propagation.\nHowever, the computation of $\\mathbf{Z}$ is performed on all data samples, and implicitly requires access to all embedding vectors at each step of computation.\nIf the size of dataset increases, it would be intractable to finish the computation of matrix $\\mathbf{Z}$.\nWe focus on producing labels for unlabeled target domain graphs in each iteration.\nTherefore, we avoid to solve the above linear system of classic label propagation via the weighted KNN classification algorithm [72] to generate pseudo-labels for target domain graph.\n"}, {"review_id": "DmRGeKwCYl", "reviewer": "Reviewer_pjo2", "summary": "The paper proposed a graph SPectral Alignment (SPA) framework which uses a coarse graph spectral alignment and neighbor-aware self-training mechanism. The authors compared the proposed method with different UDA methods using several benchmark datasets.", "questions": "1. Please add more details that how to construct a dynamic graph, especially for weighted edge and metric function.\n2. Please explain the reason why decreasing the distance of graphs is useful for solving da problem.\n3. Line 121, ``with n vertices can be from the spectrum of any other graph with n vertices\". what's the meaning of n? Do both graphs have to require n?\n4. Why uses weighed k-Nearest-Neighbor classification to obtain the pseudo-label？\n5. Please add more analysis about the results of experiments, such as Line 226, ``The experiments shows SPA consistently ourperforms than various of DA methods\".", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "The paper is generally well-written and clear. The results show the superior performance of the method in terms of accuracy in different datasets.", "weaknesses": "however, it missed some details that need to be completed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks sincerely for the constructive reviews, and we have made great efforts to address all these concerns.\n>  **[Weakness 1]** \"Please add more details that how to construct a dynamic graph, especially for weighted edge and metric function.\"\n\n**[Answer]** Thanks for your suggestion. We put different choices of metric function in the robust analysis in experiments and leave out some repeated information because of page limits. In revised version, we will follow your suggestion to add more details and analysis in Section 3.1 and experiments. \n\n\n>  **[Weakness 2]** Please explain the reason why decreasing the distance of graphs is useful for solving da problem.\n\n**[Answer]** Thanks for your suggestion. \nThe final goal of domain adaptation is to learn the domain-invariant representations (Line 20). In our paper, we first construct dynamic graphs within source domain and target domain separately and then utilize a spectral distance to project these graphs into the spectral space. After spectral alignment, source domain graphs are closer to target domain graphs in the latent space (Line 144-145). With message propagation, this alignment is further encouraged. In this way, the whole framework can perform well on domain adaptation scenario.\n\n\n>  **[Weakness 3]** Line 121, ``with n vertices can be from the spectrum of any other graph with n vertices\". what's the meaning of n? Do both graphs have to require n?\n\n**[Answer]**\nThanks for your question.\nIn our paper, the node size 'n' is exactly the batch size, which is a hyper-parameter. \nUnder our setting, following the definition of a classic graph matching problem, source domain graphs always have the same 'n' as target domain graphs. Graph matching aims at finding the vertex correspondence between the two unlabeled graphs that maximizes the total edge weight correlation. In other words, we expect two randomly sampled subsets from source/target domains shares similar intrinsical topological properties in the latent space and thus, have great transferability. \nThere are also some papers that study inexact graph matching, which allows matching two graphs of different sizes. We leave the extension to inexact graph matching for future work.\n\n>  **[Weakness 4]** \"Why uses weighed k-Nearest-Neighbor classification to obtain the pseudo-label？\"\n\n**[Answer]** \nThanks for your question. We'd like to show the superiority of our kNN pseudo-labeling algorithm from two aspects. \n\n**Motivation**: we can regard the weighted kNN method as a type of regularization. Our source domain graph and target domain graph are within a domain and follow homophily assumption. Compared with the single-point pseudo-labeling method, we believe the kNN method is able to encourage the smoothness of predictions among neighbors and hence better performance.\n\n**Technique**: \nafter graph spectral alignment, the rich structure information is coarsely transferred to the target domain and then we hope to align those fine-grained intra-domain information (Line 146-147). Message propagation is encouraged to perform this alignment. \n\nThe classic label propagation method can be represented as $\\mathbf{Z} = (\\mathbf{I} - \\alpha \\mathbf{A})^{-1}$ $\\mathbf{Y}$. The rows of $\\mathbf{Y}$ corresponding to labeled examples are one-hot encoded labels and the rest are zero. The $\\alpha \\in [0,1)$ is a parameter. The class prediction for an unlabeled example $x_i$ is $\\hat{y} = \\arg \\max_{j} z_{i, j}$, where $z_{i, j}$ is the $(i, j)$ element of matrix $\\mathbf{Z}$.\n\nHowever, the computation of propagation matrix $\\mathbf{Z}$ is usually performed on all data samples, and implicitly requires access to all embedding vectors at each step of computation. \nTherefore, we focus on batch-wise operations and avoid to solve the above linear system of message propagation via the weighted KNN classification algorithm [72] to generate pseudo-labels for target domain graphs.\n\n\n>  **[Weakness 5]** \"Please add more analysis about the results of experiments, such as Line 226, 'The experiments shows SPA consistently outperforms than various of DA methods'.\"\n\n**[Answer]**\nThanks for your suggestion. We leave out some information because of page limits and more analysis of experimental results can be found in appendix. In revised version, we will follow your suggestion to add more details and analysis for better presentation. \n"}, {"review_id": "PAtkIfMcDL", "reviewer": "Reviewer_Yk67", "summary": "The paper proposes a domain adaptation method called Spectral Alignment (SPA). The proposed SPA utilizes spectral distance defined as the difference between eigenvalues of the Laplacian matrix to quantify the distribution gap. Then SPA employs this distance as regularizer for domain alignment. Additionally, SPA incorporates pseudo-labeling for feature aggregation, enhancing the similarity between semantically related nodes. The experimental results on multiple datasets verfy the effectiveness of the proposed algorithm.", "questions": "1. The difference to the previous methods.\n2. The convergence analysis of the proposed method.", "limitations": "Yes, the authors say that \"The current method for constructing graph spectra is only a starting point and may be inadequate for more difficult scenarios such as universal domain adaptation. Additionally, this method is currently limited to visual classification tasks , and more sophisticated and generic methods to object detection or semantic segmentation are expected in the future\" in line 324.", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "Different from the previous domain adaptation methods, the paper introduces the spectral distance to measure the domain gap. In addition, the experiment results demonstrate the efficiacy of this idea.", "weaknesses": "1. The contribution of the paper is not clear. First, the paper directly employs a spectral distance from [1,20,59] without technical development to measure and narrow the distribution gap. Second, the feature aggregation with pseudo labels has been widely used in domain adaptation. So what the different of the proposed method to the previous work?\n2. Figure 1 does not effectively demonstrate the motivation and innovative aspects of this paper.\n3. Eq. (5) compute the total loss without consideration of loss scale. Specifically, Eq. (5) adopts four types of loss terms, L_{cls}，L_{adv}，L_{gsa}，L_{nas}. However, there is no trade-off parameters to balance different losses. I am not sure the convergence of the proposed method.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback, and we would like to address your concerns in detail below:\n> **[Weakness 1 + Question 1]** \"The contribution of the paper is not clear. First, the paper directly employs a spectral distance from [1,20,59] without technical development to measure and narrow the distribution gap. Second, the feature aggregation with pseudo labels has been widely used in domain adaptation. So what the different of the proposed method to the previous work?\"\n\n**[Answer]** \nThanks for the feedback. \nFirst of all, the proposed definition of spectral distance is not the same one as the existing distances [1,20,59]. In practice, different metric functions and graph laplacians can lead to different model performance. More details of choosing different metric functions and graph laplacians can refer to our experiments. \n\nBesides, our dynamic graphs motivate us to adopt graph propagation method. We did not directly apply the classic propagation method to our model because of their computation cost. We optimized this classic method with batch-wise operations. We also did a lots of technical improvement to joint the graph spectral alignment and neighbor-aware propagation and pursue a balance between the transferability and disciminability of model.\n\n\n> **[Weakness 2]** Figure 1 does not effectively demonstrate the motivation and innovative aspects of this paper.\n\n**[Answer]** Thanks for your thoughtful suggestion. This figure mainly used to illustrate the constitution of our framework. We will polish this pipeline to highlight our motivation and novelty in the revised version.\n\n>  **[Weakness 3 + Question 2]** \"Eq. (5) compute the total loss without consideration of loss scale. Specifically, Eq. (5) adopts four types of loss terms, L_{cls}，L_{adv}，L_{gsa}，L_{nas}. However, there is no trade-off parameters to balance different losses. I am not sure the convergence of the proposed method. The convergence analysis of the proposed method.\"\n\n**[Answer]** Thanks for your pointing out this problem. In our implementation, we indeed use loss scales. In Eq. (3), we also write out $\\alpha$, which is the coefficient term properly designed to grow along with iterations to mitigate the noises in the pseudo-labels at early iterations and avoid the error accumulation. In the revised version, we will fix the scale coefficients for other loss terms in Eq. (5).\n\nTo analyze the loss scales of SPA, here are more experiments of sensitivity analysis based on DANN [17] under the setting of OfficeHome dataset and we choose Gaussian similarity as the metric function. \nThe experimental results are shown in the following table. \n\nFixing the coefficient of $L_{nas}$ = 0.2, the coefficient of $L_{gsa}$ changes from 0.1 to 0.9.\n\n| The coefficient of $L_{gsa}$ = | 0.1  | 0.3  | 0.5  | 0.7  | 0.9  | $\\Delta$ |\n| ------- | ---- | ---- | ---- | ---- | ---- | -------- | \n| A2C     | 60.0 | 59.8\t| 60.3 | 60.1 | 59.0 | 1.3      |\n| C2R     | 82.4 | 82.1\t| 82.3 | 81.8 | 82.0 | 0.6      |\n\nFixing the coefficient of $L_{gsa}$ = 1.0, the coefficient of $L_{nas}$ changes from 0.1 to 0.9.\n\n| The coefficient of $L_{nas}$ = | 0.1  | 0.3  | 0.5  | 0.7  | 0.9  | $\\Delta$ |\n| ------- | ---- | ---- | ---- | ---- | ---- | -------- | \n| A2C     | 59.0 | 60.4 | 59.4 | 58.9 | 58.3 | 2.1      |\n| C2R     | 81.0 | 82.1\t| 82.8 | 83.4 | 83.2 | 2.4      |\n\nFrom the series of results,\nwe can find that in OfficeHome dataset, the choice of different coefficients result in similar results,\nwhich means that SPA is insensitive to these coefficients.\n\nBeside, we also visualize the curve of training loss and accuracy to support the convergence of our method and we put these figures in .pdf file. \n\nHope these extra experiments and analysis can address your concerns. \n\n"}, {"review_id": "o28gQdADcY", "reviewer": "Reviewer_Ecsg", "summary": "The authors present a new graph Spectral Alignment (SPA) framework for domain adaptation. The method consists of two main components: (i) a coarse graph alignment mechanism that uses a novel spectral regularizer to align domain graphs, and (ii) a fine-grained message propagation module that employs a neighbor-aware self-training mechanism to enhance discriminability in the target domain. Extensive experiments validate the effectiveness\tof SPA.", "questions": "See Weaknesses.", "limitations": "No limitations are included.", "rating": 7, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "The paper is exceptionally well-organized, with a clear and concise presentation of the proposed method. The approach itself is highly innovative and addresses a critical tradeoff in graph alignment. The authors have done an excellent job of explaining the core components of their method, including the coarse graph alignment mechanism and the fine-grained message propagation module.", "weaknesses": "I have a few concerns regarding some details in the paper that I would like to address:\n\n1. I noticed that the Neighbor-aware Propagation is abbreviated as \"L_nas\" in the paper. However, I think that \"L_nap\" would be a more appropriate abbreviation.\n\n2. In Table 4, where the results are presented without L_gsa and L_nas, the average accuracy is reported to be 68.5%. However, I am confused as to why this result is higher than the accuracy reported for CDAN in Table 2. \n\n3. I am also curious about the performance of SPA when it is not combined with existing methods such as CDAN. Have you conducted any experiments to evaluate the single SPA's performance in isolation? \n\n4. I am curious to know whether the graph in question is considered to be heavy. Additionally, I would like to inquire about the number of parameters that are present within the graph. ", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback, and we would like to address your concerns in detail below:\n> **[Weakness 1]** \"[...] Neighbor-aware Propagation is abbreviated as \"L_nas\" in the paper. However, I think that \"L_nap\" would be a more appropriate abbreviation.\"\n\n**[Answer]** Thanks for your suggestion. We will modify this abbreviation for better presentation in the revised version.\n\n\n> **[Weakness 2]** \"In Table 4, where the results are presented without L_gsa and L_nas, the average accuracy is reported to be 68.5%. However, I am confused as to why this result is higher than the accuracy reported for CDAN in Table 2.\" \n\n**[Answer]** In Table 2, following previous works [7, 12, 40], we compare the reported performance of CDAN [44] in the original paper. Besides, just as Line 182-184 state, we employ the standard cross-entropy loss with label-smoothing regularization [61] in our implementation. This label-smoothing regularization is directly applied to $L_{cls}$ , which is not related to $L_{gsa}$ or $L_{nas}$. In this way,  with this useful mechanism, even though the CDAN-based model is without $L_{gsa}$ and $L_{nas}$ in the first section of Table 4, the experimental results are better than the originally reported performance. In addition, following previous work [40], we also adopt coefficient warm-up trick during the training process, which also help improve the performance. More programming details can be referred in the code among our supplementary materials.\n\n\n> **[Weakness 3]** \"I am also curious about the performance of SPA when it is not combined with existing methods such as CDAN. Have you conducted any experiments to evaluate the single SPA's performance in isolation?\"\n\n**[Answer]** In Table 4, we point out the experiments of Ablation Study and Parameter Sensitivity are based CDAN [44]. Other ablation studies are default on DANN [17], which is just described as our Eq.(5) $L_{total}$. \nHere, we put more experimental details based on CDAN and DANN under the setting of OfficeHome dataset and we choose Gaussian similarity as the metric function.\n| OfficeHome        | A2C  | A2P  | A2R  | C2A  | C2P  | C2R  | P2A  | P2C  | P2R  | R2A  | R2C  | R2P  | avg  |\n| ----------------- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n| CDAN w/ $L_{rwk}$ | 59.8 | 79.1 | 84.1 | 74.5 | 79.9 | 82.1 | 73.1 | 57.9 | 85.0 | 77.8 | 61.4 | 87.8 | 75.2 |\n| CDAN w/ $L_{sym}$\t| 59.9 | 79.1 | 84.4 | 74.9 | 79.1 | 81.9 | 72.4 | 58.4 | 84.9 | 77.9 | 61.2 | 87.7 | 75.1 | \n| DANN w/ $L_{rwk}$\t| 60.4 | 79.7 | 85.0 | 73.6 | 81.3 | 82.1 |\t71.9 | 58.0 | 85.2 | 77.4 | 61.0 |\t88.1 | 75.3 | \n| DANN w/ $L_{sym}$ | 60.0 | 79.8 | 84.8 | 73.5 | 80.8 | 82.5 | 72.0 | 57.5 | 84.4 | 76.9 | 60.7 | 87.77 | 75.1 | \n\nFrom these above experimental results, we can see that our performance works well without CDAN.\n\n\n> **[Weakness 4]** \"I am curious to know whether the graph in question is considered to be heavy. Additionally, I would like to inquire about the number of parameters that are present within the graph.\"\n\n**[Answer]** Thanks for your thoughtful review. We can control the $k$-nearest neighbors for the graph, which is a hyper-parameter. Besides, during the graph construction process, we also can choose different metric function for edge weight. These experiments are offered in the Robust Analysis in experiments and appendix.   \n"}]

Author rebuttal:
We thank the reviews for their positive views about different aspects of our work which say that:
* our proposed method is: "an attractive method which works well and inspires follow-up research" (Reviewer AnYf), "different from the previous domain adaptation methods" (Reviewer Yk67), "highly innovative" (Reviewer Ecsg)
* our motivation is: "essential and clear" (Reviewer AnYf), "addresses a critical trade-off in graph alignment" (Reviewer Ecsg)
* our formulation is: "well-structured formulation in problem definition and methods" (Review AnYf), "an excellent job" (Reviewer Ecsg)
* our presentation is: "easy to follow" (Reviewer 54MB, Reviewer AnYf), "well-written and clear" (Reviewer pjo2), "clear writing, concise figures" (Review AnYf), "a clear and concise presentation of the proposed method" (Review Ecsg)
* our experiment is: "pretty good" (Reviewer 54MB), "comprehensive" (Reviewer AnYf), "superior" (Reviewer pjo2), "the experiment results demonstrate the efficacy of this idea" (Reviewer Yk67)

We also thank the reviewers for all the other detailed and insightful comments. We would like to address their concerns in detail below.


Meta-review: This paper introduces the Graph Spectral Alignment (SPA) framework, which effectively balances inter-domain transferability and intra-domain structures, outperforming the state-of-the-art domain adaptation methods on the standardized benchmarks. It is well-written and structured, providing a fresh perspective on the challenge of balancing intra-domain and inter-domain information in unsupervised domain adaptation, with an attractive and effective method, supported by the comprehensive experiments. However, the paper also lacks novelty in methodology, shows mixed performance results on certain benchmarks, and lacks informative feature visualization. In the rebuttal, the authors thoroughly addressed reviewers' questions and supplemented the relevant results. While there are varying opinions among the reviewers, most agreed to accept the revised paper. Despite some differing views, the AC still considers this paper to be an excellent one and therefore decides to accept it.
Decision: Accept (poster)