nips nips2006 nips2006-136 knowledge-graph by maker-knowledge-mining

136 nips-2006-Multi-Instance Multi-Label Learning with Application to Scene Classification

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Author: Zhi-hua Zhou, Min-ling Zhang

Abstract: In this paper, we formalize multi-instance multi-label learning, where each training example is associated with not only multiple instances but also multiple class labels. Such a problem can occur in many real-world tasks, e.g. an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways. We analyze the relationship between multi-instance multi-label learning and the learning frameworks of traditional supervised learning, multiinstance learning and multi-label learning. Then, we propose the M IML B OOST and M IML S VM algorithms which achieve good performance in an application to scene classiﬁcation. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 cn Abstract In this paper, we formalize multi-instance multi-label learning, where each training example is associated with not only multiple instances but also multiple class labels. [sent-4, score-0.15]

2 an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways. [sent-7, score-0.123]

3 We analyze the relationship between multi-instance multi-label learning and the learning frameworks of traditional supervised learning, multiinstance learning and multi-label learning. [sent-8, score-0.23]

4 Then, we propose the M IML B OOST and M IML S VM algorithms which achieve good performance in an application to scene classiﬁcation. [sent-9, score-0.091]

5 1 Introduction In traditional supervised learning, an object is represented by an instance (or feature vector) and associated with a class label. [sent-10, score-0.172]

6 Formally, let X denote the instance space (or feature space) and Y the set of class labels. [sent-11, score-0.057]

7 Then the task is to learn a function f : X → Y from a given data set {(x1 , y1 ), (x2 , y2 ), · · · , (xm , ym )}, where xi ∈ X is an instance and yi ∈ Y the known label of xi . [sent-12, score-0.232]

8 Although the above formalization is prevailing and successful, there are many real-world problems which do not ﬁt this framework well, where a real-world object may be associated with a number of instances and a number of labels simultaneously. [sent-13, score-0.129]

9 For example, an image usually contains multiple patches each can be represented by an instance, while in image classiﬁcation such an image can belong to several classes simultaneously, e. [sent-14, score-0.121]

10 an image can belong to mountains as well as Africa. [sent-16, score-0.083]

11 Another example is text categorization, where a document usually contains multiple sections each of which can be represented as an instance, and the document can be regarded as belonging to different categories if it was viewed from different aspects, e. [sent-17, score-0.042]

12 Web mining is a further example, where each of the links can be regarded as an instance while the web page itself can be recognized as news page, sports page, soccer page, etc. [sent-20, score-0.1]

13 In order to deal with such problems, in this paper we formalize multi-instance multi-label learning (abbreviated as M IML). [sent-21, score-0.036]

14 In this learning framework, a training example is described by multiple instances and associated with multiple class labels. [sent-22, score-0.158]

15 Formally, let X denote the instance space and Y the set of class labels. [sent-23, score-0.057]

16 Here ni denotes the number of instances in Xi and li the number of labels in Yi . [sent-25, score-0.149]

17 After analyzing the relationship between M IML and the frameworks of traditional supervised learning, multi-instance learning and multi-label learning, we propose two M IML algorithms, M IML - B OOST and M IML S VM. [sent-26, score-0.154]

18 Application to scene classiﬁcation shows that, solving some real-world problems in the M IML framework can achieve better performance than solving them in existing frameworks such as multi-instance learning and multi-label learning. [sent-27, score-0.151]

19 2 Multi-Instance Multi-Label Learning We start by investigating the relationship between M IML and the frameworks of traditional supervised learning, multi-instance learning and multi-label learning, and then we develop some solutions. [sent-28, score-0.154]

20 Multi-instance learning [4] studies the problem where a real-world object described by a number of instances is associated with one class label. [sent-29, score-0.143]

21 Formally, the task is to learn a function fM IL : 2X → {−1, +1} from a given data set {(X1 , y1 ), (X2 , y2 ), · · · , (Xm , ym )}, where Xi ⊆ X is a set of (i) (i) (i) (i) instances {x1 , x2 , · · · , xni }, xj ∈ X (j = 1, 2, · · · , ni ), yi ∈ {−1, +1} is the label of Xi . [sent-30, score-0.309]

22 1 Multi-instance learning techniques have been successfully applied to diverse applications including scene classiﬁcation [3, 7]. [sent-31, score-0.096]

23 Multi-label learning [8] studies the problem where a real-world object described by one instance is associated with a number of class labels. [sent-32, score-0.114]

24 Formally, the task is to learn a function fM LL : X → 2Y from a given data set {(x1 , Y1 ), (x2 , Y2 ), · · · , (xm , Ym )}, where xi ∈ X is an instance and Yi ⊆ Y (i) (i) (i) (i) a set of labels {y1 , y2 , · · · , yli }, yk ∈ Y (k = 1, 2, · · · , li ). [sent-33, score-0.155]

25 2 Multi-label learning techniques have also been successfully applied to scene classiﬁcation [1]. [sent-34, score-0.096]

26 In fact, the multi- learning frameworks result from the ambiguity in representing real-world objects. [sent-35, score-0.09]

27 Multi-instance learning studies the ambiguity in the input space (or instance space), where an object has many alternative input descriptions, i. [sent-36, score-0.112]

28 instances; multi-label learning studies the ambiguity in the output space (or label space), where an object has many alternative output descriptions, i. [sent-38, score-0.109]

29 We illustrate the differences among these learning frameworks in Figure 1. [sent-41, score-0.06]

30 Thus, we can tackle M IML by identifying its equivalence in the traditional supervised learning framework, using multi-instance learning or multi-label learning as the bridge. [sent-43, score-0.146]

31 1 According to notions used in multi-instance learning, (Xi , yi ) is a labeled bag while Xi an unlabeled bag. [sent-44, score-0.144]

32 Although most works on multi-label learning assume that an instance can be associated with multiple valid labels, there are also works assuming that only one of the labels associated with an instance is correct [6]. [sent-45, score-0.207]

33 2 Solution 1: Using multi-instance learning as the bridge: We can transform a M IML learning task, i. [sent-47, score-0.069]

34 to learn a function fM IM L : 2X → 2Y , into a multi-instance learning task, i. [sent-49, score-0.044]

35 We can transform this multi-instance learning task further into a traditional supervised learning task, i. [sent-54, score-0.168]

36 to learn a function fSISL : X × Y → {−1, +1}, under (i) a constraint specifying how to derive fM IL (Xi , y) from fSISL (xj , y) (j = 1, · · · , ni ). [sent-56, score-0.077]

37 Here the constraint can be fM IL (Xi , y) = n (i) i sign[ j=1 fSISL (xj , y)] which has been used in transforming multi-instance learning tasks into traditional supervised learning tasks [9]. [sent-58, score-0.143]

38 Solution 2: Using multi-label learning as the bridge: We can also transform a M IML learning task, i. [sent-60, score-0.069]

39 to learn a function fM IM L : 2X → 2Y , into a multi-label learning task, i. [sent-62, score-0.044]

40 For any zi ∈ Z, fM LL (zi ) = fM IM L (Xi ) if zi = φ(Xi ), φ : 2X → Z. [sent-65, score-0.058]

41 We can transform this multi-label learning task further into a traditional supervised learning task, i. [sent-67, score-0.168]

42 Here the mapping φ can be implemented with constructive clustering which has been used in transforming multi-instance bags into traditional single-instances [11]. [sent-72, score-0.126]

43 Note that [(Xu , yv ), Ψ(Xu , yv )] (v = 1, 2, · · · , |Y|) is a labeled multi-instance (u) (u) bag where (Xu , yv ) is a bag containing nu number of instances, i. [sent-83, score-0.412]

44 {(x1 , yv ), (x2 , yv ), · · · , (u) (xnu , yv )}, and Ψ(Xu , yv ) ∈ {+1, −1} is the label of this bag. [sent-85, score-0.294]

45 Then, from the data set a multi-instance learning function fM IL can be learned, which can accomplish the desired M IML function because fM IM L (X ∗ ) = {y| argy∈Y (sign[fM IL (X ∗ , y)] = +1)}. [sent-92, score-0.038]

46 For convenience, let (B, g) denote the bag [(X, y), Ψ(X, y)]. [sent-94, score-0.11]

47 the label Africa of an image is usually triggered by several patches jointly instead of by only one patch. [sent-99, score-0.067]

48 Table 1: The M IML B OOST algorithm 1 Transform each M IML example (Xu , Yu ) (u = 1, 2, · · · , m) into |Y| number of multiinstance bags {[(Xu , y1 ), Ψ(Xu , y1 )], · · · , [(Xu , y|Y| ), Ψ(Xu , y|Y| )]}. [sent-100, score-0.083]

49 2 Initialize weight of each bag to W (i) = 3 1 m×|Y| (i = 1, 2, · · · , m × |Y|). [sent-102, score-0.11]

50 Repeat for t = 1, 2, · · · , T iterations: (i) 3a Set Wj = W (i) /ni (i = 1, 2, · · · , m × |Y|), assign the bag’s label Ψ(X (i) , y (i) ) (i) to each of its instances (xj , y (i) ) (j = 1, 2, · · · , ni ), and build an instance-level (i) predictor ht [(xj , y (i) )] ∈ {−1, +1}. [sent-103, score-0.163]

51 3b For the ith bag, compute the error rate e(i) ∈ [0, 1] by counting the number of ni misclassiﬁed instances within the bag, i. [sent-104, score-0.125]

52 e(i) = (i) j=1 (i) [ t [(x j ,y (i) )]=Ψ(X (i) ,y (i) )] [h ] ni . [sent-106, score-0.055]

53 3c 3d 3e Compute ct = arg minct If ct ≤ 0, go to Step 4. [sent-107, score-0.048]

54 In each boosting round, the aim is to 2 r(g=−1|B) expand F(B) into F(B) + cf (B), i. [sent-114, score-0.052]

55 Assuming all instances in a bag contribute equally and independently to the bag’s label, f (B) = n1 j h(bj ) can be derived, where h(bj ) ∈ {−1, +1} is the prediction of the B instance-level classiﬁer h(·) for the jth instance in bag B, and nB is the number of instances in B. [sent-117, score-0.401]

56 It has been shown by [9] that the best f (B) to be added can be achieved by seeking h(·) which (i) ni 1 maximizes i j=1 [ ni W (i) g (i) h(bj )], given the bag-level weights W = exp(−gF(B)). [sent-118, score-0.11]

57 By assigning each instance the label of its bag and the corresponding weight W (i) /ni , h(·) can be learned by minimizing the weighted instance-level classiﬁcation error. [sent-119, score-0.189]

58 When f (B) is found, the best multiplier c > 0 can be got by directly optimizing the exponential loss: EB EG|B [exp(−gF(B) + c(−gf (B)))] = = i i W (i) exp[c − g (i) (i) j h(bj ) ni ] W (i) exp[(2e(i) − 1)c] (i) 1 where e(i) = ni j [[(h(bj ) = g (i) )]] (computed in Step 3b). [sent-121, score-0.11]

59 2 Randomly select k elements from Γ to initialize the medoids Mt (t = 1, 2, · · · , k), repeat until all Mt do not change: 2a Γt = {Mt } (t = 1, 2, · · · , k). [sent-130, score-0.045]

60 A∈Γt B∈Γ t 3 Transform (Xu , Yu ) into a multi-label example (zu , Yu ) (u = 1, 2, · · · , m), where zu = (zu1 , zu2 , · · · , zuk ) = (dH (Xu , M1 ), dH (Xu , M2 ), · · · , dH (Xu , Mk )). [sent-133, score-0.064]

61 Xu , is an unlabeled multi-instance bag instead of a single instance, we employ Hausdorff distance [5] to measure the distance. [sent-138, score-0.11]

62 With the help of these medoids, we transform the original multi-instance example Xu into a k-dimensional numerical vector zu , where the ith (i = 1, 2, · · · , k) component of zu is the distance between Xu and Mi , that is, dH (Xu , Mi ). [sent-141, score-0.153]

63 This process reassembles the constructive clustering process used by [11] in transforming multiinstance examples into single-instance examples except that in [11] the clustering is executed at the instance level while here we execute it at the bag level. [sent-143, score-0.219]

64 Then, from the data set a multi-label learning function fM LL can be learned, which can accomplish the desired M IML function because fM IM L (X ∗ ) = fM LL (z ∗ ). [sent-147, score-0.038]

65 That is, the test example is labeled by all the class labels with positive S VM scores, except that when all the S VM scores are negative, the test example is labeled by the class label which is with the top (least negative) score. [sent-151, score-0.094]

66 4 Application to Scene Classiﬁcation The data set consists of 2,000 natural scene images belonging to the classes desert, mountains, sea, sunset, and trees, as shown in Table 3. [sent-152, score-0.091]

67 Some images were from the C OREL image collection while some were collected from the Internet. [sent-153, score-0.046]

68 Table 3: The image data set (d: desert, m: mountains, s: sea, su: sunset, t: trees) label d m s su t 4. [sent-155, score-0.129]

69 The former is the core of a successful multi-label learning system B OOS T EXTER [8], while the latter has achieved excellent performance in scene classiﬁcation [1]. [sent-158, score-0.127]

70 For M IML B OOST and M IML S VM, each image is represented as a bag of nine instances generated by the S BN method [7]. [sent-159, score-0.209]

71 Here each instance actually corresponds to an image patch, and better performance can be expected with better image patch generation method. [sent-160, score-0.116]

72 MH and M L S VM, each image is represented as a feature vector obtained by concatenating the instances of M IML B OOST or M IML S VM. [sent-162, score-0.099]

73 Gaussian kernel L IBSVM [2] is used to implement M L S VM, where the cross-training strategy is used to build the classiﬁers while the T-Criterion is used to label the images [1]. [sent-163, score-0.055]

74 MH and M L S VM make multi-label predictions, here the performance of the compared algorithms are evaluated according to ﬁve multi-label evaluation metrics, as shown in Tables 4 to 7, where ‘↓’ indicates ‘the smaller the better’ while ‘↑’ indicates ‘the bigger the better’. [sent-167, score-0.038]

75 Details of these evaluation metrics can be found in [8]. [sent-168, score-0.041]

76 Note that since in each boosting round M IML B OOST performs more operations than A DA B OOST. [sent-170, score-0.052]

77 MH does, for fair comparison, the boosting rounds used by A DA B OOST. [sent-171, score-0.097]

78 Table 4: The performance of M IML B OOST with different boosting rounds boosting rounds 5 10 15 20 25 evaluation metric hamm. [sent-173, score-0.246]

79 MH with different boosting rounds boosting rounds 50 100 150 200 250 4 evaluation metric hamm. [sent-228, score-0.229]

80 023 Table 7: The performance of M L S VM with different γ used in Gaussian kernel Gaussian kernel γ=1 γ=2 γ=3 γ=4 γ=5 evaluation metric hamm. [sent-343, score-0.052]

81 05 signiﬁcance level reveal that the worst performance of M IML B OOST (with 5 boosting rounds) is even signiﬁcantly better than the best performance of A DA B OOST. [sent-400, score-0.086]

82 MH (with 250 boosting rounds) on all the evaluation metrics, and is signiﬁcantly better than the best performance of M L S VM (with γ = 2) in terms of coverage while comparable on the remaining metrics; the worse performance of M IML S VM (with γ = . [sent-401, score-0.146]

83 5) is even comparable to the best performance of M L S VM and is signiﬁcantly better than the best performance of A DA B OOST. [sent-402, score-0.034]

84 These observations conﬁrm that formalizing the scene classiﬁcation task as a M IML problem to solve by M IML B OOST or M IML S VM is better than formalizing it as a multi-label learning problem to solve by A DA B OOST. [sent-404, score-0.181]

85 2 Comparison with Multi-Instance Learning Algorithms Since the scene classiﬁcation task has been successfully tackled by multi-instance learning algorithms [7], we compare the M IML algorithms with established multi-instance learning algorithms D IVERSE D ENSITY [7] and E M - DD [10]. [sent-407, score-0.165]

86 The former is one of the most inﬂuential multi-instance learning algorithm and has achieved excellent performance in scene classiﬁcation [7], while the latter has achieved excellent performance on multi-instance benchmark tests [10]. [sent-408, score-0.158]

87 That is, each image is represented as a bag of nine instances generated by the S BN method [7]. [sent-410, score-0.209]

88 1, with 25 boosting rounds for M IML B OOST while γ = . [sent-413, score-0.097]

89 Note that for M IML B OOST and M IML S VM, the top ranked class is regarded as the single-label prediction. [sent-418, score-0.041]

90 Tenfold cross-validation is performed and ‘mean ± std’ is presented in Table 8, where the best performance on each image class is bolded. [sent-419, score-0.062]

91 We can ﬁnd from Table 8 that M IML B OOST achieves the best performance on image classes desert and trees while M IML S VM achieves the best performance on the remaining image classes. [sent-421, score-0.145]

92 These observations conﬁrm that formalizing the scene classiﬁcation task as a M IML problem to solve by M IML B OOST or M IML S VM is better than formalizing it as a multi-instance learning problem to solve by D IVERSE D ENSITY or E M - DD. [sent-425, score-0.181]

93 Table 8: Compare predictive accuracy of M IML B OOST, M IML S VM, D IVERSE D ENSITY and E M - DD Image class desert mountains sea sunset trees overall 5 M IML B OOST . [sent-426, score-0.166]

94 054 Conclusion In this paper, we formalize multi-instance multi-label learning where an example is associated with multiple instances and multiple labels simultaneously. [sent-474, score-0.18]

95 Although there were some works investigating the ambiguity of alternative input descriptions or alternative output descriptions associated with an object, this is the ﬁrst work studying both these ambiguities simultaneously. [sent-475, score-0.115]

96 We show that an M IML problem can be solved by identifying its equivalence in the traditional supervised learning framework, using multi-instance learning or multi-label learning as the bridge. [sent-476, score-0.146]

97 The proposed algorithms, M IML B OOST and M IML S VM, have achieved good performance in the application to scene classiﬁcation. [sent-477, score-0.091]

98 Moreover, it remains an open problem that whether M IML can be tackled directly, possibly by exploiting the connections between the instances and the labels. [sent-479, score-0.098]

99 It is also interesting to discover the relationship between the instances and labels. [sent-480, score-0.084]

100 Logistic regression and boosting for labeled bags of instances. [sent-542, score-0.103]

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