iccv iccv2013 iccv2013-227 knowledge-graph by maker-knowledge-mining

227 iccv-2013-Large-Scale Image Annotation by Efficient and Robust Kernel Metric Learning


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Author: Zheyun Feng, Rong Jin, Anil Jain

Abstract: One of the key challenges in search-based image annotation models is to define an appropriate similarity measure between images. Many kernel distance metric learning (KML) algorithms have been developed in order to capture the nonlinear relationships between visual features and semantics ofthe images. Onefundamental limitation in applying KML to image annotation is that it requires converting image annotations into binary constraints, leading to a significant information loss. In addition, most KML algorithms suffer from high computational cost due to the requirement that the learned matrix has to be positive semi-definitive (PSD). In this paper, we propose a robust kernel metric learning (RKML) algorithm based on the regression technique that is able to directly utilize image annotations. The proposed method is also computationally more efficient because PSD property is automatically ensured by regression. We provide the theoretical guarantee for the proposed algorithm, and verify its efficiency and effectiveness for image annotation by comparing it to state-of-the-art approaches for both distance metric learning and image annotation. ,

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Many kernel distance metric learning (KML) algorithms have been developed in order to capture the nonlinear relationships between visual features and semantics ofthe images. [sent-2, score-0.48]

2 Onefundamental limitation in applying KML to image annotation is that it requires converting image annotations into binary constraints, leading to a significant information loss. [sent-3, score-0.274]

3 In this paper, we propose a robust kernel metric learning (RKML) algorithm based on the regression technique that is able to directly utilize image annotations. [sent-5, score-0.354]

4 We provide the theoretical guarantee for the proposed algorithm, and verify its efficiency and effectiveness for image annotation by comparing it to state-of-the-art approaches for both distance metric learning and image annotation. [sent-7, score-0.495]

5 Introduction The objective of image annotation is to automatically annotate an image with appropriate keywords, often referred to as tags, which reflect its visual content. [sent-9, score-0.209]

6 Their key idea is to annotate a test image I the common tags shared by the subset of trainwith ing images tthh atht are visually gsism sihlaarr etod b Iy. [sent-11, score-0.146]

7 Distance metric learning (DML) tackles this problem by learning a metric that pulls semantically similar images close and pushes semantically dissimilar images far apart. [sent-14, score-0.358]

8 Many studies on DML are restricted to learning a linear Mahalanobis distance metric, failing to capture the nonlinear relationj ain} @ c s e . [sent-15, score-0.227]

9 Several nonlinear DML algorithms have been proposed to overcome this limitation. [sent-18, score-0.087]

10 In the case of image annotation, it could be difficult to construct these binary constraints as two images with different annotations may still share several common keywords. [sent-24, score-0.099]

11 In particular, to ensure the learned metric to be Positive SemiDefinite (PSD), the existing methods need to project the learned matrix into a PSD cone whose computational cost is O(d3). [sent-29, score-0.21]

12 Finally, the high dimensionality of KML may lead to the overfitting of training data [18]. [sent-30, score-0.138]

13 In this paper, we propose a regression based approach for KML, termed Regression based Kernel Metric Learning (RKML), that explicitly addresses the challenges arising from high dimensionality and limitations of binary constraints. [sent-32, score-0.117]

14 RKML directly utilizes image tags to compute a real-valued semantic similarity, and therefore do not need to construct the binary constraints. [sent-33, score-0.189]

15 The projection step is avoided by exploiting the special property of regression, and the overfitting risk is alleviated by appropriately reg11660099 ularizing the rank of the learned kernel metric. [sent-34, score-0.32]

16 We demonstrate the robustness of the proposed RKML algorithm to high dimensionality by proving the theoretical guarantee of the learned kernel metric. [sent-35, score-0.242]

17 We also verify the efficiency and effectiveness of RKML for search-based image annotation by comparing it to the state-of-the-art approaches for both DML and image annotation on several benchmark datasets. [sent-36, score-0.414]

18 Related Work In this section we review the related work on image annotation and distance metric learning. [sent-38, score-0.368]

19 Recent studies on image annotation show that search based approaches are more effective than both generative and discriminative models. [sent-41, score-0.212]

20 Distance Metric Learning Many algorithms have been developed to learn a linear DML from pairwise constraints [35], and some of them are designed exclusively for image annotation [17, 32, 34]. [sent-47, score-0.261]

21 Recently, a number of nonlinear DML approaches have been developed to handle nonlinear and multimodal patterns. [sent-48, score-0.222]

22 They are usually classified into two categories, boosting based approaches [14, 15, 26] and kernel based approaches, depending on how the nonlinear mapping is constructed. [sent-49, score-0.263]

23 Many KML algorithms, such as Kernel DCA [16], KLMCA [28] and Kernel ITML [7], directly extend their linear counterparts to KML using the kernel trick. [sent-50, score-0.159]

24 To handle the high dimensionality challenge in KML, a common approach is to apply dimensionality reduction before learning the metric [5, 28]. [sent-51, score-0.263]

25 Although these studies show dimensionality reduction helps alleviate the overfitting risk in KML, no theoretical support is provided. [sent-52, score-0.183]

26 ) : Rd Rd → R be a kernel function, and Hκ be the corresponding Reproducing K keerrnneell fHuinlbcetirotn Space. [sent-66, score-0.138]

27 Without a metric, the similarity between two instances xa and xb could be assessed by the kernel function as ? [sent-67, score-0.381]

28 HThe objective of KML is to learn a PSD linear operator T that is consistent with the class assignments of training examples. [sent-74, score-0.084]

29 Note that this is different from similarity learning [4] because we require T to be PSD. [sent-75, score-0.082]

30 Regression based Kernel Metric Learning The proposed RKML is a kernel metric learning algorithm based on the regression technique. [sent-79, score-0.354]

31 Let si,j ∈ R be the similarity measure between two images xi and xj b Ras ebde on their annotations yi and yj . [sent-80, score-0.161]

32 We adopt a regression model to learn a kernel distance metric consistent with the similarity measure si,j by solving the optimization problem: T? [sent-85, score-0.402]

33 Following the representer theorem of kernel learning [24], it is sufficient to assume that T? [sent-91, score-0.179]

34 |2F, (2) where K = [κ(xi , xj)]n×n is the kernel matrix and S = [si,j]n×n includes all the pairwise se kmerannetlic m saitmriixla arintides S Sb e=- tween any two training images. [sent-107, score-0.159]

35 Note that when the semantic similarity matrix S is PSD, A will also be PSD, thus no additional projectSion is i Ps SnDe,ed Aed w tiol len alfsoorc bee t PheS Dlin,e tahru operator Tt? [sent-109, score-0.115]

36 e best rank r approximation of K, and express A as A = Kr−1SK−r1. [sent-112, score-0.092]

37 (3) Evidently, the rank r makes the tradeoff between bias and variance in estimating A: the larger the rank r, the lower the bias and higher the variance. [sent-113, score-0.12]

38 , the similarity between any two data instances xa and x? [sent-116, score-0.161]

39 Theoretical Guarantee of RKML We will show that the linear operator learned by the proposed algorithm is stochastically consistent, i. [sent-133, score-0.089]

40 , the lin- ear operator learned from finite samples provides a good approximation to the optimal one learned from an infinite number of samples. [sent-135, score-0.146]

41 To simplify our analysis, we assume that the semantic similarity measure si,j = yi? [sent-136, score-0.073]

42 aLtievte gk ( s·m) a blle, wtheh prediction function for the k-th ? [sent-161, score-0.098]

43 e W pree dmicatkioe nth feu following assumption fsosr, gk (·) in our analysis: A1 : gk(·) ∈ Hκ, k = 1, . [sent-165, score-0.073]

44 Assumption A1 essentially assumes that it is possible to accurately learn the prediction function gk (·) given sufficiently large number of training examples. [sent-169, score-0.119]

45 W) gei vaelsno unofftiethat assumption A1 holds if gk (·) is a smooth function and κ(·, ·) is a universal kernel [23(]·). [sent-170, score-0.23]

46 , (6) where Krs is the best rank r approximation of Ks = [κ( x? [sent-193, score-0.092]

47 2 ≤ O(1/√ns), that K˜r is an accurate approximation implying of Kr provided the number of samples ns is sufficiently large. [sent-200, score-0.087]

48 , kernel matrix K can be well approximated by the Nytr o¨m method when ns is a few thousands. [sent-203, score-0.193]

49 According to our implementation, we observe that further approximating Kb in (6) to rank r usually yields more accurate prediction for tags. [sent-204, score-0.112]

50 Three benchmark datasets for image annotation are used in our study and their statistics are summarized in Table 1. [sent-217, score-0.182]

51 Given a test image, we first identify the k most visually similar images from the training set using the learned distance metric, and then rank the tags by a majority vote over the k nearest neighbors, where k is chosen by cross-validation. [sent-227, score-0.274]

52 An RBF kernel is used in our study for all KML algorithms. [sent-228, score-0.138]

53 38m based on our experience, and determine the kernel width and rank r by cross-validation. [sent-231, score-0.198]

54 Besides, annotation based on the Euclidean distance, denoted by Euclid, is used as a reference in our comparison. [sent-233, score-0.182]

55 Since most DMLs are developed against mustlinks and cannot-links, we apply the procedure described in [32] to generate the binary constraints by performing a probabilistic clustering over the images based on their tags. [sent-234, score-0.096]

56 We evaluate the annotation accuracy by the average precision for the top ranked image tags. [sent-236, score-0.211]

57 Following [33, 34], we first compute the precision for each test image by comparing the top 10 annotated tags with the ground truth, and then take the average over the test set. [sent-237, score-0.177]

58 Comparison with State-of-the-art Distance Metric Learning Algorithms Comparison to nonlinear DML algorithms. [sent-243, score-0.087]

59 , Distance Boost (DBoost) [14], Kernel Boost (KBoost) [15], and metric learning with boosting (BoostM) [26], for comparison. [sent-247, score-0.217]

60 11661122 Figure 1 shows the average precision for the top t annotated tags obtained by nonlinear DML baselines and the proposed RKML. [sent-252, score-0.264]

61 Surprisingly, we observe that most of the nonlinear DML algorithms are only able to yield performance similar to that based on the Euclidean distance, and more disturbingly, some of the nonlinear DML algorithms even perform significantly worse than the Euclidean distance. [sent-253, score-0.201]

62 As described before, all DML algorithms require converting image annotations into binary constraints, which does not make full use of the annotation information. [sent-257, score-0.274]

63 To verify this point, we run RKML with similarity measure si,j computed from the binary constraints that are generated for the baseline DML algorithms, and denote this method by RKMLH. [sent-258, score-0.134]

64 Comparison of various extensions of RKML for the top t annotated tags on the IAPR TC12. [sent-268, score-0.148]

65 Figure 3 shows the average annotation precision for the linear DML baselines. [sent-272, score-0.232]

66 Similar to KML, we observe that even the best linear DML algorithm is only slightly better than the Euclidean distance, while RKML significantly outperforms all linear DML baselines. [sent-273, score-0.069]

67 Again, we believe that the failure of linear DML is likely due to the binary constraints generated from image annotations. [sent-274, score-0.089]

68 Since none of the baseline algorithms, neither linear nor nonlinear DML, is able to significantly outperform the Euclidean distance, it remains unclear if kernel DML is advantageous to a linear DML. [sent-275, score-0.267]

69 It is clear that RKML significantly outperforms its linear counterpart RLML, verifying the advantage of using kernel in DML. [sent-278, score-0.159]

70 Average precision for the first tag predicted by RMKL using different values of rank r on IAPR TC12 data. [sent-281, score-0.134]

71 To make the overfitting effect clearer, we turn off the Nystr ¨om approximation in this experiment. [sent-282, score-0.107]

72 We finally examine the role of rank r in the proposed algorithm by evaluating the prediction accuracy with varied r on the IAPRTC 12 dataset for both training and testing images (Figure 2). [sent-284, score-0.13]

73 We observe that while the average accuracy of test images initially improves significantly with increasing rank r, it becomes saturated after certain rank. [sent-286, score-0.087]

74 On the other hand, the prediction accuracy of training data increases almost linearly with respect to the rank, and becomes almost 1for very large r, a clear indication of overfitting training data. [sent-287, score-0.142]

75 and ns can be found in the supplementary document. [sent-293, score-0.082]

76 We include Pop as a comparison reference which simply ranks tags based on their occurring frequency in the training set. [sent-298, score-0.14]

77 Average precision for the top t annotated tags using nonlinear distance metrics. [sent-301, score-0.312]

78 Average precision for the top t annotated tags using linear distance metrics. [sent-303, score-0.246]

79 TIMEDCALMNNITMLLDMLDBoostBoostMKPCAGDAKDCAKLFDAKITMLMLKRRKML Figure 4 shows the comparison of average precision obtained by different image annotation models. [sent-307, score-0.211]

80 It is not surprising to observe that most annotation methods significantly outperform Pop, while the proposed RMKL method outperforms all the state-of-the-art image annotation methods on IAPR TC12 and ESP Game datasets, and only performs slightly worse than TP-D on the Flickr 1M dataset. [sent-308, score-0.391]

81 ning time includes the time for both learning a distance metric and predicting image tags. [sent-322, score-0.227]

82 We observe that compared to the other annotation methods, the proposed RKML algorithm is particularly efficient for large datasets (i. [sent-323, score-0.209]

83 Conclusions and Future Work In this paper, we propose a robust and efficient method for kernel metric learning (KML). [sent-327, score-0.317]

84 The proposed method addresses (i) high computational cost by avoiding the projection into PSD cone, (ii) limitation of binary constraints in tags by adopting a real-valued similarity measure, as well as (iii) the overfitting problem by appropriately regularizing the learned kernel metric. [sent-328, score-0.488]

85 Experiments with large-scale image annotation demonstrate the effectiveness and efficiency of the proposed algorithm by comparing it to the state-ofthe-art approaches for DML and image annotation. [sent-329, score-0.207]

86 In the future, we plan to improve the annotation performance by developing a more robust semantic similarity measure. [sent-330, score-0.255]

87 Supervised learning of semantic classes for image annotation and retrieval. [sent-352, score-0.255]

88 Large scale online learning of image similarity through ranking. [sent-359, score-0.082]

89 On the nystr ¨om method for approximating a gram matrix for improved kernel-based learning. [sent-387, score-0.086]

90 Multi-level annotation of natural scenes using dominant image components and semantic concepts. [sent-393, score-0.214]

91 TagProp: discriminative metric learning in nearest neighbor models for image auto-annotation. [sent-417, score-0.204]

92 Boosting margin [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] based distance functions for clustering. [sent-431, score-0.071]

93 Learning a kernel function for classification with small training samples. [sent-438, score-0.159]

94 Learning distance metrics with contextual constraints for image retrieval. [sent-445, score-0.078]

95 Labeling images by integrating sparse multiple distance learning and semantic context modeling. [sent-452, score-0.121]

96 Positive [27] [28] [29] [30] [3 1] [32] [33] [34] [35] semidefinite metric learning with boosting. [sent-510, score-0.201]

97 Dimensionality reduction of multimodal labeled data by local fisher discriminant analysis. [sent-515, score-0.08]

98 Distance metric learning for large margin nearest neighbor classification. [sent-536, score-0.227]

99 Distance metric learning from uncertain side information with application to automated photo tagging. [sent-551, score-0.179]

100 Mining social images with distance metric learning for automated image tagging. [sent-567, score-0.227]


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