cvpr cvpr2013 cvpr2013-442 knowledge-graph by maker-knowledge-mining

442 cvpr-2013-Transfer Sparse Coding for Robust Image Representation


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Author: Mingsheng Long, Guiguang Ding, Jianmin Wang, Jiaguang Sun, Yuchen Guo, Philip S. Yu

Abstract: Sparse coding learns a set of basis functions such that each input signal can be well approximated by a linear combination of just a few of the bases. It has attracted increasing interest due to its state-of-the-art performance in BoW based image representation. However, when labeled and unlabeled images are sampled from different distributions, they may be quantized into different visual words of the codebook and encoded with different representations, which may severely degrade classification performance. In this paper, we propose a Transfer Sparse Coding (TSC) approach to construct robust sparse representations for classifying cross-distribution images accurately. Specifically, we aim to minimize the distribution divergence between the labeled and unlabeled images, and incorporate this criterion into the objective function of sparse coding to make the new representations robust to the distribution difference. Experiments show that TSC can significantly outperform state-ofthe-art methods on three types of computer vision datasets.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 com {dinggg , Abstract Sparse coding learns a set of basis functions such that each input signal can be well approximated by a linear combination of just a few of the bases. [sent-3, score-0.257]

2 However, when labeled and unlabeled images are sampled from different distributions, they may be quantized into different visual words of the codebook and encoded with different representations, which may severely degrade classification performance. [sent-5, score-0.365]

3 In this paper, we propose a Transfer Sparse Coding (TSC) approach to construct robust sparse representations for classifying cross-distribution images accurately. [sent-6, score-0.247]

4 Specifically, we aim to minimize the distribution divergence between the labeled and unlabeled images, and incorporate this criterion into the objective function of sparse coding to make the new representations robust to the distribution difference. [sent-7, score-0.9]

5 As a powerful tool for finding succinct representations of stimuli and capturing high-level semantics in visual data, sparse coding can represent images using only a few active coefficients. [sent-11, score-0.458]

6 This makes the sparse representations easy to interpret and manipulate, and facilitates efficient content-based image indexing and retrieval. [sent-12, score-0.203]

7 Sparse coding is receiving increasing ∗Corresponding author: Jianmin Wang. [sent-13, score-0.209]

8 One major computational problem of sparse coding is to improve the quality of the sparse representation while maximally preserving the signal fidelity. [sent-20, score-0.511]

9 [6] introduced a Laplacian term of coefficients in sparse coding, which was extended to an efficient algorithm in Cai et al. [sent-25, score-0.172]

10 However, when labeled and unlabeled images are sampled from different distributions, they may be quantized into different visual words of the codebook and encoded with different representations. [sent-33, score-0.336]

11 In this case, the dictionary learned from the labeled images cannot effectively encode the unlabeled images with high fidelity, and also the unlabeled images may reside far away from the labeled images under the new representation. [sent-34, score-0.655]

12 This distribution difference will greatly challenge the robustness of existing sparse coding algorithms for cross-distribution image classification problems. [sent-35, score-0.413]

13 Recently, the literature has witnessed an increasing focus on transfer learning [15] problems where the labeled training data and unlabeled test data are sampled from different probability distributions. [sent-36, score-0.519]

14 In this case, standard classifiers such as SVM and logistic regression trained on the labeled data may fail to make correct predictions on the unlabeled data [13, 14, 16, 17]. [sent-38, score-0.323]

15 [13, 14] proposed to extract a “good” feature representation through which the probability distributions of labeled and unlabeled data are drawn close. [sent-40, score-0.391]

16 444000557 Inspired by recent progress in sparse coding and transfer learning, we propose a novel Transfer Sparse Coding (TSC) algorithm to construct robust sparse representations for classifying cross-distribution images accurately. [sent-42, score-0.721]

17 We aim to minimize the distribution divergence between labeled and unlabeled images using a nonparametric distance measure. [sent-43, score-0.39]

18 Specifically, we incorporate this criterion into the objective function of sparse coding to make the new representations of the labeled and unlabeled images close to each other. [sent-44, score-0.737]

19 In this way, the induced representations are made robust for cross-distribution image classification problems. [sent-45, score-0.115]

20 Moreover, to enrich the new representations with more discriminating power, we also incorporate the graph Laplacian term of coefficients [24] in our objective function. [sent-46, score-0.236]

21 Related Work In this section, we discuss prior works that are most related to ours, including sparse coding and transfer learning. [sent-49, score-0.474]

22 Recently, sparse coding has been a hot research focus in computer vision. [sent-50, score-0.348]

23 For adapting the dictionary to achieve sparse representation, Aharon et al. [sent-54, score-0.224]

24 Our work aims to discover a shared dictionary which can encode both labeled and unlabeled data sampled from different probability distributions. [sent-56, score-0.44]

25 To improve the quality of sparse representations, researchers have modified the sparse constraint by adding nonnegative constraint [10], graph regularization [6, 24], weighted ℓ2-norm constraint [20], etc. [sent-57, score-0.4]

26 Our approach aims to construct robust sparse representations for cross-distribution image classification problems, which is a different learning goal from the previous works. [sent-58, score-0.276]

27 In the machine learning literature, transfer learning [15], which aims to transfer knowledge between the labeled and unlabeled data sampled from different distributions, has also attracted extensive research interest. [sent-59, score-0.589]

28 proposed a Transfer Component Analysis (TCA) method to reduce the Maximum Mean Discrepancy (MMD) [7] between the labeled and unlabeled data, and simultaneously minimize the reconstruction error of the input data using PCA. [sent-61, score-0.304]

29 Different from their method, our work focuses on learning robust image representations by building an adaptive model based on sparse coding. [sent-62, score-0.225]

30 [16, 17] have explored sparse coding to extract features for knowledge transfer. [sent-64, score-0.348]

31 However, their method adopts a kernel density estimation (KDE) technique to estimate the PDFs of distributions and then minimizes the Jensen-Shannon divergence between them. [sent-65, score-0.138]

32 Moreover, our work additionally incorporates the graph Laplacian term of coefficients [24] in the objective function, which can discover more discriminating representations for classification tasks. [sent-67, score-0.221]

33 , b푘] ∈ ℝ푚× be the dictionary matrix where each column b푖] represents a basis vector in the dictionary, and let S = [s1, . [sent-77, score-0.134]

34 , s푛] ∈ ℝ푘×푛 be the coding matrix where each column s푖 is a sparse representation for a data point x푖. [sent-80, score-0.392]

35 The goal of sparse coding is to learn a dictionary (over-complete if > 푚) and corresponding sparse codes such that input data can be well approximated [16]. [sent-81, score-0.648]

36 ,푘 (1) where 휆 is a tunable regularization parameter to trade off the sparsity of coding and the approximation of input data. [sent-87, score-0.342]

37 , 푘∑ (2) where 훾 is a graph regularization parameter to trade off the weight between sparse coding and geometric preservation. [sent-112, score-0.528]

38 Transfer Sparse Coding In this section, we present the Transfer Sparse Coding (TSC) algorithm for robust image representation, which extends GraphSC by taking into account the minimization of distribution divergence between labeled and unlabeled data. [sent-114, score-0.412]

39 Problem Definition 풟푙 Given labeled data = {(x1, 푦1) , . [sent-117, score-0.114]

40 Assume t]h ∈at ℝthe labeled and unlabeled data are sampled from different probability distributions in an 푚-dimensional feature space. [sent-127, score-0.424]

41 Problem 1(Transfer Sparse Coding) Given labeled data and unlabeled data 풟푢 under different distributions, our g풟oaal nisd t uon lleaabrenl a d dicattiaon 풟ary B and a sparse coding S which performs robustly across the labeled and unlabeled data. [sent-129, score-0.956]

42 In this way, a supervised classifier trained on the labeled data can generalize better on the unlabeled data. [sent-131, score-0.322]

43 Objective Function To make sparse coding robust to different probability distributions, one may expect that the basis vectors can capture the commonality underlying both the labeled and unlabeled data, rather than only the individual property in the labeled data. [sent-134, score-0.792]

44 However, even in the extracted 푘-dimensional sparse representation, the distribution difference between labeled and unlabeled data will still be significantly large. [sent-135, score-0.479]

45 To realize this idea, a natural strategy is to make the probability distributions of labeled and unlabeled data close to each other in the sparse representation. [sent-137, score-0.53]

46 That is, by representing all data points X with the learned coding matrix S, the probability distributions of the sparse codes for the labeled and unlabeled data should be close enough. [sent-138, score-0.84]

47 XMSLBgraipdnchipMcoLtudioMatnp dDgla rtmcy ai ma tnra imtxriaxtr computes the distance between the sample means of the labeled and unlabeled data in the 푘-dimensional coefficients: ? [sent-143, score-0.304]

48 trix and is computed as follows 푀푖푗= ⎧⎨1 푛−/푙푛 1푢푙2푢 , xo t푖 h,ex r푗 w∈i se 풟 푙푢 (4) By regularizing E⎩quation (2) with Equation (3), dictionary matrix B is refined and the probability distributions of labeled and unlabeled data are drawn close under the new representation S. [sent-157, score-0.501]

49 , 푘 (5) where 휇 > 0 is the MMD regularization parameter trading off the weight between GraphSC and distribution matching. [sent-163, score-0.142]

50 To compare the effectiveness between MMD regularization and graph regularization (GraphSC), we refer to the special case of TSC with 훾 = 0 as TSCMMD and test it empirically. [sent-164, score-0.159]

51 By minimizing MMD, TSC can match distributions between labeled and unlabeled data based on sparse coding. [sent-168, score-0.512]

52 Following [9, 11, 24], we divide the optimization of TSC into two iterative steps: 1) learning transfer sparse codes S with dictionary B fixed, i. [sent-169, score-0.407]

53 , an ℓ1-regularized least squares problem; and 2) learning dictionary B with transfer sparse codes S fixed, i. [sent-171, score-0.437]

54 Learning Transfer Sparse Codes We solve optimization problem (5) for transfer sparse codes S. [sent-176, score-0.322]

55 By fixing dictionary B, problem (5) becomes mSin∥X − BS∥2퐹+ tr(S(휇M + 훾L)ST) + 휆∑푖푛=1 ∣s푖∣ (7) Unfortunately, problem (7) is nondifferentiable when s푖 takes values of 0, which makes standard unconstrained optimization techniques infeasible. [sent-177, score-0.143]

56 Several recent approaches 444000779 Algorithm 1: Learning Transfer Sparse Codes Input: Data matrix X, dictionary B, MMD matrix M, graph Laplacian matrix L, MMD/graph/sparsity regularization parameters 휇, 훾, 휆. [sent-178, score-0.247]

57 Output: Current optimal coding matrix S∗ = [s∗1 s푛∗] . [sent-179, score-0.234]

58 In nonsmooth optimization methods for solving nondifferentiable problems, a necessary condition for a parameter vector to be a local minimum is that the zero-vector is an element of the subdifferential— the set containing all subgradients at the parameter vector [5]. [sent-186, score-0.143]

59 , 휃푘] while updating each s푖, and systematically searches for the optimal active set and coefficients signs which minimize objective function (9). [sent-206, score-0.128]

60 Learning Dictionary Learning the dictionary B with the coding S fixed is reduced to the following ℓ2-constrained optimization problem mBin∥X − BS∥2퐹, 푠. [sent-213, score-0.313]

61 To speed up experiments, we construct one dataset USPS vs MNIST by randomly sampling 1,800 images in USPS to form the training data, and randomly sampling 2,000 images in MNIST to form the test data. [sent-230, score-0.113]

62 We construct one dataset PIE1 vs PIE2 by selecting all 2,856 images in PIE1 to form the training data, and all 3,329 images in PIE2 to form the test data. [sent-252, score-0.113]

63 We construct one dataset MSRC vs VOC by selecting all 1,269 images in MSRC to form the training data, and all 1,530 images in VOC2007 to form the test data. [sent-258, score-0.113]

64 2 Implementation Details Following [24, 14], SC, GraphSC, TSCMMD, and TSC are performed on both labeled and unlabeled data as an unsupervised dimensionality reduction procedure, then a super- vised LR classifier is trained on labeled data to classify unlabeled data. [sent-287, score-0.627]

65 Under our experimental setup, it is impossible to automatically tune the optimal parameters for the target classifier using cross validation, since the labeled and unlabeled data are sampled from different distributions. [sent-289, score-0.337]

66 c The TSC approach has three model parameters: MMD regularization parameter 휇, graph regularization parameter 훾, and sparsity regularization parameter 휆. [sent-308, score-0.312]

67 html DatasetUSPS vs MNIST PIE1 vs PIE2 MSRC vs VOC TPSLGaRCSbr Al[epM9h3]S. [sent-321, score-0.242]

68 ) E isx tpheer liambeeln ptraeld Ricteesdu bltys t The classification accuracy of TSC and the five baseline methods on the three cross-distribution image datasets USPS vs MNIST, PIE1 vs PIE2, and MSRC vs VOC is illustrated in Table 3. [sent-336, score-0.269]

69 This verifies that TSC can construct robust sparse representations for classifying cross-distribution images accurately. [sent-347, score-0.275]

70 This validates that minimizing the distribution divergence is very important to make the induced representations robust for cross-distribution image classification. [sent-349, score-0.218]

71 In particular, TSCMMD has significantly outperformed GraphSC, which indicates that minimizing the distribution divergence is more important than preserving the geometric structure when labeled and unlabeled images are sampled from different distributions. [sent-350, score-0.444]

72 By incorporating the graph Laplacian term of coefficients into TSC, we aim to enrich the sparse representations with more discriminating power to benefit the classification problems. [sent-352, score-0.383]

73 , LR, treat input data from different distributions as if they were sampled from the same distribution. [sent-359, score-0.121]

74 In real applications, this strict assumption is usually violated, since labeled training data and unlabeled test data are usually collected in different time periods, or under different conditions. [sent-360, score-0.342]

75 In this case, the optimal decision hyperplane trained from the labeled data cannot discriminate the unlabeled data effectively, leading to poor classification performance, as is shown in Table 3. [sent-361, score-0.352]

76 A possible reason for preferring PCA is that it can extract a low-dimensional subspace, where the distribution divergence may be reduced to some extent. [sent-366, score-0.153]

77 The reason for preferring SC and GraphSC is that the sparse representations can capture more succinct high-level semantics for image understanding. [sent-372, score-0.259]

78 By taking into account the graph Laplacian regularizer, GraphSC can further outperform SC, which verifies that the geometric structure can indeed enrich the sparse representations with more discriminating power. [sent-373, score-0.37]

79 However, since the labeled data and unlabeled data are sampled from different distributions as in our adopted datasets, SC and GraphSC may further enlarge the distribution divergence due to the sparse representation. [sent-374, score-0.687]

80 By extracting sparse representations and matching different distributions simultaneously, TSC and TSCMMD can greatly enhance the robustness of sparse coding, shown in Table 3. [sent-376, score-0.411]

81 We visualize in Figure 2 the values of matrices obtained by running TSC on USPS vs MNIST with 휇 = 0 and 휇 = 105, and then computing W in Equation (2) on sparse representation S. [sent-380, score-0.211]

82 Note that, the first 90 images are from the labeled training data while the last 100 images are from the unlabeled test data. [sent-382, score-0.323]

83 Most existing sparse coding methods, such as SC and GraphSC, have not explicitly minimized the distribution difference, resulting in unsatisfactory performance for cross-distribution problems. [sent-386, score-0.384]

84 This naturally leads to better generalization capability, that is, with sparse representation S, a supervised classifier trained on the labeled training data is expected to perform much better on the unlabeled test data. [sent-389, score-0.48]

85 Parameter Sensitivity We conduct empirical analysis on parameter sensitivity using all datasets, which validates that TSC can achieve optimal performance under a wide range of parameter values. [sent-392, score-0.11]

86 An extreme case is 휇 → ∞, where only distribution matching is guaranteed, ibsu t휇 b →oth ∞ sparse coding daisndtr geometric preservation afontre tehde, input images are discarded. [sent-395, score-0.474]

87 Another extreme case is 휇 → 0, iwnpheurte i only sparse coding da. [sent-396, score-0.379]

88 In both extreme cases, TSC cannot extract robust sparse representations for cross-distribution image classification. [sent-398, score-0.256]

89 Wuese run T inSC F iwguitrhe varying dva claunes c hofo graph regularization parameter 훾. [sent-403, score-0.116]

90 Theoretically, 훾 controls the weight of graph regularization, and larger values of 훾 will make the geometric preservation more important in TSC. [sent-404, score-0.138]

91 iTsh 훾en → →TS 0C, wwhilel degenerate etot TicSC prMeMseDr-, which cannot enrich the new representations with discriminating power. [sent-408, score-0.148]

92 Theoretically, 휆 controls the complexity of coding matrix S, and can prevent TSC from over-fitting the input data or degenerating to trivial solutions during the iterative procedure. [sent-417, score-0.274]

93 An important advantage of TSC is the robustness to the distribution difference between the labeled and unlabeled images, which can substantially improve cross-distribution image classification problems. [sent-433, score-0.35]

94 Extensive experimental results on several benchmark datasets show that TSC can achieve superior performance against state-of-the-art sparse coding methods. [sent-434, score-0.348]

95 K-svd: An algorithm for designing overcomplete dictionaries for sparse representation. [sent-440, score-0.139]

96 Spectral regression: A unified approach for sparse subspace learning. [sent-451, score-0.139]

97 Local features are not lonely laplacian sparse coding for image classification. [sent-473, score-0.4]

98 Knowledge transfer with low-quality data: A feature extraction issue. [sent-554, score-0.126]

99 Knowledge transfer with low-quality data: A feature extraction issue. [sent-560, score-0.126]

100 Linear spatial pyramid matching using sparse coding for image classification. [sent-601, score-0.348]


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