Reliable Weighted Optimal Transport for Unsupervised Domain Adaptation
Renjun Xu∗, Pelen Liu, Liyan Wang, Chao Chen
Zhejiang University, China

Jindong Wang
Microsoft Research

Abstract

contain data collected from different perspectives or by different sensors, leading to a large domain gap.

Recently, extensive researches have been proposed to address the UDA problem, which aims to learn transferrable
models for the unlabeled target domain. Among them,the optimal transport is a promising metric to align the
representations of the source and target domains. However, most existing works based on optimal transport ignore
the intra-domain structure, only achieving coarse pair-wisematching. The target samples distributed near the edgeof the clusters, or far from their corresponding class centers are easily to be misclassified by the decision boundary learned from the source domain. In this paper, we
present Reliable Weighted Optimal Transport (RWOT) for
unsupervised domain adaptation, including novel Shrinking Subspace Reliability (SSR) and weighted optimal transport strategy. Specifically, SSR exploits spatial prototypical information and intra-domain structure to dynamicallymeasure the sample-level domain discrepancy across domains. Besides, the weighted optimal transport strategy
based on SSR is exploited to achieve the precise-pair-wise
optimal transport procedure, which reduces negative transfer brought by the samples near decision boundaries in thetarget domain. RWOT also equips with the discriminative
centroid clustering exploitation strategy to learn transferfeatures. A thorough evaluation shows that RWOT outperforms existing state-of-the-art method on standard domain
adaptation benchmarks.

For unsupervised domain adaptation, a major line ofwork reduces the domain gap by learning domain invariant
feature representation, such as Maximum Mean Discrepancy (MMD) [38, 30], Correlation Alignment (CORAL)[36, 24] and Kullback-Leiber divergence (KL) [51]. Besides, another promising direction is based on the adversarial training [1, 37], where a discriminator (domain classifier) is trained to distinguish between the source and target
representations. Meanwhile, duo to its ability of encodingclass-structure in distributions, the optimal transport thatminimizes a global transportation effort or cost between distributions, has been widely used to reduce the domain shift
under complex distributions [5, 33, 47, 40]. However, existing optimal transport approaches in domain adaptation do
not consider intra-domain structure [44] of both domains,only achieving coarse pair-wise matching. Moreover, some
images that are significantly dissimilar across domains in
the feature space may cause a gross mismatch during optimal transport procedure, leading to negative transfer.

1. Introduction
Deep learning recently has achieved remarkable successin diverse computer vision tasks such as image classification, object detection and semantic segmentation with thehelp of large-scale labeled datasets [43]. Unfortunately, it
is always expensive and time-consuming to collect extensive amounts of labeled data. To avoid labeling efforts,
domain adaptation [26] serves as a promising solution toenhance the learning performance on a label-scarce domain(i.e., target domain) by transferring knowledge from a labelrich domain (i.e., source domain). The target domain may∗ Corresponding author: rux@zju.edu.cn

To address the aforementioned issues, we propose a Reliable Weighted Optimal Transport (RWOT) for domain
adaptation. Inspired by the prototypical networks which
has achieved significant performance in domain adaptation[27], we exploit the prototypical information in the feature
space to mitigate the wrong transport procedure. Besides,
we also take into account the discriminative feature learning to benefit the adaptation performance, which has been
widely used to learn the deep invariant features [49, 52].
Our proposed RWOT, therefore, consists of Shrinking Subspace Reliability (SSR) and weighted optimal transport
strategy, which can be seen in Figure 1. Moreover, wedemonstrate the necessity of shrinking subspace reliability
and the procedure of weighted optimal transport strategy.
RWOT also equips with a discriminative centroid exploitation strategy to improve transfer performance. The main
contributions of this paper are:(1) We propose shrinking subspace reliability to measure
the sample-level domain discrepancy across domains by exploiting spatial prototypical information and intra-domain
structure dynamically. The method can be used as a pre-

4394

(a)

(c)

(b)

𝑄

Source

𝑄

𝑄

(d)

𝑄

𝑄

𝑄

TargetSourceTargetSource𝑄

𝑄

TargetSourceTargetFigure 1. An overview of the proposed RWOT approach. Chromatic: Source samples; Gray: Target samples. Colorful imaginary lines:
hyperplane learned from source domain. Red dots: shared class centers. Different kinds of shapes: different classes. (a) An example ofunsupervised domain adaptation, where hard-aligned target samples distributed near the decision boundary, causing negative transfer. (b)The classification results of previous methods. (c) RWOT, with shrinking subspace reliability and discriminative centroid loss, exploits
spatial prototypical information and intra-domain structure. (d) The final situation, our proposal achieves intra-class compactness andinter-class separability in the source and target domains. Best viewed in color.

processing step for existing domain adaptation techniques,
improving efficiency significantly.
(2) We devise a weighted optimal transport strategy based on shrinking subspace reliability to achieve
the precise-pair-wise optimal transport, reducing negativetransfer brought by the samples near decision boundaries inthe target domain. A discriminative centroid exploitation
strategy is proposed to learn deep discriminative features.
(3) We analytically demonstrate that the combination ofshrinking subspace reliability and optimal transport strategy can make deep features more distinguished and significantly enhance robustness and efficacy. Experimental results show that RWOT works stably in various datasets andoutperforms existing methods.

2. Related work
Most of the discrepancy-based alignment methods are
based on minimizing a divergence that measures the discrepancy between the source and target distributions. A
representative work Maximum Mean Discrepancy (MMD)[38] aligns the source and target domains. Domain Adaptation Network (DAN) [21] utilizes multi-kernel strategies[11] in computing MMD to obtain a better performance.
Another work Deep Correlation Alignment (Deep CORAL)[36] aligns the covariance of the source and target features. Weighted-MMD (WDAN) [46] introduces classspecific auxiliary weights into the original MMD to exploit
the class prior probability on the source and target domains.
Recent Joint Discriminative Domain Adaptation (JDDA)[4] claims that discriminative feature representations canenhance the performance of domain alignment. Contrastive
Adaptation Network (CAN) [17] optimizes a new metricto explicitly model the intra-class domain discrepancy andthe inter-class domain discrepancy. Deep Transfer Network(DTN) [49] utilizes pseudo label in conditional alignment.
Easy-TL [43] programs intra-domain structures and Transferrable Prototypical Networks (TPN) [27] exploits prototypical distance [35] to avoid misclassification. Wang et al.
[44, 42, 41] dynamic evaluate the importance of marginal

and conditional distributions for distribution alignment.
Adversarial learning is another critical category to perform domain adaptation. GANs [12] have a generator that
captures data distribution and a discriminator that predicts
whether a sample is from the real data distribution or thegenerator. Based on this, to maximally confuse the domainclassifier, Domain Adversarial Neural Network (DANN) [1]is proposed with a feature extractor. Deep Adversarial Metric Learning [9] considers distance metric in adversarial domain adaptation. Later, several extensions were proposed,such as Multi-Adversarial Domain Adaption (MADA) [28],and Conditional Domain Adversarial Networks (CDANs)[22] enable the alignment of multi-modal distributions.
Domain-Symmetric Networks [50] learns invariant featuresin the domain adaptation. DANN [48] dynamically aligns
the adversarial representations.
Optimal transport has been applied in domain adaptation
to align the representations in the source and target domains
with associated theoretical guarantees. Wasserstein Distance Guided Representation Learning (WDGRL) [34] uses
Wasserstein distance as a core loss in promoting similarities
between embedded representations by the dual formulationof the problem. The most famous attempt is Deep Joint
Optimal Transport (DeepJDOT)[7], which applies the coupling matrix γ to transport the source samples to the target
domain by an estimated mapping, achieving high accuracy
on many transfer tasks. However, only adopting pure squareroot as a cost matrix for computing coupling γ will be quite
weak, especially for hard-aligned samples in a more complicated task. Recently, researchers propose a feature selection procedure [10] that is implemented in optimal transport
to leverage domain shift, but it is mainly based on the entropy regularization that cannot reduce negative transfer.

3. Reliable Weighted Optimal Transport
Most existing works resolve unsupervised domain adaptation by matching the shifted marginal distributions ofsource and target domains [22, 23]. A sophisticated approach is to formally define a statistical distance in the prob-

4395

𝜕ℒ
𝜕𝜃𝐺𝑓

𝐺𝑓

SourceTied

Target

Tied

Tied

(a)

𝜕ℒ
𝜕𝜃𝐺𝑦

Tied

Bottleneck
Layer

𝐺𝑦

𝑸

ℒ 𝑐𝑙𝑠

ℒ𝑔
ℒ𝑝

Decision
Boundary(b)

Decision
Boundaryℒ=ℒ𝑐𝑙𝑠 +𝛼ℒ 𝑝 +𝛽ℒ𝑔
𝜕ℒ𝜕𝜃

Back-propagation

SourceTargetSourceTargetFigure 2. The architectures of Reliable Weighted Optimal Transport (RWOT), where Gf is the feature generator, Gy is the adaptiveclassifier; Lg is the proposed weighted optimal transport loss based on shrinking subspace realibility, Lp is the discriminative centroid
loss, Lcls is the standard cross-entropy loss; α and β are hyper-parameters. The shrinking subspace realibility cost matrix Q is designed
to balance the contribution of spatial prototypical information and intra-domain structures dynamicly during the training: (a) The decisionboundary learned from source domain is not reliable to classify target samples, and the source samples are pushed to the spatial prototypesof corresponding classes correctly. (b) The decision boundary obtain reliable intra-domain structure of target samples, achieving better
performance. Best viewed in color.

abilistic metric space and learn the optimal transport coupling to minimize that distance [7, 5, 33]. However, despite
the great success, there is a common intrinsic limitationof this line of work: optimal transport is coarse pair-wisematching. Each image is reasoned as a whole to be transferred or not, without exploiting its intra-domain structures.
In this work, following the settings of unsupervised
domain adaptation, we define a source domain Ds =s{(xsi , yis )}ni=1with ns labeled samples and a target domaintt nt
D = {(xi )}i=1 with nt unlabeled samples. The source
and target domains follow joint probability distributions p
and q respectively, and note that p 6= q. The discrepancy between these two distributions raises the key technical challenge of domain adaptation. The goal of this paper is to design a deep neural network that enables end-to-end trainingof a transferable feature generator and an adaptive classifier
to minimize the distribution discrepancy across domains.
Following earlier works [7, 4], we choose two-stream
siamese CNN architecture with shared weights. We propose Reliable Weighted Optimal Transport (RWOT) for
unsupervised domain adaptation, which is an end-to-end
method that learns a feature generator Gf and a classifier
Gy , as illustrated in Figure 2. The main parts of RWOT
are Shrinking Subspace Reliability (SSR) and weighted optimal transport strategy. The shrinking subspace reliability
exploits spatial prototypical information and intra-domain
structures, which is demonstrated to be of the great benefitof domain alignment and final classification. The weighted
optimal transport strategy based on SSR achieves precise
pair-wise matching to reduce negative transfer. Moreover,
RWOT can learn discriminative transfer information by proposed centroid loss. In the following sections, we present
the details of RWOT.

edge of the clusters, or far from their corresponding classcenters are easily to be misclassified by the hyperplanelearned from the source domain. Inspired from self-labelingfor domain adaptation [43], we exploit spatial prototypesof each class learned from labeled source data to assign
the target samples a “pseudo” label. Considering negative transfer caused by target samples distributed near theedge of clusters, we propose Shrinking Subspace Reliability (SSR) to measure the sample-level domain discrepancy
across domains, including spatial prototypical information
to normalize prototypical distance and intra-domain structure computes the probability of target sample i belonging
to the class k.
For quantifying spatial prototypical information in both
domains, we define cs as the class centers of deep featuresin the source domain, and cs ∈ RC×d , where C denotes thenumber of classes in Ds . d is the number of output neurons
in the bottleneck layer. The spatial prototypical information
is defined by matrix D ∈ Rn×C as:t

D(i, k) = PCm=1 e−d(Gf (xti ),csm )),(1)

where d(Gf (xti ), csk )) is the distance between the target
sample Gf (xti ) and k-th source class center csk , where k ∈{1, 2, ..., C}. n represents the batch-size for training. Compared with single kernel methods to measure the discrepancy of both domains monotonously, we focus on multiple
kernels [13] to enhance the transferability of feature representation for deep domain adaptation comprehensively.
Therefore, the multi-kernel formulation of d(Gf (xti ), csk ))can be defined as:d(Gf (xti ), csk )) =K(csk , csk ) − 2K(Gf (xti ), csk )+K(Gf (xti ), Gf (xti )),3.1. Shrinking Subspace Reliability
In a previous study [4], domain adaptation methods ignore the situation that target samples distributed near these−d(Gf (xi ),ck ))(2)

The characteristic kernel associated with the feature map φ,
the kernel K(xs , xt ) = hφ(xs ), φ(xt )i, is defined as the4396

convex combination of m PSD kernels {Ku }:
(
m
m
X
X
K=

βu = 1, βu ≥ 0, ∀u

βu K u :

K=

u=1

u=1

3.2. Weighted Optimal Transport
)

,

(3)

where K denotes the multi-prototypical kernel set. The constraints on coefficients {βu } are imposed to guarantee thatthe derived multi-kernel K is characteristic. As studied theoretically in Gretton et al. [13], the multi-kernel K can utilize different kernels to ensure lower test error, leading toa principled approach for optimal prototypical distance representations.
To convey the likelihood of intra-domain information by
the pseudo classification probability of target samples, wedefine the sharpen probability annotation matrix M as:
Gy (Gf (xti ))M (i, k) = P y = k|Sof tmax,(4)τwhere M ∈ Rn×C , and M (i, k) denotes the probability ofthe target samples i belongs to the label class k. τ is thetemperature hyper-parameter [15] to obtain discriminative
probability and reduce domain shift.
The purpose of shrinking subspace reliability is to quantitatively evaluate the importance of both spatial prototypical information, D(i, k), and the intra-domain structure oftarget samples, M (i, k). Formally, SSR is defined by Q as:
Q(i, k) = PC

dA(k) D(i, k) + (2 − dA(k) )M (i, k)

m=1

dA(m) D(i, m) + (2 − dA(m) )M (i, m),Optimal transport for domain adaptation performs thealignment of the sample representations in the source andtarget domains. However, existing optimal transport strategies fail to utilize the intra-domain structures, causing negative transfer arising from ambiguity coarse pair-wise matching. Therefore, to reduce the wrong pair-wise transport
procedure, we devise the weighted optimal transport strategy by exploiting the proposed SSR. The optimizationof weighted optimal transport is based on weighted Kantorovich problem [2] which seeks for a general couplingγ ∈ X (Ds , Dt ) between Ds and Dt :Zγ∗ =R(xt , y(xs ))C(xs , xt ) dγ(xs , xt ),(6)
whereX (Ds , Dt ) denotes the probability distribution between Ds and Dt . y(xs ) is the label of source data xs
and R(xt , y(xs )) represents the adaptive matrix based on
deep reliable prior knowledge according to the intra-domain
structures. The cost function matrix C(xs , xt ) = ||xs −xt ||k denotes the cost to move probability mass from xs
to xt , where k = 2 [7, 6]. In our optimal transport problem, the weighted optimal transport strategy needs to estimate the adaptive transport coupling γ ∗ between two distributions and achieve feature transformation by minimizing
the cost of γ ∗ . Here is the discrete reformulation:(5)

where Q(i, k) weights the uncertainty of a target sample
i belonging to class k. The motivation for the numerator of Eq 5: while both D(i, k) and M (i, k) measure thelikelihood of target sample i having a label k, D(i, k) is
a distance measuring target sample i in the deep feature
space to the class center csk defined in the source domain,and M (i, k) is measured by the classifier Gy . During theearly training stage, D(i, k) is much more reliable than thepseudo label given by classifier Gy . Fortunately, we can use
the A -distance dA to adjust the weights.The A -distance,dA(k) (Dks , Dkt ) = 2(1 − 2ǫ(hk )), followed from the definition of [3, 44], measures the discrepancy between the source
and target domains. ǫ(hk ) is the error of a linear SVM classifier hk discriminating the two domains. In the context oftransfer learning, during the early training stage, the target
domain is expected to be quite different from the source domain in the deep feature space, and one can have a near
perfect classifier hk , or ǫ(hk ) → 0 and dA(k) → 2. The
second term of numerator in Eq 5 vanishes, and the network is mainly trained through the first term. Finally, when
the distributions of two domains coincide with each other,
the classifier hk cannot differentiate between two domains,
and thus ǫ(hk ) = 0.5 and dA(k) = 0. Now we can rely on
Gy , and the second term M (i, k) is the main contributor.
The dynamic process is shown in Figure 2.

arg minγ∈X (D s ,D t ) D s ×D tγ∗ =arg min hγ, ZiF =γ∈X (D s ,D t )arg min hγ, R · CiF ,γ∈X (D s ,D t )(7)

where γ ∗ ∈ Rn×n is the weighted ideal coupling matrix
between the source and target domains, representing as a
joint probability measure. h·, ·iF is the Frobenius dot product and Z ∈ Rn×n is the adaptive cost function matrix.
Choosing different weighted cost matrix will bring totallydifferent pairwise matching [8]. It is crucial to utilize deep
reliable prior knowledge R(x, y).
Considering SSR cost matrix Q which evaluates the spatial prototypical information and the intra-domain structureof target samples, we first propose a precise-pair-wise optimal transport mechanism by exploiting SSR. The discrete
formulation of adaptive cost matrix Z can be defined as:
Z(i, j) = Gf (xsi ) − Gf (xtj )2· (1 − Q(j, yis )),(8)

The further constraints of the (1 − Q(j, yis )) help to resolve the pairing ambiguity of traditional optimal transport
strategy. As the bottleneck layer encodes both semantic
and spatial information, discriminative representations allow a speedy computation of a transportation coupling withsignificant performance gains. With the above analysis,
weighted optimal transport optimizes jointly in this feature
space by reducing sample-wise distance of the same classes.

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Then, the solution to this problem can be achieved by minimizing the following objective function:
X
∗
Lg =
γi,j
(||Gf (xti ) − Gf (xsj )||2
i,j
(9)
+ F1 (Sof tmax(Gy (Gf (xti )), yjs )),where F1 is the cross-entropy function.

3.3. Discriminative Centroid Exploitation
The motivation of discriminative domain alignment isthat samples belonging to the same class should be as closer
as possible in the feature space. Inspired by the Center Loss[45], we propose discriminative centroid loss Lp for unsupervised domain adaptation as below:
Lp =

n
X

Gf (xsi ) − csyis

2
2

i=1

+

C X
n
X

Q(i, k) Gf (xti ) − csk

k=1 i=1

C
X

+λ

2

(10)

2

max(0, ν − csk1 − csk2

2),
2

k1 ,k2 =1,k1 6=k2

where λ is a hyper-parameter and ν is a constraint margin tocontrol the distance between the paired inter-class samples.
And csyis , as the yis -th class center in the source domain, canbe approximately evaluated by averaging deep features ofseveral batch-size samples as
Nb

csk =

1X
Gf (xsi )φ(yis , k),S(11)where α, β denote hyper-parameters that respectively tradeoff the contribution of weighted optimal transport strategy and discriminative domain alignment under different
datasets. The training process is shown in Algorithm 1.
Algorithm 1 The optimization strategy of RWOTs
, target data
Require: source data as Ds = {(xsi , yis )}ni=1tt nt
as D = {(xi )}i=1 . T is set as the total number oftraining iterations, and n represents the batch-size fortraining. Nb is the number of samples to compute thesource class centers in Eq 11.
1: Initialize two-stream CNN architectures.
2: for i = 1 to T dob
3:
Randomly choose Nb source samples {(xsi , yis )}N
i=1 .
s
4:
Calculate class centers cj in the source domain according to the Eq.(11).
5:
Randomly choose source samples {(xsi , yis )}ni=1 ∈Ds and target samples {(xti )}ni=1 ∈ Dt .
6:
Calculate spatial prototypical matrix D following
Eq.(1) and sharpen probability annotation matrix M
following Eq.(4). Update shrinking subspace reliability cost matrix Q following Eq.(5).
7:Calculate Lg following Eq.(9), Lp according toEq.(10), and Lcls according to Eq.(12).
8:Update parameters of Gy and Gf following Eq.(13).
9: end for

4. Experiment
We conduct experiments to evaluate our approach withstate-of-the-art domain adaptation methods.

i=1

where φ(yis , k) = 1 if yis = k, otherwise φ(yis , k) = 0.
PNb
S = i=1
φ(yis , k) and k ∈ {1, 2, · · · , C} is the class indicator. Ideally the class centers should be calculated basedon all the samples while the procedure is time-consuming.
Herein, we compute the class centers using Nb samples,
where Nb = mb × n, and mb ∈ {3, 4, 5} is recommended.

3.4. Training
In this section, we introduce the training process of
RWOT. We first define the standard classification loss ofthe source domain to train a classifier as follow:ns

Lcls =1 X
F1 (Gy (Gf (xsi )), yis ),
ns

(12)

i=1

Considering weighted optimal transport based on shrinking
subspace reliability and discriminative centroid loss, the total training objective of RWOT can be described as:
min Lcls + αLp + βLg ,Gy ,Gf(13)

4.1. Setup
Digits contains three standard digit classification datasets:
MNIST [19], USPS[16] and SVHN [25]. Each dataset
consists of 10 classes of digits, ranging from 0 to 9. We
follow previous work [4] to construct three transfer tasks:
USPS→MNIST, MNIST→USPS and SVHN→MNIST.
Office-31 [32] is a standard domain adaptation dataset
which contains 4110 images from 31 categories with threedomains: Amazon (A), with images collected from amazon.com, Webcam (W) and DSLR (D), with images shotby web camera and digital SLR camera respectively. By
permuting the three domains, we obtain six transfer tasks:
A→W, A→D, D→W, W→D, D→A and W→A.
ImageNet-Caltech is a large dataset built with ImageNet1K [31] and Caltech-256. They share 84 classes, thus
we select the same classes in both domains and form two
transfer tasks: ImageNet (84) → Caltech (84) and Caltech(84)→ ImageNet (84).
Office-Home [39] is a well organized, standard benchmark
for visual domain adaptation, consisting of 15,500 images

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Table 1. Classification accuracy (%) on Office-31 and ImageNet-Caltech dataset for unsupervised domain adaptation (ResNet)

Office-31

MethodImageNet-Caltech

Avg

A→W

A→D

D→W

W→D

D→A

W→A

Avg

I→C

C→I

ResNet [14]
DeepCORAL [36]DANN [1]ADDA [37]
CDAN [22]TPN [27]
DeepJDOT [7]70.0±0.3
83.0±0.1
81.5±0.3
86.2±0.3
94.1±0.1
91.2±0.3
88.9±0.3

65.5±0.471.5±0.274.3±0.278.8±0.492.9±0.2
89.9±0.288.2±0.1

96.1±0.2
97.9±0.2
97.1±0.1
96.8±0.2
98.6±0.1
97.7±0.2
98.5±0.1

99.3±0.3
98.0±0.2
99.6±0.4
99.1±0.2
100.0±099.5±0.1
99.6±0.262.8±0.463.7±0.3
65.5±0.2
69.5±0.1
69.3±0.1
70.5±0.2
72.1±0.460.5±0.1
64.5±0.2
63.2±0.2
68.5±0.1
71.0±0.373.5±0.1
70.1±0.4

75.7
79.8
80.2
83.2
87.7
87.1
86.2

91.5±0.3
92.0±0.4
96.2±0.3
96.5±0.3
97.7±0.3
96.1±0.2
95.0±0.1

78.0±0.385.5±0.2
87.0±0.1
89.1±0.2
91.3±0.3
90.8±0.385.3±0.2

84.8
88.8
91.6
92.8
94.5
93.5
90.2

RWOT-M
RWOT-D
RWOT-C
RWOT

92.5±0.1
93.9±0.1
94.7±0.2
95.1±0.2

89.5±0.292.4±0.3
94.0±0.2
94.5±0.2

99.2±0.2
99.4±0.3
99.4±0.2
99.5±0.2

100.0±0100.0±0100.0±0100.0±075.1±0.276.2±0.277.1±0.277.5±0.174.5±0.2
76.1±0.377.4±0.377.9±0.3

88.5
89.6
90.4
90.8

95.9±0.1
97.4±0.3
97.7±0.1
97.9±0.1

90.1±0.292.4±0.2
92.7±0.2
92.7±0.2

93.0
94.9
95.2
95.3

Table 2. Classification accuracy (%) on VisDA-2017 dataset for unsupervised domain adaptation (ResNet)
Method

plane

bcycl

bus

car

horse

knife

mcycl

personplant

sktbrd

train

truck

Avg

ResNet [14]DANN [1]SWD [20]
TPN [27]
DeepJDOT [7]
RWOT

70.6
75.9
90.8
93.7
85.4
95.1

51.8
70.5
82.5
85.1
73.4
80.3

55.8
65.3
81.7
69.2
77.3
83.7

8.9
17.3
70.5
81.6
87.3
90.0

67.9
72.8
91.7
93.5
84.1
92.4

7.6
38.6
69.5
61.9
64.7
68.0

48.3
58.0
86.3
89.3
91.5
92.5

54.5
77.2
77.5
81.4
79.3
82.2

71.1
72.5
87.4
93.5
91.9
87.9

27.9
40.4
63.6
81.6
44.4
78.4

64.6
70.4
85.6
84.5
88.5
90.4

5.6
44.7
29.2
49.9
61.8
68.2

54.5
58.6
76.4
80.4
77.4
84.0

Table 3. Classification accuracy (%) on Digits dataset for unsupervised domain adaptation (LeNet)
Method

S→M

M→U

U→M

Avg

LeNet [19]DANN [1]ADDA [37]
DeepCORAL [36]DeepJDOT [7]68.3±0.385.5±0.489.2±0.488.3±0.2
96.1±0.3

65.3±0.584.9±0.685.4±0.484.1±0.3
96.3±0.566.2±0.2
86.3±0.3
96.5±0.493.6±0.2
96.7±0.2

66.6
85.6
90.4
88.7
96.4

RWOT-M
RWOT-D
RWOT-C
RWOT

97.2±0.2
97.9±0.2
98.5±0.1
98.8±0.1

97.5±0.3
98.0±0.1
98.5±0.2
98.5±0.2

96.8±0.4
97.3±0.3
97.5±0.2
97.5±0.2

97.1
97.7
98.1
98.3

ment (DeepCORAL) [36] applies correlational matrix for
marginal alignment in deep domain adaptation. (5) Conditional Domain Adversarial Network (CDAN) [22] designs a conditional alignment network based on adversarial learning. (6) Deep Joint Distribution Optimal Transport(DeepJDOT) [7] adapts optimal transport strategy in deep
domain adaptation. (7) Transferrable Prototypical Network(TPN) [27] explores the prototypical information for discriminative feature alignment. (8) Sliced Wasserstein Discrepancy (SWD) [20] utilizes the Wasserstein Distance indomain alignment.

4.2. Implementation Details
in 65 object classes in office and home settings, with four
dissimilar domains: Artistic images (Ar), Clip Art (Cl),
Product images (Pr) and Real-World (Rw).
VisDA-2017 [29] is a large-scale computer vision datasetwith two domains: Synthetic, renderings of 3D models from different angles and different lighting conditions;
Real, real-world images. It has 280K images in 12 classes.
This scale brings challenges to domain adaptation.
We compare the proposed RWOT model with state-ofthe-art domain adaptation methods: (1) ResNet-50 [14]. (2)Domain Adversarial Neural Network (DANN) [1] matchesdifferent domains by making them indistinguishable fora domain discriminator. (3) Adversarial Discriminative
Domain Adaptation (ADDA) [37] designs a robust twostage unsupervised domain adaptation model based on adversarial learning objectives. (4) Deep Correlation Align-Standard protocols for unsupervised domain adaptation
have been followed. For Office-31 and VisDA dataset,
ResNet-50 [14] is used as the backbone network and themodels are fine-tuned from ResNet-50 pretrained on ImageNet. For experiments on digits dataset, we use the sample LeNet architecture following previous work [4]. We
perform five random experiments and record the averaged
accuracy for all transfer tasks.
For RWOT, we adopt a Gaussian kernel K(a, b) =exp(−||Gf (a)−Gf (b)||/σ) with the bandwidth σ set to themedian pair-wise distances on the training data. Following
existing works [21, 13], we consider a family of m Gaussian−8
kernels {ku }mσ
u=1 by varying bandwidth σu between 2
1
8
and 2 σ with a multiplicative step-size of 2 2 . The multikernel strategy can measure prototypical distances and capture useful transferable information. We use all labeled

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Figure 3. The t-SNE visualization of SVHN→MNIST and A→D tasks. Figure (a-d) represents category information (Each color denotes
a class). Figure (e-h) represents domain information (Blue: Source domain; Red: Target domain).

source examples and unlabeled examples for training.
We optimize the network by the Stochastic Gradient Descent (SGD) optimizer with a momentum of 0.9 and batchsize 128, namely total 256 images from the source andtarget domains. The learning rate and progressive training strategies are the same as [7]. Note that λ, as thehyper-parameter in centroid clustering, is set to 0.001 andthe constraint margin ν is fixed as 50 throughout experiments. The constraint temperature parameter τ is fixed as
0.5. As for trade-off hyper-parameters α ∈ [10−3 , 1] andβ ∈ [10−2 , 10], we select α = 0.01 and β = 0.1 for alltransfer tasks. And we choose mb = 4 for class centercomputation. In our experiments, we compare the average
accuracy of each method on five random experiments.

4.3. Result and Discussion
The unsupervised adaptation results on six Office-31 andtwo ImageNet-Caltech transfer tasks are reported in Table
1. For a fair comparison, the results for most comparison
methods are from their original papers. We can observe that
RWOT significantly outperforms all previous methods onmost tasks. It is worth noting that our proposal improves theclassification accuracy substantially on hard transfer tasks,
e.g. A→D and D→A, and achieves comparable classification performance on easy transfer tasks, e.g. D→W and
W→D, where source and target are similar. Compared with
DeepJDOT, the proposed framework exploits spatial prototypical information and aligns discriminative representationof each class centers of both domains, achieving intra-classcompactness and inter-class separability.
The results on VisDA-2017 are shown in Table 2. Dueto the large domain gap between the source and target
domains, we observe that the comparison methods obtain
poor performance in some classes. The RWOT approachachieves performance boost in total, indicating that our ar-chitecture of reliable weight optimal transport via SSR isable to transfer more dissimilar categories. Considering thelarge size of VisDA-2017 dataset, our proposal gains significant improvement.
We further compare RWOT with previous approaches on
the Digits dataset, as reported in Table 3. In contrast to
Office-31 datasets, Digits dataset has a much larger domain
size. We observe that RWOT overpasses all comparison
methods on most transfer tasks and achieves almost stateof-the-art performance. It is remarkable that our proposal
promotes the classification accuracy substantially on hardtransfer tasks, e.g. SVHN→MNIST, where the source andtarget domains are substantially different (in scale, background clutter, blurring, slanting). The significant results
suggest that RWOT is robust to a large domain gap and able
to learn more transferable representations for unsupervised
domain adaptation. Due to the limit of space, the results ofOffice-Home and ImageNet-Caltech are shown in the Supplementary Material.

4.4. Analysis
Ablation Study. To tooth apart the separate contributions of the weighted optimal transport strategy and discriminative centroid loss, we compare RWOT with DeepJDOT and three variants of RWOT on Office-31 and Digits datasets: (1) RWOT-M, the variant only with reliable
intra-domain structure (Ls + βLg , Q=M). (2) RWOTD, the variant only with spatial prototypical information(Ls + βLg , Q=D). (3) RWOT-C, the variant without centroid loss (Ls + βLg ). RWOT-C without SSR is essentially DeepJDOT. Since RWOT-C and all the variants of
RWOT outperform DeepJDOT in each task of our experiments significantly, and RWOT-C works better on thosedifficult tasks than RWOT-M and RWOT-D, it demonstrates
that SSR weighted optimal transport is vital to match the4400

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Figure 5. Comparison between RWOT and other state-ofthe-art approaches in the convergence performance on the
SVHN→MNIST (left) and the A→D (right) tasks.

source and target samples associated with the same class.
Moreover, RWOT also improves with a large room over all
three variants and DeepJDOT, validating the complement ofweighted optimal transport strategy and discriminative centroid loss.
Feature visualization. To show the feature transferability, we visualize the t-SNE embeddings [18] of thebottleneck representation by DeepJDOT and RWOT on
SVHN→MNIST and A→D tasks. Figure 3(a)-3(c) display that the features learned by DeepJDOT for different
categories are mixed up. Figure 3(e)-3(g) shows that thedomains are not well aligned while even worse, the target samples are aligned to the entire source data with possibly wrong classes, causing negative transfer. Note that,
Figure 3(f)-3(h) show that the representations generated by
RWOT achieves exactly 31 clusters with clear boundaries
on A→D task. The significant visualization results suggestthat our proposal is able to match the complex structuresof the source and target domains and maximize the margin
between different classes.
Distribution Discrepancy. The domain adaptation theory [3] suggests proxy A-distance as a measure of crossdomain discrepancy. We adopt dA(i) (Dis , Dit ) = 2(1 −2ǫ(hi )) to analyze the distance between two domains. Note
that, ǫ(hi ) is the generalization error of a linear classifier hdiscriminating the source domain Dis and the target domain
Dit [22]. Figure 4(a) demonstrates the maximum discrepancy (maxi dA(i) ) and average discrepancy (avgi dA(i) ) on
A→D task with the features of Source only, DeepJDOT,
CDAN, TPN and RWOT. A much smaller discrepancy ofeither maximum or average has been observed by using

RWOT features than compared approach features, which
implies an effective reduction in domain gap. Figure 4(b)shows the convergence performance of our approach via
A-distance of the training process on A→D. We observethat RWOT achieves rapid convergence performance andsignificantly lower A-distance due to it considers the intradomain structure of the same classes in training.
Parameter Sensitivity. We evaluate the effects of theparameter α, β which balances the contribution of weighted
optimal transport strategy and discriminative centroid loss,
respectively. Figure 4(c) shows the variation of average accuracy as α or β on A→D task. We find that the accuracy
increases first and then decreases as α or β increases, which
demonstrates a proper trade-off can improve transfer performance. The wide-range significant performances validate
the robustness and flexibility of RWOT.
Convergence. To illustrate the convergence of RWOT,
we evaluate the test errors of all comparison methods on
SVHN→MNIST and A→D tasks, as shown in Figure 5.
The result reveals that our achieves stable convergence performance and significantly lower test error on the target domain. What is more, the trend of convergence curve suggests that RWOT considers spatial prototypical informationand intra-domain structure. Such a phenomenon implies
that RWOT can be trained efficiently and stably than previous domain adaptation methods.

5. Conclusions
This paper presented Reliable Weighted Optimal Transport (RWOT) for unsupervised domain adaptation withpowerful Shrinking Subspace Reliability (SSR) and discriminative centroid loss. It exploits spatial prototypicalinformation and intra-domain structure to reduce negativetransfer brought by the samples near decision boundaries inthe target domain. The proposed centroid loss also substantially enhances the performance of the hard-aligned samples
in the more difficult transfer tasks. Comprehensive experiments show that our proposal outperforms state-of-the-art
results on various domain adaptation datasets.

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