iccv iccv2013 iccv2013-435 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Mahsa Baktashmotlagh, Mehrtash T. Harandi, Brian C. Lovell, Mathieu Salzmann
Abstract: Domain-invariant representations are key to addressing the domain shift problem where the training and test examples follow different distributions. Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. This space, however, may not be directly suitable for such a comparison, since some of the features may have been distorted by the domain shift, or may be domain specific. In this paper, we introduce a Domain Invariant Projection approach: An unsupervised domain adaptation method that overcomes this issue by extracting the information that is invariant across the source and target domains. More specifically, we learn a projection of the data to a low-dimensional latent space where the distance between the empirical distributions of the source and target examples is minimized. We demonstrate the effectiveness of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on a standard domain adaptation benchmark dataset.
Reference: text
sentIndex sentText sentNum sentScore
1 au Abstract Domain-invariant representations are key to addressing the domain shift problem where the training and test examples follow different distributions. [sent-6, score-0.389]
2 Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. [sent-7, score-0.846]
3 This space, however, may not be directly suitable for such a comparison, since some of the features may have been distorted by the domain shift, or may be domain specific. [sent-8, score-0.559]
4 In this paper, we introduce a Domain Invariant Projection approach: An unsupervised domain adaptation method that overcomes this issue by extracting the information that is invariant across the source and target domains. [sent-9, score-1.044]
5 More specifically, we learn a projection of the data to a low-dimensional latent space where the distance between the empirical distributions of the source and target examples is minimized. [sent-10, score-0.747]
6 We demonstrate the effectiveness of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on a standard domain adaptation benchmark dataset. [sent-11, score-0.466]
7 Introduction Domain shift is a fundamental problem in visual recognition tasks as evidenced by the recent surge of interest in domain adaptation [22, 15, 16]. [sent-13, score-0.586]
8 On the other hand, labeling sufficiently many images from the target domain to train a discriminative classifier specific to this domain is prohibitively time-consuming and impractical in realistic scenarios. [sent-19, score-0.747]
9 To relate the source and target domains, several state-ofthe-art methods have proposed to create intermediate representations [15, 16]. [sent-21, score-0.466]
10 However, these representations do not explicitly try to match the probability distributions of the source and target data, which may make them sub-optimal for classification. [sent-22, score-0.577]
11 Sample selection, or re-weighting, approaches [14, 21] explicitly attempt to match the source and target distributions by finding the most appropriate source examples for the target data. [sent-23, score-1.055]
12 However, they fail to account for the fact that the image features themselves may have been distorted by the domain shift, and that some of the image features may be specific to one domain and thus irrelevant for classification in the other one. [sent-24, score-0.559]
13 In light of the above discussion, we propose to tackle the problem of domain shift by extracting the information that is invariant across the source and target domains. [sent-25, score-0.837]
14 To this end, we introduce a Domain Invariant Projection (DIP) approach, which aims to learn a low-dimensional latent space where the source and target distributions are similar. [sent-26, score-0.626]
15 Learning such a projection allows us to account for the potential distortions induced by the domain shift, as well as for the presence of domain-specific image features. [sent-27, score-0.34]
16 Furthermore, since the distributions of the source and target data in the latent space are similar, we expect a classifier trained on the source examples to perform well on the target domain. [sent-28, score-1.104]
17 In this work, we make use of the Maximum Mean Discrepancy (MMD) [17] to measure the dissimilarity between the empirical distributions of the source and target examples. [sent-29, score-0.577]
18 Learning the latent space that minimizes the MMD between the source and target domains can then be formulated as an optimization problem on a Grassmann manifold. [sent-30, score-0.648]
19 This lets us utilize Grassmannian geometry to effectively obtain our domain invariant projection. [sent-31, score-0.363]
20 Although designed to be fully unsupervised, our formalism naturally allows us to exploit label information from either domain during the training process. [sent-32, score-0.294]
21 In short, we introduce the idea of finding a domain invariant representation of the data by matching the source and target distributions in a low-dimensional latent space, and propose an effective algorithm to learn our Domain In776699 variant Projection. [sent-34, score-0.944]
22 We demonstrate the benefits of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on the standard domain adaptation benchmark dataset [26]. [sent-35, score-0.466]
23 In the former category, modifications of Support Vector Machines (SVM) [12, 3] and other statistical classifiers [10] have been proposed to exploit the availability of labeled and unlabeled data from the target domain. [sent-38, score-0.333]
24 Co-regularization of similar classifiers was also introduced to utilize unlabeled target data during training [9]. [sent-39, score-0.258]
25 For visual recognition, metric learning [26] and transformation learning [23] were shown to be effective at making use of the labeled target examples. [sent-40, score-0.266]
26 Furthermore, semi-supervised methods have also been proposed to tackle the case where multiple source domains are available [11, 20]. [sent-41, score-0.339]
27 While semi-supervised methods are often effective, in many applications, labeled target examples are not available and cannot easily be acquired. [sent-42, score-0.309]
28 To address this issue, unsupervised domain adaptation approaches that rely on purely unsupervised target data have been proposed [28, 7, 8]. [sent-43, score-0.863]
29 Subspace-based approaches [4, 16, 15] model the domain shift by representing the data with multiple subspaces. [sent-45, score-0.346]
30 Rather than limiting the representation to one source and one target subspaces, several techniques exploit intermediate subspaces, which link the source data to the target data. [sent-47, score-0.933]
31 This idea was originally introduced in [16], where the subspaces were modeled as points on a Grassmann manifold, and intermediate subspaces were obtained by sampling points along the geodesic between the source and target subspaces. [sent-48, score-0.651]
32 While this formulation nicely characterizes the change between the source and target data, it is not clear why all the subspaces along this path should yield meaningful representations. [sent-50, score-0.534]
33 In contrast, sample re-weighting, or selection, approaches, have focused more directly on comparing the distributions of the source and target data. [sent-52, score-0.577]
34 In particular, in [21, 18], the source examples are re-weighted so as to minimize the MMD between the source and target distributions. [sent-53, score-0.69]
35 More recently, an approach to selecting landmarks among the source examples based on MMD was introduced [14]. [sent-54, score-0.289]
36 Despite their success, it is important to note that sample re-weighting and selection methods compare the source and target distributions directly in the original feature space. [sent-56, score-0.608]
37 This space, however, may not be appropriate for this task, since the image features may have been distorted by the domain shift, and since some of the features may only be relevant to one specific domain. [sent-57, score-0.297]
38 In contrast, in this work, we compare the source and target distributions in a low-dimensional latent space where these effects are removed, or reduced. [sent-58, score-0.626]
39 We employ the maximum mean discrepancy [17] between two distributions s and t to measure their dissimilarity. [sent-72, score-0.193]
40 Grassmann Manifolds In our formulation, we model the projection ofthe source and target data to a low-dimensional space as a point W on a Grassmann manifold G(d, D). [sent-107, score-0.67]
41 The Grassmann manifold aG G(d,r aDss)m caonnnsis mtsa noiff otlhde Gse(td ,ofD a)l. [sent-108, score-0.157]
42 Learning the projection then involves non-linear optimization on the Grassmann manifold, which requires some notions of differential geometry WTW reviewed below. [sent-111, score-0.15]
43 In differential geometry, the shortest path between two points on a manifold is a curve called a geodesic. [sent-112, score-0.157]
44 The tangent space at a point on a manifold is a vector space that consists of the tangent vectors of all possible curves passing through this point. [sent-113, score-0.231]
45 In particular, we make use of a conjugate gradient (CG) algorithm on the Grassmann manifold [13]. [sent-117, score-0.207]
46 CG on a Grassmann manifold can be summarized by the following steps: (i) Compute the gradient ∇fW of the objective function fC on pthutee em tahneif goraldd iaetn tthe ∇ fcurrent estimate W as ∇fW = ∂fW − WWT∂fW , (1) with ∂fW the matrix of usual partial derivatives. [sent-120, score-0.157]
47 Domain Invariant Projection (DIP) In this section, we introduce our approach to unsupervised domain adaptation. [sent-125, score-0.349]
48 We first derive the optimization problem at the heart of our approach, and then discuss the details of our Grassmann manifold optimization method. [sent-126, score-0.231]
49 Intuitively, with such a representation, a classifier trained on the source domain should perform equally well on the target domain. [sent-130, score-0.697]
50 To achieve invariance, we search for a projection to a lowdimensional subspace where the source and target distributions are similar, or, in other words, a projection that minimizes a distance measure betwe? [sent-131, score-0.772]
51 Wdiset sreibaurtcihon fso ro af Dthe× sdou prrcoeand target samples in the resulting d-dimensional subspace are as similar as possible. [sent-150, score-0.262]
52 Such constraints prevent our model from wrongly matching the two distributions by distorting the data, and make it very unlikely that the resulting subspace only contains the noise of both domains. [sent-176, score-0.181]
53 Therefore, here, we also consider using the polynomial kernel of degree two. [sent-196, score-0.151]
54 The fact that this kernel yields a distribution distance that only compares the first and second moment of the two distributions [17] will be shown to have little impact on our experimental results, thus showing the robustness of our approach to the choice of kernel. [sent-197, score-0.272]
55 Replacing the Gaussian kernel with this polynomial kernel in our objective function yields D2(WTXs, WTXt) = (5) n12i? [sent-198, score-0.281]
56 ∈ R(n+m)×(n+m), and = ⎧⎨−1 / (mn 2 m) oit,hje∈ rwTSise (6) with S and T th⎩e sets of source and target indices, respectively. [sent-208, score-0.435]
57 2, we make use of a conjugate gradient method on the manifold to obtain W∗ . [sent-218, score-0.207]
58 1 Encouraging Class Clustering (DIP-CC) In the DIP formulation described above, learning the projection W is done in a fully unsupervised manner. [sent-221, score-0.197]
59 Note, however, that even in the so-called unsupervised setting, domain adaptation methods have access to the labels of the source examples. [sent-222, score-0.765]
60 Intuitively, we are interested in finding a projection that not only minimizes the distance between the distribution of the projected source and target data, but also yields good classification performance. [sent-224, score-0.593]
61 Note that in our formulation, the mean of the projected examples is equivalent to the projection of the mean. [sent-238, score-0.15]
62 7 and 8 fall into the unsupervised domain adaptation category, since they do not exploit any labeled target examples. [sent-245, score-0.851]
63 In the unsupervised setting, this classifier is only trained using the source examples. [sent-250, score-0.299]
64 With Semi-Supervised DIP (SS-DIP), the labeled target examples can be taken into account in two different manners. [sent-251, score-0.309]
65 7, since no labels are used when learning W, we only employ the labeled target examples along with the source ones to train the final classifier. [sent-253, score-0.521]
66 8, we utilize the target labels in the regularizer when learning W, as well as when learning the final classifier. [sent-255, score-0.302]
67 This lets us rewrite our constrained optimization problem as an unconstrained problem on the manifold G(d, D). [sent-260, score-0.239]
68 More specifically, manifold optimization methods often have better convergence behavior than iterative projection methods, which can be crucial with a nonlinear objective function [1]. [sent-263, score-0.322]
69 2 that CG on a Grassmann manifold involves (i) computing the gradient on the manifold ∇fW, (ii) estimating the search direction H, and (iii) performing a line search along a geodesic. [sent-267, score-0.314]
70 1shows that × the gradient on the manifold depends on the partial derivatives of the objective function w. [sent-269, score-0.157]
71 In our experiments, we first applied PCA to the concatenated source and target data, kept all the data variance, and initialized W to the truncated identity matrix. [sent-291, score-0.435]
72 In all our experiments, we set the variance σ of the Gaussian kernel to the median squared distance between all source examples, and the weight λ of the regularizer to 4/σ when using the regularizer. [sent-295, score-0.37]
73 Cross-domain WiFi Localization We first evaluated our approach on the task of indoor WiFi localization using the public wifi data set published in the 2007 IEEE ICDM Contest for domain adaptation [29]. [sent-298, score-0.683]
74 In our experiments, we used all the source data and 400 randomly sampled target examples. [sent-307, score-0.435]
75 Visual Object Recognition We then evaluated our approach on the task of visual object recognition using the benchmark domain adaptation dataset introduced in [26]. [sent-382, score-0.466]
76 The Amazon domain consists of images acquired in a highly-controlled environment with studio light- ing conditions. [sent-384, score-0.298]
77 The DSLR domain consists of high resolution images of 3 1 categories that are taken with a digital SLR camera in a home environment under natural lighting. [sent-386, score-0.328]
78 For recognition, we trained an SVM classifier with a polynomial kernel of degree 2 on the projected source examples. [sent-399, score-0.392]
79 In a first experiment on this dataset, we used the evaluation protocol introduced in [14]: For each source/target pair, all the available examples in both domains are exploited at once, rather than splitting the datasets into multiple training/testing partitions. [sent-401, score-0.284]
80 1 This protocol was motivated by the fact that, in [14], selecting landmarks requires a sufficient number of source examples to be available. [sent-402, score-0.403]
81 For the same reason, the DSLR dataset is never used as source domain, since it contains too few examples per class. [sent-403, score-0.255]
82 Table 1 shows the recognition accuracies on the target examples for the 9 pairs of source and target domains. [sent-405, score-0.742]
83 Note that, in this case, our classclustering regularizer is not crucial to achieve good accu1This evaluation protocol was explained 777744 to us by the authors of [14]. [sent-407, score-0.193]
84 Recognition accuracies on 6 pairs of source/target domains using the evaluation protocol of [26]. [sent-487, score-0.282]
85 Recognition accuracies on the remaining 6 pairs of source/target domains using the evaluation protocol of [26]. [sent-568, score-0.282]
86 With this protocol, all possible combinations of source and target domains were evaluated. [sent-575, score-0.562]
87 Following the evaluation protocol of [26], we made use of 3 labeled samples per category from the target domain. [sent-579, score-0.41]
88 Here however, the class-clustering regularizer boosts the accuracy more consistently, which suggests the importance of such a regularizer in the presence of small amounts of labeled data. [sent-583, score-0.201]
89 Conclusion and Future Work In this paper, we have introduced an approach to unsupervised domain adaptation that focuses on extracting a domain-invariant representation of the source and target data. [sent-588, score-0.988]
90 To this end, we have proposed to match the source and target distributions in a low-dimensional latent space, rather than in the original feature space. [sent-589, score-0.626]
91 Our experiments have evidenced the importance of exploiting distribution invariance for domain adaptation by revealing that our DIP approach consistently outperformed the state-of-the-art methods in the task of visual object recognition. [sent-590, score-0.502]
92 However, it is unclear how to regularize nonlinear transformations to prevent them from deteriorating the data distribution to the point of making two inherently dissimilar distributions similar. [sent-594, score-0.192]
93 Finally, we also plan to investigate how ideas from the deep learning literature could be employed to obtain domain invariant features. [sent-595, score-0.318]
94 Recognition accuracies on 6 pairs of source/target domains using the semi-supervised evaluation protocol of [26]. [sent-695, score-0.282]
95 Recognition accuracies on the remaining 6 pairs of source/target domains using the semi-supervised evaluation protocol of [26]. [sent-792, score-0.282]
96 Exploiting weakly-labeled web images to improve object classification: a domain adaptation approach. [sent-809, score-0.466]
97 Domain adaptation problems: A dasvm classification technique and a circular validation strategy. [sent-840, score-0.204]
98 Connecting the dots with landmarks: Discriminatively learning domain-invariant features for unsupervised domain adaptation. [sent-883, score-0.349]
99 Online domain adaptation of a pretrained cascade of classifiers. [sent-945, score-0.466]
100 What you saw is not what you get: Domain adaptation using asymmetric kernel transforms. [sent-951, score-0.283]
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