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+# Unsupervised Domain Adaptation via Structurally Regularized Deep Clustering
+
+Hui Tang, Ke Chen, and Kui Jia*
+
+South China University of Technology
+
+381 Wushan Road, Tianhe District, Guangzhou, Guangdong, China
+
+eehuitang@mail.scut.edu.cn,{chenk,kuijia}@scut.edu.cn
+
+# Abstract
+
+Unsupervised domain adaptation (UDA) is to make predictions for unlabeled data on a target domain, given labeled data on a source domain whose distribution shifts from the target one. Mainstream UDA methods learn aligned features between the two domains, such that a classifier trained on the source features can be readily applied to the target ones. However, such a transferring strategy has a potential risk of damaging the intrinsic discrimination of target data. To alleviate this risk, we are motivated by the assumption of structural domain similarity, and propose to directly uncover the intrinsic target discrimination via discriminative clustering of target data. We constrain the clustering solutions using structural source regularization that hinges on our assumed structural domain similarity. Technically, we use a flexible framework of deep network based discriminative clustering that minimizes the KL divergence between predictive label distribution of the network and an introduced auxiliary one; replacing the auxiliary distribution with that formed by ground-truth labels of source data implements the structural source regularization via a simple strategy of joint network training. We term our proposed method as Structurally Regularized Deep Clustering (SRDC), where we also enhance target discrimination with clustering of intermediate network features, and enhance structural regularization with soft selection of less divergent source examples. Careful ablation studies show the efficacy of our proposed SRDC. Notably, with no explicit domain alignment, SRDC outperforms all existing methods on three UDA benchmarks.
+
+# 1. Introduction
+
+Given labeled data on a source domain, unsupervised domain adaptation (UDA) is to make predictions in the same label space for unlabeled data on a target domain, where there may exist divergence between the two domains. Main-
+
+stream methods are motivated by the classic UDA theories [2, 3, 40] that specify the learning bounds involving domain divergences, whose magnitudes depend on the feature space and the hypothesis space of classifier. Consequently, these methods (e.g., those recent ones based on adversarial training of deep networks [16, 48]) strive to learn aligned features between the two domains, such that classifiers trained on the source features can be readily applied to the target ones. In spite of impressive results achieved by these methods, they have a potential risk of damaging the intrinsic structures of target data discrimination, as discussed in [9, 50, 69]. Attempts are made in [9, 50] to alleviate this risk, however, explicit domain alignments are still pursued in their proposed solutions.
+
+To address this issue, we first instantiate the general assumption of domain closeness in UDA problems [2, 50] as structural domain similarity, which spells as two notions of domain-wise discrimination and class-wise closeness — the former notion assumes the existence of intrinsic structures of discriminative data clusters in individual domains, and the later one assumes that clusters of the two domains corresponding to the same class label are geometrically close. This assumption motivates us to consider a UDA approach that directly uncovers the intrinsic data discrimination via discriminative clustering of target data, where we propose to constrain the clustering solutions using structural source regularization hinging on our assumed structural similarity.
+
+Among various deep network based clustering algorithms [4, 8, 14, 61], we choose a simple but flexible nongenerative framework [14], which performs discriminative clustering by minimizing the KL divergence between predictive label distribution of the network and an introduced auxiliary one. Structural source regularization is simply achieved via a simple strategy of joint network training, by replacing the auxiliary distribution with that formed by ground-truth labels of source data. We term our proposed method as Structurally Regularized Deep Clustering (SRDC). In SRDC, we also enhance target discrimination with clustering of intermediate network features, and enhance structural regularization with soft selection of less
+
+divergent source examples. We note that quite a few recent UDA methods [13, 27, 41, 51] consider clustering of target data as well; however, they still do explicit feature alignment between the two domains via alignment of cluster centers/samples, thus prone to the aforementioned risk of damaged intrinsic target discrimination. Experiments on benchmark UDA datasets show the efficacy of our proposed SRDC. We finally summarize our contributions as follows.
+
+- To address a potential issue of damaging the intrinsic data discrimination by explicitly learning domain-aligned features, we propose in this work a source-regularized, deep discriminative clustering method in order to directly uncover the intrinsic discrimination among target data. The method is motivated by our assumption of structural similarity between the two domains, for which we term the proposed method as Structurally Regularized Deep Clustering (SRDC).  
+- To technically achieve SRDC, we use a flexible deep clustering framework that first introduces an auxiliary distribution, and then minimizes the KL divergence between the introduced one and the predictive label distribution of the network; replacing the auxiliary distribution with that of ground-truth labels of source data implements the structural source regularization via a simple strategy of joint network training. In SRDC, we also design useful ingredients to enhance target discrimination with clustering of intermediate network features, and to enhance structural regularization with soft selection of less divergent source examples.  
+- We conduct careful ablation studies on benchmark UDA datasets, which verify the efficacy of individual components proposed in SRDC. Notably, with no explicit domain alignment, our proposed SRDC outperforms all existing methods on the benchmark datasets.
+
+# 2. Related works
+
+Alignment based domain adaptation. A typical line of works [16, 43, 53, 63] leverages a domain-adversarial task to align the source and target domains as a whole so that class labels can be transferred from the source domain to the unlabeled target one. Another typical line of works directly minimizes the domain shift measured by various metrics, e.g., maximum mean discrepancy (MMD) [34, 36, 37]. These methods are based on domain-level domain alignment. To achieve class-level domain alignment, the works of [35, 42] utilize the multiplicative interaction of feature representations and class predictions so that the domain discriminator can be aware of the classification boundary. Based on the integrated task and domain classifier, [52] encourages a mutually inhibitory relation between category and domain predictions for any input instance. The works of
+
+[7, 13, 41, 59] align the labeled source centroid and pseudolabeled target centroid of each shared class in the feature space. Some works [31, 47, 48] use individual task classifiers for the two domains to detect non-discriminative features and reversely learn a discriminative feature extractor. Some works [30, 56, 57] focus attention on transferable regions to derive a domain-invariant classification model. To help achieve target-discriminative features, [28, 49] generate synthetic images from the raw input data of the two domains via GANs [19]. The recent work of [9] improves adversarial feature adaptation, where the discriminative structures of target data may be deteriorated [69]. The work of [60] adapts the feature norms of the two domains to a large range of values so that the learned features are not only task-discriminative but also domain-invariant.
+
+Clustering based domain adaptation. The cluster assumption states that the classification boundary should not pass through high-density regions, but instead lie in low-density regions [6]. To enforce the cluster assumption, conditional entropy minimization [20, 32] is widely used in the UDA community [11, 44, 45, 50, 51, 60, 64, 68]. The work of [27] adopts the spherical  $K$ -means to assign target labels. The recent work of [13] employs a Fisher-like criterion based deep clustering loss [38]. However, they use target clustering just as an incremental technique to improve explicit feature alignment. The previous work of [50] is based on the clustering criterion of mutual information maximization, which still explicitly forces domain alignment. In contrast, with no explicit domain alignment, SRDC aims to uncover the intrinsic target discrimination by discriminative target clustering with structural source regularization.
+
+Latent domain discovery. Methods of latent domain discovery [10, 18, 22, 39] focus on capturing latent structures of the source, target data or a mixed one under the assumption that data may practically comprise multiple diverse distributions. Our proposed SRDC shares the same motivation with these methods, but differs in the aim to uncover the intrinsic discrimination among target classes by structurally source regularized deep discriminative target clustering, in a distinctive perspective of utilizing structural similarity between the source and target domains.
+
+# 3. The strategies of transferring versus uncovering the intrinsic target discrimination
+
+Consider a source domain  $S$  with  $n_s$  labeled examples  $\{(x_j^s, y_j^s)\}_{j=1}^{n_s}$ , and a target domain  $\mathcal{T}$  with  $n_t$  unlabeled examples  $\{x_i^t\}_{i=1}^{n_t}$ . Unsupervised domain adaptation (UDA) assumes a shared label space  $\mathcal{V}$  between  $S$  and  $\mathcal{T}$ . Let  $|\mathcal{V}| = K$  and we have  $y^s \in \{1, 2, \ldots, K\}$  for any source instance  $\boldsymbol{x}^s$ . The objective of transductive UDA is to predict  $\{\hat{y}_i^t\}_{i=1}^{n_t}$  of  $\{x_i^t\}_{i=1}^{n_t}$  by learning a feature embedding function  $\varphi: \mathcal{X} \to \mathcal{Z}$  that lifts any input instance  $\boldsymbol{x} \in \mathcal{X}$  to
+
+the feature space  $\mathcal{Z}$ , and a classifier  $f: \mathcal{Z} \to \mathbb{R}^{K}$ . Subtly different from transductive UDA, inductive UDA is to measure performance of the learned  $\varphi(\cdot)$  and  $f(\cdot)$  on held-out instances sampled from the same  $\mathcal{T}$ . This subtle difference is in fact important since we expect to use the learned  $\varphi(\cdot)$  and  $f(\cdot)$  as off-the-shelf models, and we expect them to be consistent when learning with different source domains.
+
+Domain closeness is generally assumed in UDA either theoretically [2, 40] or intuitively [50]. In this work, we summarize the assumptions in [50] as the structural similarity between the source and target domains, which include the following notions of domain-wise discrimination and class-wise closeness, as illustrated in Figure 1.
+
+- Domain-wise discrimination assumes that there exist intrinsic structures of data discrimination in individual domains, i.e., data in either source or target domains are discriminatively clustered corresponding to the shared label space.  
+- Class-wise closeness assumes that clusters of the two domains corresponding to the same class label are geometrically close.
+
+Based on these assumptions, many of exiting works [16, 35, 42, 48, 53, 66] take the transferring strategy of learning aligned feature representations between the two domains, such that classifiers trained on source features can be readily applied to the target ones. However, such a strategy has a potential risk of damaging the intrinsic data discrimination on the target domain, as discussed in recent works of [9, 50, 69]. An illustration of such damage is also given in Figure 1. We note that more importantly, classifiers adapting to the damaged discrimination of target data would be less effective for tasks of inductive UDA, since they deviate too much from the oracle target classifier, i.e. an ideal one trained on the target data with the ground-truth labels.
+
+Based on the above analysis, we are motivated to directly uncover the intrinsic target discrimination via discriminative clustering of target data. To leverage the labeled source data, we propose to constrain the clustering solutions using structural source regularization that hinges on our assumed structural similarity across domains. Section 4 presents details of our method, with an illustration given in Figure 1. We note that quite a few recent methods [13, 27, 41, 51] consider clustering of target data as well; however, they still do explicit feature alignment across domains via alignment of cluster centers/samples, thus prone to the aforementioned risk of damaged intrinsic target discrimination.
+
+# 4. Discriminative target clustering with structural source regularization
+
+We parameterize the feature embedding function  $\varphi (\cdot ;\pmb {\theta})$  and classifier  $f(\cdot ;\pmb {\vartheta})$  as a deep network [21, 25, 26, 65],
+
+![](images/f4bc5bb3193d2648d8a5f8a5625dd61222c3f2677a209cffe803a90b9d5e55e4.jpg)  
+Source ▲ Target ▲ Class 1
+
+![](images/23c8faa945dd50f2f96d2fc95c2053c395842f3bf331eb233a5e7ea588a83e4b.jpg)
+
+![](images/7d25964741341f2abaf004fa4c01be59d13d17958756362e5f11d76caa4feacc.jpg)  
+Class 2  
+Figure 1. (Best viewed in color.) (a) Illustration of the assumption of structural domain similarity (cf. Section 3). The orange line denotes the classifier trained on the labeled source data and the green one denotes the classifier trained on the labeled target data, i.e. the oracle target classifier. (b) Illustration of damaging intrinsic structures of data discrimination on the target domain by the existing transferring strategy. The dashed line denotes the source classifier adapting to the damaged discrimination of target data, which has a sub-optimal generalization. (c) Illustration of our proposed uncovering strategy. Discriminative target clustering with structural source regularization uncovers intrinsic target discrimination.
+
+where  $\{\theta, \vartheta\}$  collects the network parameters. We also write them as  $\varphi(\cdot)$  and  $f(\cdot)$  for simplicity, and use  $f \circ \varphi$  to denote the whole network. For an input instance  $\pmb{x}$ , the network computes feature representation  $\pmb{z} = \varphi(\pmb{x})$ , and outputs a probability vector  $\pmb{p} = \operatorname{softmax}(f(\pmb{z})) \in [0,1]^K$  after the final softmax operation.
+
+As discussed in Section 3, in order to uncover the intrinsic discrimination of the target domain, we opt for direct clustering of target instances with structural regularization from the source domain. Among various clustering methods [4, 8, 14, 61], we choose a flexible framework of deep discriminative clustering [14], which minimizes the KL divergence between predictive label distribution of the network and an introduced auxiliary one; by replacing the auxiliary distribution with that of ground-truth labels of source data, we easily implement the structural source regularization via a simple strategy of network joint training, for which we term our proposed method as Structurally Regularized Deep Clustering (SRDC). In SRDC, we also enhance target discrimination with clustering of intermediate network features, and enhance structural regularization with soft selection of less divergent source examples.
+
+# 4.1. Deep discriminative target clustering
+
+For the unlabeled target data  $\{\pmb{x}_i^t\}_{i=1}^{n_t}$ , the network predicts, after softmax operation, the probability vectors  $\{\pmb{p}_i^t\}_{i=1}^{n_t}$  that we collectively write as  $P^t$ . We also write as  $p_{i,k}^t$  the  $k^{th}$  element of  $\pmb{p}_i^t$  for the target instance  $\pmb{x}_i^t$ .  $P^t$  thus approximates the predictive label distribution of the network for samples of  $\mathcal{T}$ . Similar to [14, 24], we first introduce an auxiliary counterpart  $Q^t$ , and the proposed SRDC then alternates in (1) updating  $Q^t$ , and (2) using the updated  $Q^t$  as labels to train the network to update parameters  $\{\theta, \vartheta\}$ , which optimizes the following objective of deep
+
+discriminative clustering
+
+$$
+\min  _ {\boldsymbol {Q} ^ {t}, \{\boldsymbol {\theta}, \boldsymbol {\vartheta} \}} \mathcal {L} _ {f \circ \varphi} ^ {t} = \mathrm {K L} (\boldsymbol {Q} ^ {t} | | \boldsymbol {P} ^ {t}) + \sum_ {k = 1} ^ {K} \varrho_ {k} ^ {t} \log \varrho_ {k} ^ {t}, \tag {1}
+$$
+
+where  $\varrho_{k}^{t} = \frac{1}{n_{t}}\sum_{i = 1}^{n_{t}}q_{i,k}^{t}$  and the second term in (1) is used to balance cluster assignments in  $\{\pmb {q}_i^t\}_{i = 1}^{n_t}$  otherwise degenerate solutions would be obtained that merge clusters by removing cluster boundaries [29]. In addition, it encourages entropy maximization of the label distribution on the target domain, i.e., encouraging cluster size balance. In aware of the lack of prior knowledge about target label distribution, we simply rely on the second term to account for a uniform one. The first term computes the KL divergence between discrete probability distributions  $P^t$  and  $Q^t$  as
+
+$$
+\mathrm {K L} (\pmb {Q} ^ {t} | | \pmb {P} ^ {t}) = \frac {1}{n _ {t}} \sum_ {i = 1} ^ {n _ {t}} \sum_ {k = 1} ^ {K} q _ {i, k} ^ {t} \log \frac {q _ {i , k} ^ {t}}{p _ {i , k} ^ {t}}.
+$$
+
+More specifically, the optimization of objective (1) takes the following alternating steps.
+
+- Auxiliary distribution update. Fix network parameters  $\{\theta, \vartheta\}$  (and  $\{p_i^t\}_{i=1}^{n_t}$  of target instances are fixed as well). By setting the approximate gradient of (1) as zero, we have the following closed-form solution [14]
+
+$$
+q _ {i, k} ^ {t} = \frac {p _ {i , k} ^ {t} / \left(\sum_ {i ^ {\prime} = 1} ^ {n _ {t}} p _ {i ^ {\prime} , k} ^ {t}\right) ^ {\frac {1}{2}}}{\sum_ {k ^ {\prime} = 1} ^ {K} p _ {i , k ^ {\prime}} ^ {t} / \left(\sum_ {i ^ {\prime} = 1} ^ {n _ {t}} p _ {i ^ {\prime} , k ^ {\prime}} ^ {t}\right) ^ {\frac {1}{2}}}. \tag {2}
+$$
+
+- Network update. By fixing  $Q^t$ , this step is equivalent to training the network via a cross-entropy loss using  $Q^t$  as labels, giving rise to
+
+$$
+\min  _ {\boldsymbol {\theta}, \boldsymbol {\vartheta}} - \frac {1}{n _ {t}} \sum_ {i = 1} ^ {n _ {t}} \sum_ {k = 1} ^ {K} q _ {i, k} ^ {t} \log p _ {i, k} ^ {t}. \tag {3}
+$$
+
+In this work, we also enhance uncovering of target discrimination via discriminative clustering in the feature space  $\mathcal{Z}$ . More specifically, let  $\{\pmb{\mu}_k\}_{k=1}^K$  be the learnable cluster centers of both the source and target data in the space  $\mathcal{Z}$ . We follow [58] and define a probability vector  $\widetilde{\pmb{p}}_i^t$  of soft cluster assignments of the instance feature  $\pmb{z}_i^t = \varphi(\pmb{x}_i^t)$  based on instance-to-center distances in the space  $\mathcal{Z}$ , whose  $k^{th}$  element is defined as
+
+$$
+\widetilde {p} _ {i, k} ^ {t} = \frac {\exp \left(\left(1 + \left| \left| \boldsymbol {z} _ {i} ^ {t} - \boldsymbol {\mu} _ {k} \right| \right| ^ {2}\right) ^ {- 1}\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \exp \left(\left(1 + \left| \left| \boldsymbol {z} _ {i} ^ {t} - \boldsymbol {\mu} _ {k ^ {\prime}} \right| \right| ^ {2}\right) ^ {- 1}\right)}. \tag {4}
+$$
+
+We write  $\{\widetilde{p}_i^t\}_{i = 1}^{n_t}$  collectively as  $\widetilde{P}^t$  . By introducing a corresponding auxiliary distribution  $\widetilde{Q}^t$  , we have the following objective of deep discriminative clustering in the space  $\mathcal{Z}$
+
+$$
+\min  _ {\widetilde {\boldsymbol {Q}} ^ {t}, \boldsymbol {\theta}, \left\{\boldsymbol {\mu} _ {k} ^ {t} \right\} _ {k = 1} ^ {K}} \mathcal {L} _ {\varphi} ^ {t} = \mathrm {K L} (\widetilde {\boldsymbol {Q}} ^ {t} | | \widetilde {\boldsymbol {P}} ^ {t}) + \sum_ {k = 1} ^ {K} \widetilde {\varrho} _ {k} ^ {t} \log \widetilde {\varrho} _ {k} ^ {t}, \tag {5}
+$$
+
+where  $\widetilde{\varrho}_k^t = \frac{1}{n_t}\sum_{i = 1}^{n_t}\widetilde{q}_{i,k}^t$ . The objective (5) can be optimized in the same alternating fashion as for (1), by deriving formulations similar to (2) and (3), where we note that features  $\{z_i^t\}_{i = 1}^{n_t}$  are computed with the updated network parameters  $\pmb{\theta}$ , and we also re-initialize  $\{\pmb{\mu}_k\}_{k = 1}^K$  at the start of each training epoch based on the current cluster assignments of  $\{z_i^t\}_{i = 1}^{n_t}$  (together with labeled source  $\{z_j^s\}_{j = 1}^{n_s}$ ).  $\{\pmb{\mu}_k\}_{k = 1}^K$  are continuously updated during training iterations of each epoch via back-propagated gradients of (5).
+
+Combining (1) and (5) gives our objective of deep discriminative target clustering, which will be used as the first term of our overall objective of SRDC algorithm
+
+$$
+\min  _ {\boldsymbol {Q} ^ {t}, \tilde {\boldsymbol {Q}} ^ {t}, \{\boldsymbol {\theta}, \boldsymbol {\vartheta} \}, \left\{\mu_ {k} \right\} _ {k = 1} ^ {K}} \mathcal {L} _ {\mathrm {S R D C}} ^ {t} = \mathcal {L} _ {f \circ \varphi} ^ {t} + \mathcal {L} _ {\varphi} ^ {t}. \tag {6}
+$$
+
+Remarks. Given unlabeled target data alone, the objective (1) itself is not guaranteed to has sensible solutions to uncover the intrinsic discrimination of target data, since the auxiliary distribution  $Q^t$  could be arbitrary whose optimization is subject to no proper constraints. Incorporation of (5) into the overall objective (6) would alleviate the issue by soft assignments of  $\{z_i^t\}_{i=1}^{n_t}$  to properly initialized cluster centers  $\{\pmb{\mu}_k\}_{k=1}^K$ . To guarantee sensible solutions, deep clustering methods [14, 58] usually employ an additional reconstruction loss as a data-dependent regularizer. In our proposed SRDC for domain adaptation, the following introduced structural source regularization serves a similar purpose as that of the reconstruction ones used in [14, 58].
+
+# 4.2. Structural source regularization
+
+Based on the UDA assumption made in Section 3 that specifies the structural similarity between the source and target domains, we propose to transfer the global, discriminative structure of labeled source data via a simple strategy of jointly training the same network  $f \circ \varphi$ . Note that the  $K$ -way classifier  $f$  defines hyperplanes that partition the feature space  $\mathcal{Z}$  into regions, of which  $K$  ones are uniquely responsible for the  $K$  classes. Since the two domains share the same label space, joint training would ideally push instances of the two domains from same classes into same regions in  $\mathcal{Z}$ , thus implicitly achieving feature alignment between the two domains. Figure 1 gives an illustration.
+
+Technically, for the labeled source data  $\{(\pmb{x}_j^s,y_j^s)\}_{j = 1}^{n_s}$ , we simply replace the auxiliary distribution in (1) with that formed by the ground-truth labels  $\{y_j^s\}_{j = 1}^{n_s}$ , resulting in a supervised network training via cross-entropy minimization
+
+$$
+\min  _ {\boldsymbol {\theta}, \boldsymbol {\vartheta}} \mathcal {L} _ {f \circ \varphi} ^ {s} = - \frac {1}{n _ {s}} \sum_ {j = 1} ^ {n _ {s}} \sum_ {k = 1} ^ {K} I [ k = y _ {j} ^ {s} ] \log p _ {j, k} ^ {s}, \tag {7}
+$$
+
+where  $p_{j,k}^{s}$  is the  $k^{th}$  element of the predictive probability vector  $\pmb{p}_{j}^{s}$  of source instance  $\pmb{x}_{j}^{s}$ , and  $\mathrm{I}[\cdot]$  is the function of
+
+indicator. We also enhance source discrimination in the feature space  $\mathcal{Z}$ , in parallel with (5), resulting in
+
+$$
+\min  _ {\boldsymbol {\theta}, \left\{\boldsymbol {\mu} _ {k} \right\} _ {k = 1} ^ {K}} \mathcal {L} _ {\varphi} ^ {s} = - \frac {1}{n _ {s}} \sum_ {j = 1} ^ {n _ {s}} \sum_ {k = 1} ^ {K} I \left[ k = y _ {j} ^ {s} \right] \log \widetilde {p} _ {j, k} ^ {s}, \tag {8}
+$$
+
+where
+
+$$
+\widetilde {p} _ {j, k} ^ {\mathrm {s}} = \frac {\exp \left(\left(1 + \left| \left| z _ {j} ^ {\mathrm {s}} - \boldsymbol {\mu} _ {k} \right| \right| ^ {2}\right) ^ {- 1}\right)}{\sum_ {k ^ {\prime} = 1} ^ {K} \exp \left(\left(1 + \left| \left| z _ {j} ^ {\mathrm {s}} - \boldsymbol {\mu} _ {k ^ {\prime}} \right| \right| ^ {2}\right) ^ {- 1}\right)}. \tag {9}
+$$
+
+Combining (7) and (8) gives the training objective using labeled source data
+
+$$
+\min  _ {\{\theta , \vartheta \}, \left\{\mu_ {k} \right\} _ {k = 1} ^ {K}} \mathcal {L} _ {\text {S R D C}} ^ {s} = \mathcal {L} _ {f \circ \varphi} ^ {s} + \mathcal {L} _ {\varphi} ^ {s}. \tag {10}
+$$
+
+Using (10) as the structural source regularizer, we have our final objective of SRDC algorithm
+
+$$
+\min  _ {\boldsymbol {Q} ^ {t}, \widetilde {\boldsymbol {Q}} ^ {t}, \{\boldsymbol {\theta}, \boldsymbol {\vartheta} \}, \left\{\mu_ {k} \right\} _ {k = 1} ^ {K}} \mathcal {L} _ {\text {S R D C}} = \mathcal {L} _ {\text {S R D C}} ^ {t} + \lambda \mathcal {L} _ {\text {S R D C}} ^ {s}, \tag {11}
+$$
+
+where  $\lambda$  is a penalty parameter.
+
+# 4.3. Enhancement via soft source sample selection
+
+It is commonly hypothesized in transfer learning [23, 62] that importance of source samples varies for learning transferable models. A simple strategy to implement this hypothesis is to re-weight source instances based on their similarities to target ones [7, 17, 67]. In this work, we also employ this strategy into SRDC.
+
+Specifically, let  $\{\pmb{c}_k^t\in \mathcal{Z}\}_{k = 1}^K$  be the  $K$  target cluster centers in the feature space. For any labeled source example  $(\pmb{x}^{s},y^{s})$ , we compute its similarity to  $\pmb{c}_{y^s}^t$ , i.e., the target center of cluster  $y^{s}$ , based on the following cosine distance
+
+$$
+w ^ {s} \left(\boldsymbol {x} ^ {s}\right) = \frac {1}{2} \left(1 + \frac {\boldsymbol {c} _ {y ^ {s}} ^ {t \top} \boldsymbol {x} ^ {s}}{| | \boldsymbol {c} _ {y ^ {s}} ^ {t} | | | | \boldsymbol {x} ^ {s} | |\right) \in [ 0, 1 ]. \tag {12}
+$$
+
+We compute  $\{\pmb{c}_k^t\}_{k = 1}^K$  once every epoch during network training. Note that  $\{\pmb{c}_k^t\}_{k = 1}^K$  are different from  $\{\pmb{\mu}_k\}_{k = 1}^K$  in (4) and (9), which are cluster centers of both the source and target data that are continuously updated during training iterations of each epoch. We compute weights for all  $\{(x_j^s,y_j^s)\}_{j = 1}^{n_s}$  using (12), and enhance (7) and (8) using the following weighted version of objectives
+
+$$
+\mathcal {L} _ {f \circ \varphi (\cdot ; \{w _ {j} ^ {s} \} _ {j = 1} ^ {n _ {s}})} ^ {s} = - \frac {1}{n _ {s}} \sum_ {j = 1} ^ {n _ {s}} w _ {j} ^ {s} \sum_ {k = 1} ^ {K} I [ k = y _ {j} ^ {s} ] \log p _ {j, k} ^ {s}, \tag {13}
+$$
+
+$$
+\mathcal {L} _ {\varphi \left(\cdot ; \left\{w _ {j} ^ {s} \right\} _ {j = 1} ^ {n _ {s}}\right)} ^ {s} = - \frac {1}{n _ {s}} \sum_ {j = 1} ^ {n _ {s}} w _ {j} ^ {s} \sum_ {k = 1} ^ {K} I \left[ k = y _ {j} ^ {s} \right] \log \widetilde {p} _ {j, k} ^ {s}. \tag {14}
+$$
+
+Experiments in Section 5 show that SRDC based on the above weighted objectives achieves improved results.
+
+# 5. Experiments
+
+# 5.1. Setups
+
+Office-31 [46] is the most popular real-world benchmark dataset for visual domain adaptation, which contains 4,110 images of 31 classes shared by three distinct domains: Amazon (A), Webcam (W), and DSLR (D). We evaluate all methods on all the six transfer tasks.
+
+ImageCLEF-DA [1] is a benchmark dataset with 12 classes shared by three domains: Caltech-256 (C), ImageNet ILSVRC 2012 (I), and Pascal VOC 2012 (P). There are 50 images in each class and 600 images in each domain. We evaluate all methods on all the six transfer tasks.
+
+Office-Home [55] is a more challenging benchmark dataset, with 15,500 images of 65 classes shared by four extremely distinct domains: Artistic images (Ar), Clip Art (Cl), Product images (Pr), and Real-World images (Rw). We evaluate all methods on all the twelve transfer tasks.
+
+Implementation details. We follow the standard protocol for UDA [16, 33, 35, 48, 60] to use all labeled source samples and all unlabeled target samples as the training data. For each transfer task, we use center-crop target domain images for reporting results and report the classification result of mean(±std) over three random trials. We use the ImageNet [12] pre-trained ResNet-50 [21] as the base network, where the last FC layer is replaced with the task-specific FC layer(s) to parameterize the classifier  $f(\cdot)$ . We implement our experiments in PyTorch. We fine-tune from the pre-trained layers and train the newly added layer(s), where the learning rate of the latter is 10 times that of the former. We adopt mini-batch SGD with the learning rate schedule as [16]: the learning rate is adjusted by  $\eta_p = \eta_0 (1 + \alpha p)^{-\beta}$ , where  $p$  is the process of training epochs normalized to be in [0, 1], and  $\eta_0 = 0.001$ ,  $\alpha = 10$ ,  $\beta = 0.75$ . We follow [16] to increase  $\lambda$  from 0 to 1 by  $\lambda_p = 2 (1 + \exp (-\gamma p))^{-1} - 1$ , where  $\gamma = 10$ . The other implementation details are provided in the supplementary material. The code is available at https://github.com/huitangtang/SRDC-CVPR2020.
+
+# 5.2. Ablation studies and analysis
+
+Ablation study. To investigate the effects of individual components of our proposed SRDC, we conduct ablation studies using Office-31 based on ResNet-50 by evaluating several variants of SRDC: (1) Source Model, which fine-tunes the base network on labeled source samples; (2) SRDC (w/o structural source regularization), which fine-tunes a source pre-trained model using (6), i.e. without structural source regularization; (3) SRDC (w/o feature discrimination), which denotes training without source and target discrimination in the feature space  $\mathcal{Z}$ ; (4) SRDC (w/o soft source sample selection), which denotes training without enhancement via soft source sample selection. The re
+
+<table><tr><td>Method</td><td>A →W</td><td>A →D</td><td>D →A</td><td>W →A</td><td>Avg</td></tr><tr><td>Source Model</td><td>77.8±0.2</td><td>82.1±0.2</td><td>64.5±0.2</td><td>66.1±0.2</td><td>72.6</td></tr><tr><td>SRDC (w/o structural source regularization)</td><td>87.3±0.0</td><td>92.1±0.1</td><td>73.9±0.1</td><td>75.0±0.1</td><td>82.1</td></tr><tr><td>SRDC (w/o feature discrimination)</td><td>94.2±0.4</td><td>94.3±0.4</td><td>74.3±0.2</td><td>75.5±0.4</td><td>84.6</td></tr><tr><td>SRDC (w/o soft source sample selection)</td><td>94.8±0.2</td><td>94.6±0.3</td><td>74.6±0.3</td><td>75.7±0.3</td><td>84.9</td></tr><tr><td>SRDC</td><td>95.7±0.2</td><td>95.8±0.2</td><td>76.7±0.3</td><td>77.1±0.1</td><td>86.3</td></tr></table>
+
+![](images/b25ac45e32c157ff2d445174235c71af5ce3945f85effd101a0b72b31a9f7ffd.jpg)  
+Figure 2. The images on the left are randomly sampled from the target domain  $\mathbf{A}$  and those on the right are the top-ranked (the  $3^{rd}$  column) and bottom-ranked (the  $4^{th}$  column) samples from the source domain  $\mathbf{W}$  for three classes. Note that the red numbers are the source weights computed by (12).
+
+Table 1. Ablation studies using Office-31 based on ResNet-50. Please refer to the main text for how different methods are defined.  
+
+<table><tr><td>Method</td><td>A →W</td><td>A →D</td><td>D →A</td><td>W →A</td><td>Avg</td></tr><tr><td>Source Model</td><td>79.3</td><td>81.6</td><td>63.1</td><td>65.7</td><td>72.4</td></tr><tr><td>DANN [16]</td><td>80.8</td><td>82.4</td><td>66.0</td><td>64.6</td><td>73.5</td></tr><tr><td>MCD [48]</td><td>86.5</td><td>86.7</td><td>72.4</td><td>70.9</td><td>79.1</td></tr><tr><td>SRDC</td><td>91.9</td><td>91.6</td><td>75.6</td><td>75.7</td><td>83.7</td></tr><tr><td>Oracle Model</td><td>98.8</td><td>97.6</td><td>87.8</td><td>87.8</td><td>93.0</td></tr></table>
+
+Table 2. Comparative experiments under inductive UDA setting.
+
+sults are reported in Table 1. We can observe that when any one of our designed components is removed, the performance degrades, verifying that (1) both feature discrimination and structural source regularization are effective for improving target clustering; (2) the proposed soft source sample selection scheme leads to better regularization.
+
+Source refinement. To affirm that our proposed soft source sample selection scheme can select more transferable source samples, we show the images randomly sampled from the target domain  $\mathbf{A}$ , and the top-ranked and bottom-ranked samples from the source domain  $\mathbf{W}$  in Figure 2. Here, the red numbers are the source weights computed by (12). We can observe that (1) the lowest weight is more than 0.5, which is reasonable since all source samples are related to the target domain in that the two domains share the same label space; (2) the highest weight is less than 1, which is reasonable since there exists distribution
+
+shift between the two domains; (3) the source images with a canonical viewpoint have the higher weights than those with top-down, bottom-up, and side viewpoints, which is intuitive since all target images are shown only from a canonical viewpoint [46]. The above observations affirm the rationality of our proposed soft source sample selection scheme.
+
+Comparison under inductive UDA setting. To verify that our proposed strategy of uncovering the intrinsic target discrimination can derive the clustering solutions closer to the oracle target classifier than the existing transferring strategy of learning aligned feature representations between the two domains [16, 48], we design comparative experiments under the setting of inductive UDA. We follow a  $50\% / 50\%$  split scheme to divide each domain of Office-31 into the training and test sets. We use the both labeled sets of the source domain and the unlabeled training set of the target domain as the training data. In Table 2, we report results on the test set of the target domain using the best-performing model on the target training set. Here, Oracle Model fine-tunes the base network on the labeled target training set. We can see that our proposed uncovering strategy SRDC achieves closer results to Oracle Model, verifying the motivation of this work and the efficacy of our proposed SRDC. Feature visualization. We utilize t-SNE [54] to visualize embedded features on the target domain by Source Model and SRDC for two reverse transfer tasks of  $\mathbf{A} \rightarrow \mathbf{W}$  and  $\mathbf{W} \rightarrow \mathbf{A}$  in Figure 3. We can qualitatively observe that compared to Source Model, the target domain features can be much better discriminated by SRDC, which is based on data clustering to uncover the discriminative data structures.
+
+Confusion matrix. We give confusion matrices in terms of accuracy achieved by Source Model and SRDC on two reverse transfer tasks of  $\mathbf{A} \rightarrow \mathbf{W}$  and  $\mathbf{W} \rightarrow \mathbf{A}$  in Figure 4. Similar to the qualitative result of Figure 3, we can observe quantitative improvements from Source Model to SRDC, further confirming the advantages of SRDC.
+
+Convergence performance. We verify the convergence performance of Source Model and SRDC with the test errors on two reverse transfer tasks of  $\mathbf{A} \rightarrow \mathbf{W}$  and  $\mathbf{W} \rightarrow \mathbf{A}$  in Figure 5. We can observe that SRDC enjoys faster and smoother convergence performance than Source Model.
+
+# 5.3. Comparisons with the state of the art
+
+Results on Office-31 based on ResNet-50 are reported in Table 3, where results of existing methods are quoted from
+
+![](images/eaf6b475b851fbbd0a6008ce708c6301b2614e57e703a273337751d7d802d246.jpg)  
+(a) Source Model:  $\mathbf{A}\rightarrow \mathbf{W}$
+
+![](images/0f43d89c4b4b4fb14674c93b06684ddf2a850b3ffad6e27ce31da972257b67be.jpg)  
+(b) SRDC:  $\mathbf{A}\rightarrow \mathbf{W}$
+
+![](images/9a1279446de04f88056d23e3e4b8c774796a5b4b524384368baaf122f7d94941.jpg)  
+(c) Source Model:  $\mathbf{W}\rightarrow \mathbf{A}$
+
+![](images/afc565f0f07d2fad7e3646362422529b834a491688165ceeec41ab883a4faa29.jpg)  
+(d) SRDC:  $\mathbf{W}\rightarrow \mathbf{A}$
+
+![](images/e202e53d9946d7231757ea7163c7009de29f7f1625c477dfe2c937907417799e.jpg)  
+Figure 3. The t-SNE visualization of embedded features on the target domain. Note that different classes are denoted by different colors.  
+(a) Source Model:  $\mathbf{A}\rightarrow \mathbf{W}$
+
+![](images/fab39a6db99b398fafcfc84f1cf03c1ad0c0dd2e4b714f64de444c6ef2063bf1.jpg)  
+(b) SRDC:  $\mathbf{A}\rightarrow \mathbf{W}$
+
+![](images/a012c9cb42775f86429a5544d40492cacc66ce096b62f13c0720c7565ba305dc.jpg)  
+(c) Source Model:  $\mathbf{W}\rightarrow \mathbf{A}$
+
+![](images/72b4dd3fa993d9f34fe6047481e62ab8f22d2e6d5f3e3419bfef9895c13be9cf.jpg)  
+(d) SRDC:  $\mathbf{W}\to \mathbf{A}$
+
+![](images/96014adc5e6ed241ef8ca4562ac2b986f109d68c09d748a8cdbbfbde2a80ef1c.jpg)  
+Figure 4. The confusion matrix on the target domain. (Zoom in to see the exact class names!)  
+Figure 5. Convergence.
+
+their respective papers or the works of [5, 33, 35]. We can see that SRDC outperforms all compared methods on almost all transfer tasks. It is noteworthy that SRDC significantly enhances the classification results on difficult transfer tasks, e.g.  $\mathbf{A} \rightarrow \mathbf{W}$  and  $\mathbf{W} \rightarrow \mathbf{A}$ , where the two domains are quite different. SRDC exceeds the latest work of BSP aiming to improve the discriminability for adversarial feature adaptation, showing that data clustering could be a more promising direction for target discrimination.
+
+Results on ImageCLEF-DA based on ResNet-50 are reported in Table 4, where results of existing methods are quoted from their respective papers or the work of [35]. SRDC achieves much better results than all compared methods on all transfer tasks and substantially improves the re
+
+sults on hard transfer tasks, e.g.  $\mathbf{C} \rightarrow \mathbf{P}$  and  $\mathbf{P} \rightarrow \mathbf{C}$ , verifying the efficacy of SRDC on transfer tasks with the source and target domains of equal size and class balance.
+
+Results on Office-Home based on ResNet-50 are reported in Table 5, where results of existing methods are quoted from their respective papers or the works of [35, 45]. We can observe that SRDC significantly exceeds all compared methods on most transfer tasks, with still a large room for improvement. This is reasonable since the four domains in Office-Home contain more categories, are visually more different from each other, and have much lower in-domain classification results [55]. It is inspiring that SRDC largely improves over the current state-of-the-art method MDD on such difficult tasks, which underlines the importance of discovering the discriminative structures by data clustering.
+
+# 6. Conclusion
+
+In this work, motivated by the assumption of structural domain similarity, we propose a source regularized, deep discriminative clustering method, termed as Structurally Regularized Deep Clustering (SRDC). SRDC addresses a potential issue of damaging the intrinsic data discrimination by the existing alignment based UDA methods, via directly uncovering the intrinsic discrimination of target data. Technically, we use a flexible framework of deep network based discriminative clustering that minimizes the KL divergence between predictive label distribution of the network and an introduced auxiliary one; replacing the auxiliary distribution with that formed by ground-truth labels of
+
+<table><tr><td>Method</td><td>A → W</td><td>D → W</td><td>W → D</td><td>A → D</td><td>D → A</td><td>W → A</td><td>Avg</td></tr><tr><td>Source Model [21]</td><td>77.8±0.2</td><td>96.9±0.1</td><td>99.3±0.1</td><td>82.1±0.2</td><td>64.5±0.2</td><td>66.1±0.2</td><td>81.1</td></tr><tr><td>DAN [34]</td><td>81.3±0.3</td><td>97.2±0.0</td><td>99.8±0.0</td><td>83.1±0.2</td><td>66.3±0.0</td><td>66.3±0.1</td><td>82.3</td></tr><tr><td>DANN [16]</td><td>81.7±0.2</td><td>98.0±0.2</td><td>99.8±0.0</td><td>83.9±0.7</td><td>66.4±0.2</td><td>66.0±0.3</td><td>82.6</td></tr><tr><td>ADDA [53]</td><td>86.2±0.5</td><td>96.2±0.3</td><td>98.4±0.3</td><td>77.8±0.3</td><td>69.5±0.4</td><td>68.9±0.5</td><td>82.9</td></tr><tr><td>VADA [51]</td><td>86.5±0.5</td><td>98.2±0.4</td><td>99.7±0.2</td><td>86.7±0.4</td><td>70.1±0.4</td><td>70.5±0.4</td><td>85.4</td></tr><tr><td>SimNet [43]</td><td>88.6±0.5</td><td>98.2±0.2</td><td>99.7±0.2</td><td>85.3±0.3</td><td>73.4±0.8</td><td>71.8±0.6</td><td>86.2</td></tr><tr><td>MSTN [59]</td><td>91.3</td><td>98.9</td><td>100.0</td><td>90.4</td><td>72.7</td><td>65.6</td><td>86.5</td></tr><tr><td>GTA [49]</td><td>89.5±0.5</td><td>97.9±0.3</td><td>99.8±0.4</td><td>87.7±0.5</td><td>72.8±0.3</td><td>71.4±0.4</td><td>86.5</td></tr><tr><td>MCD [48]</td><td>88.6±0.2</td><td>98.5±0.1</td><td>100.0±0.0</td><td>92.2±0.2</td><td>69.5±0.1</td><td>69.7±0.3</td><td>86.5</td></tr><tr><td>SAFN+ENT [60]</td><td>90.1±0.8</td><td>98.6±0.2</td><td>99.8±0.0</td><td>90.7±0.5</td><td>73.0±0.2</td><td>70.2±0.3</td><td>87.1</td></tr><tr><td>DAAA [28]</td><td>86.8±0.2</td><td>99.3±0.1</td><td>100.0±0.0</td><td>88.8±0.4</td><td>74.3±0.2</td><td>73.9±0.2</td><td>87.2</td></tr><tr><td>iCAN [63]</td><td>92.5</td><td>98.8</td><td>100.0</td><td>90.1</td><td>72.1</td><td>69.9</td><td>87.2</td></tr><tr><td>CDAN+E [35]</td><td>94.1±0.1</td><td>98.6±0.1</td><td>100.0±0.0</td><td>92.9±0.2</td><td>71.0±0.3</td><td>69.3±0.3</td><td>87.7</td></tr><tr><td>MSTN+DSBN [5]</td><td>92.7</td><td>99.0</td><td>100.0</td><td>92.2</td><td>71.7</td><td>74.4</td><td>88.3</td></tr><tr><td>TADA [56]</td><td>94.3±0.3</td><td>98.7±0.1</td><td>99.8±0.2</td><td>91.6±0.3</td><td>72.9±0.2</td><td>73.0±0.3</td><td>88.4</td></tr><tr><td>TAT [33]</td><td>92.5±0.3</td><td>99.3±0.1</td><td>100.0±0.0</td><td>93.2±0.2</td><td>73.1±0.3</td><td>72.1±0.3</td><td>88.4</td></tr><tr><td>SymNets [68]</td><td>90.8±0.1</td><td>98.8±0.3</td><td>100.0±0.0</td><td>93.9±0.5</td><td>74.6±0.6</td><td>72.5±0.5</td><td>88.4</td></tr><tr><td>BSP+CDAN [9]</td><td>93.3±0.2</td><td>98.2±0.2</td><td>100.0±0.0</td><td>93.0±0.2</td><td>73.6±0.3</td><td>72.6±0.3</td><td>88.5</td></tr><tr><td>MDD [66]</td><td>94.5±0.3</td><td>98.4±0.1</td><td>100.0±0.0</td><td>93.5±0.2</td><td>74.6±0.3</td><td>72.2±0.1</td><td>88.9</td></tr><tr><td>CAN [27]</td><td>94.5±0.3</td><td>99.1±0.2</td><td>99.8±0.2</td><td>95.0±0.3</td><td>78.0±0.3</td><td>77.0±0.3</td><td>90.6</td></tr><tr><td>SRDC</td><td>95.7±0.2</td><td>99.2±0.1</td><td>100.0±0.0</td><td>95.8±0.2</td><td>76.7±0.3</td><td>77.1±0.1</td><td>90.8</td></tr></table>
+
+Table 3. Results  $(\%)$  on Office-31 (ResNet-50).  
+
+<table><tr><td>Methods</td><td>I → P</td><td>P → I</td><td>I → C</td><td>C → I</td><td>C → P</td><td>P → C</td><td>Avg</td></tr><tr><td>Source Model [21]</td><td>74.8±0.3</td><td>83.9±0.1</td><td>91.5±0.3</td><td>78.0±0.2</td><td>65.5±0.3</td><td>91.2±0.3</td><td>80.7</td></tr><tr><td>DAN [34]</td><td>74.5±0.4</td><td>82.2±0.2</td><td>92.8±0.2</td><td>86.3±0.4</td><td>69.2±0.4</td><td>89.8±0.4</td><td>82.5</td></tr><tr><td>DANN [16]</td><td>75.0±0.6</td><td>86.0±0.3</td><td>96.2±0.4</td><td>87.0±0.5</td><td>74.3±0.5</td><td>91.5±0.6</td><td>85.0</td></tr><tr><td>JAN [37]</td><td>76.8±0.4</td><td>88.0±0.2</td><td>94.7±0.2</td><td>89.5±0.3</td><td>74.2±0.3</td><td>91.7±0.3</td><td>85.8</td></tr><tr><td>CDAN+E [35]</td><td>77.7±0.3</td><td>90.7±0.2</td><td>97.7±0.3</td><td>91.3±0.3</td><td>74.2±0.2</td><td>94.3±0.3</td><td>87.7</td></tr><tr><td>TAT [33]</td><td>78.8±0.2</td><td>92.0±0.2</td><td>97.5±0.3</td><td>92.0±0.3</td><td>78.2±0.4</td><td>94.7±0.4</td><td>88.9</td></tr><tr><td>SAFN+ENT [60]</td><td>79.3±0.1</td><td>93.3±0.4</td><td>96.3±0.4</td><td>91.7±0.0</td><td>77.6±0.1</td><td>95.3±0.1</td><td>88.9</td></tr><tr><td>SymNets [68]</td><td>80.2±0.3</td><td>93.6±0.2</td><td>97.0±0.3</td><td>93.4±0.3</td><td>78.7±0.3</td><td>96.4±0.1</td><td>89.9</td></tr><tr><td>SRDC</td><td>80.8±0.3</td><td>94.7±0.2</td><td>97.8±0.2</td><td>94.1±0.2</td><td>80.0±0.3</td><td>97.7±0.1</td><td>90.9</td></tr></table>
+
+Table 4. Results (%) on ImageCLEF-DA (ResNet-50).  
+
+<table><tr><td>Methods</td><td>Ar→Cl</td><td>Ar→Pr</td><td>Ar→Rw</td><td>Cl→Ar</td><td>Cl→Pr</td><td>Cl→Rw</td><td>Pr→Ar</td><td>Pr→Cl</td><td>Pr→Rw</td><td>Rw→Ar</td><td>Rw→Cl</td><td>Rw→Pr</td><td>Avg</td></tr><tr><td>Source Model [21]</td><td>34.9</td><td>50.0</td><td>58.0</td><td>37.4</td><td>41.9</td><td>46.2</td><td>38.5</td><td>31.2</td><td>60.4</td><td>53.9</td><td>41.2</td><td>59.9</td><td>46.1</td></tr><tr><td>DAN [34]</td><td>43.6</td><td>57.0</td><td>67.9</td><td>45.8</td><td>56.5</td><td>60.4</td><td>44.0</td><td>43.6</td><td>67.7</td><td>63.1</td><td>51.5</td><td>74.3</td><td>56.3</td></tr><tr><td>DANN [16]</td><td>45.6</td><td>59.3</td><td>70.1</td><td>47.0</td><td>58.5</td><td>60.9</td><td>46.1</td><td>43.7</td><td>68.5</td><td>63.2</td><td>51.8</td><td>76.8</td><td>57.6</td></tr><tr><td>JAN [37]</td><td>45.9</td><td>61.2</td><td>68.9</td><td>50.4</td><td>59.7</td><td>61.0</td><td>45.8</td><td>43.4</td><td>70.3</td><td>63.9</td><td>52.4</td><td>76.8</td><td>58.3</td></tr><tr><td>SE [15]</td><td>48.8</td><td>61.8</td><td>72.8</td><td>54.1</td><td>63.2</td><td>65.1</td><td>50.6</td><td>49.2</td><td>72.3</td><td>66.1</td><td>55.9</td><td>78.7</td><td>61.5</td></tr><tr><td>DWT-MEC [45]</td><td>50.3</td><td>72.1</td><td>77.0</td><td>59.6</td><td>69.3</td><td>70.2</td><td>58.3</td><td>48.1</td><td>77.3</td><td>69.3</td><td>53.6</td><td>82.0</td><td>65.6</td></tr><tr><td>CDAN+E [35]</td><td>50.7</td><td>70.6</td><td>76.0</td><td>57.6</td><td>70.0</td><td>70.0</td><td>57.4</td><td>50.9</td><td>77.3</td><td>70.9</td><td>56.7</td><td>81.6</td><td>65.8</td></tr><tr><td>TAT [33]</td><td>51.6</td><td>69.5</td><td>75.4</td><td>59.4</td><td>69.5</td><td>68.6</td><td>59.5</td><td>50.5</td><td>76.8</td><td>70.9</td><td>56.6</td><td>81.6</td><td>65.8</td></tr><tr><td>BSP+CDAN [9]</td><td>52.0</td><td>68.6</td><td>76.1</td><td>58.0</td><td>70.3</td><td>70.2</td><td>58.6</td><td>50.2</td><td>77.6</td><td>72.2</td><td>59.3</td><td>81.9</td><td>66.3</td></tr><tr><td>SAFN [60]</td><td>52.0</td><td>71.7</td><td>76.3</td><td>64.2</td><td>69.9</td><td>71.9</td><td>63.7</td><td>51.4</td><td>77.1</td><td>70.9</td><td>57.1</td><td>81.5</td><td>67.3</td></tr><tr><td>TADA [56]</td><td>53.1</td><td>72.3</td><td>77.2</td><td>59.1</td><td>71.2</td><td>72.1</td><td>59.7</td><td>53.1</td><td>78.4</td><td>72.4</td><td>60.0</td><td>82.9</td><td>67.6</td></tr><tr><td>SymNets [68]</td><td>47.7</td><td>72.9</td><td>78.5</td><td>64.2</td><td>71.3</td><td>74.2</td><td>64.2</td><td>48.8</td><td>79.5</td><td>74.5</td><td>52.6</td><td>82.7</td><td>67.6</td></tr><tr><td>MDD [66]</td><td>54.9</td><td>73.7</td><td>77.8</td><td>60.0</td><td>71.4</td><td>71.8</td><td>61.2</td><td>53.6</td><td>78.1</td><td>72.5</td><td>60.2</td><td>82.3</td><td>68.1</td></tr><tr><td>SRDC</td><td>52.3</td><td>76.3</td><td>81.0</td><td>69.5</td><td>76.2</td><td>78.0</td><td>68.7</td><td>53.8</td><td>81.7</td><td>76.3</td><td>57.1</td><td>85.0</td><td>71.3</td></tr></table>
+
+Table 5. Results  $(\%)$  on Office-Home (ResNet-50).
+
+source data implements the structural source regularization via joint network training. In SRDC, we also enhance target discrimination with clustering of intermediate network features, and enhance structural regularization with soft selection of less divergent source examples. Experiments on benchmarks testify the efficacy of our method.
+
+Acknowledgments. This work is supported in part by National Natural Science Foundation of China (Grant No.: 61771201), Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No.: 2017ZT07X183), Guangdong R&D key project of China (Grant No.: 2019B010155001), and Microsoft Research Asia.
+
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