cvpr cvpr2013 cvpr2013-261 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Zinan Zeng, Shijie Xiao, Kui Jia, Tsung-Han Chan, Shenghua Gao, Dong Xu, Yi Ma
Abstract: We study in this paper the problem of learning classifiers from ambiguously labeled images. For instance, in the collection of new images, each image contains some samples of interest (e.g., human faces), and its associated caption has labels with the true ones included, while the samplelabel association is unknown. The task is to learn classifiers from these ambiguously labeled images and generalize to new images. An essential consideration here is how to make use of the information embedded in the relations between samples and labels, both within each image and across the image set. To this end, we propose a novel framework to address this problem. Our framework is motivated by the observation that samples from the same class repetitively appear in the collection of ambiguously labeled training images, while they are just ambiguously labeled in each image. If we can identify samples of the same class from each image and associate them across the image set, the matrix formed by the samples from the same class would be ideally low-rank. By leveraging such a low-rank assump- tion, we can simultaneously optimize a partial permutation matrix (PPM) for each image, which is formulated in order to exploit all information between samples and labels in a principled way. The obtained PPMs can be readily used to assign labels to samples in training images, and then a standard SVM classifier can be trained and used for unseen data. Experiments on benchmark datasets show the effectiveness of our proposed method.
Reference: text
sentIndex sentText sentNum sentScore
1 com Abstract We study in this paper the problem of learning classifiers from ambiguously labeled images. [sent-13, score-0.589]
2 For instance, in the collection of new images, each image contains some samples of interest (e. [sent-14, score-0.18]
3 , human faces), and its associated caption has labels with the true ones included, while the samplelabel association is unknown. [sent-16, score-0.319]
4 The task is to learn classifiers from these ambiguously labeled images and generalize to new images. [sent-17, score-0.556]
5 An essential consideration here is how to make use of the information embedded in the relations between samples and labels, both within each image and across the image set. [sent-18, score-0.272]
6 Our framework is motivated by the observation that samples from the same class repetitively appear in the collection of ambiguously labeled training images, while they are just ambiguously labeled in each image. [sent-20, score-1.265]
7 If we can identify samples of the same class from each image and associate them across the image set, the matrix formed by the samples from the same class would be ideally low-rank. [sent-21, score-0.51]
8 By leveraging such a low-rank assump- tion, we can simultaneously optimize a partial permutation matrix (PPM) for each image, which is formulated in order to exploit all information between samples and labels in a principled way. [sent-22, score-0.426]
9 The obtained PPMs can be readily used to assign labels to samples in training images, and then a standard SVM classifier can be trained and used for unseen data. [sent-23, score-0.333]
10 Introduction Learning classifiers for recognition purposes generally requires intensive labor work of labeling/annotating a large amount of training data. [sent-26, score-0.158]
11 For example, in face recognition [28, 32, 13, 10], it is well known that collecting training samples with manual annotation for precise face alignment is the key to achieve high recognition accuracy. [sent-27, score-0.302]
12 On the other hand, however, an unlimited number of images/videos with accompanying captions are freely available from the Internet, e. [sent-28, score-0.147]
13 , images containing human faces and their associated text captions from the news websites. [sent-30, score-0.325]
14 It becomes possible to avoid the intensive labor work if we can train good classifiers using these freely available data in the wild. [sent-31, score-0.213]
15 The main difficulty comes from the ambiguous association between samples in images and their labels in the corresponding image captions, as illustrated in Fig. [sent-33, score-0.537]
16 Learning classifiers from the ambiguously labeled data falls in the category of ambiguous learning. [sent-35, score-0.801]
17 The ambiguous association between samples and labels make the learning task more challenging than that in standard supervised learning. [sent-36, score-0.57]
18 For example, Multiple Instance Learning (MIL) has been proposed [1, 6, 25, 33] to learn classifiers from ambiguously labeled data, in which an image is treated as a bag, and the bag is labeled as positive if it contains at least one true positive instance, and negative otherwise. [sent-38, score-0.633]
19 MIL essentially learns a classifier for each class of samples by iteratively estimating the instance label by some predefined losses. [sent-39, score-0.287]
20 To explore the relations between samples and their ambiguous annotations, co-occurrence model [2, 3, 30, 20] has been proposed to infer their correspondences using the Expectation Maximization. [sent-40, score-0.554]
21 Iterative clustering and learning approach was also proposed in [4] to assign human faces to named entities. [sent-41, score-0.177]
22 In [12, 24], an ambiguous loss was proposed to learn a discriminant function for classification. [sent-42, score-0.33]
23 [ News From Washington Post ] BryantandAndrewBynumhavebe n named starters Western Conference at gua rd and center All-Star respectively. [sent-46, score-0.081]
24 This is Bryant's 14th time starting the league's annual showcase game. [sent-47, score-0.029]
25 Sample photos from news websites and the corresponding text caption. [sent-50, score-0.174]
26 In general, most of the news websites do not provide the face-name correspondence, hence it is a challenging task for the standard supervised learning method to automatically perform face recognition on such freely available data. [sent-51, score-0.323]
27 vant samples as background class, 2) uniqueness constraint - samples of the same class cannot simultaneously appear in an image except the background class (e. [sent-52, score-0.752]
28 , multiple faces of the same person cannot appear in an image), and 3) nonpairing constraint - samples of different classes and their true labels cannot consistently appear together across the training images (e. [sent-54, score-0.45]
29 , the faces from two subjects will not always co-occur in most of the images). [sent-56, score-0.105]
30 With these assumptions in mind, the task of ambiguous learning is essentially to model the ambiguous relations between samples and labels both within each image and across the image set. [sent-57, score-0.902]
31 A good approach should be able to make use of all constraints available in the sample-label relations in a principled way. [sent-58, score-0.17]
32 To this end, we propose a novel framework to address the ambiguous learning problem. [sent-60, score-0.278]
33 We are particularly interested in the problem of face recognition using ambiguously labeled images. [sent-61, score-0.551]
34 Our framework is motivated by the observation that samples from the same class, assuming intra-class variations are reduced within a certain level, can be characterized by a low-dimensional subspace embedded in the ambient space. [sent-62, score-0.18]
35 [10] showed that face images of the same person can be represented as a low-rank matrix. [sent-64, score-0.061]
36 Based on this low-rank assumption, our framework simultaneously optimizes a partial permutation matrix (PPM) for each of the training images by rank minimization. [sent-65, score-0.139]
37 The PPMs are formulated so that after optimization, they can associate samples of the same classes from different images to form low-rank matrices. [sent-66, score-0.209]
38 To address the intra-class variations, a sparse error term for each class is also introduced to achieve better robustness. [sent-67, score-0.075]
39 The obtained PPMs can be used as indicators to assign the labels to samples in each image. [sent-68, score-0.294]
40 Indeed, our method relies on the facts that PPMs are formulated and optimized so that the intrinsic constraints from both the intra-image and inter-image sample-label relations can be explored. [sent-69, score-0.158]
41 For the intra-image relations, the PPM is constrained to simultaneously and exclusively assign one label to one sample in each image, where other priors could also be incorporated. [sent-70, score-0.081]
42 For the inter-image relations, the PPMs are simultaneously optimized by rank minimization so that the aforementioned non-pairing assumption (3) in ambiguous learning can be used. [sent-71, score-0.393]
43 Once the sample-label correspon- dences are established, standard supervised learning methods can be applied to perform the prediction on unseen data. [sent-75, score-0.072]
44 Related work Learning visual classifiers from caption-accompanying images has been an active topic in computer vision [1, 2, 20, 3 1, 24], of which learning face classifiers from such data is of particular interest [3, 18, 12, 24]. [sent-78, score-0.226]
45 There are a few methods that explicitly take face-name (sample-label) correspondences into account. [sent-79, score-0.037]
46 The work in [18] first iteratively clusters faces using EM based on face similarity and constraints from the caption. [sent-81, score-0.203]
47 Based on these clusters, a weighted bipartite graph modelling the null assignment (i. [sent-82, score-0.158]
48 , faces that are not assigned to any names and names that are not assigned to any faces) and caption constraints is constructed for face-name assignment. [sent-84, score-0.491]
49 On the other hand, Support Vector Machine (SVM) based methods directly learn discriminant classifiers using the ambiguously labeled data. [sent-85, score-0.585]
50 [12] proposed a max-margin for777777000000977797 mulation by introducing an ambiguous 0/1 loss to replace the loss in the standard SVM formulation, in which they defined the ambiguous 0/1 loss as 0 if the predicted name is in the image caption, and 1otherwise. [sent-87, score-0.658]
51 Based on this ambiguous loss, they defined a convex loss that penalized the prediction of names as the ones not present in the caption. [sent-88, score-0.372]
52 This formulation did not consider the uniqueness constraint, hence it generally cannot perform well for images with multiple faces. [sent-89, score-0.108]
53 [24] extended the idea of ambiguous loss for images with multiple faces, in which they enforced the uniqueness constraint by assigning names to faces at a set level (via labeling vectors) in each image. [sent-91, score-0.646]
54 Recently, low-rank property of a set of linearly correlated images shows its usefulness in many computer vision problems, such as subspace segmentation [22], face recognition [10], multi-label image classification [7], image alignment [27] and image segmentation [11]. [sent-92, score-0.061]
55 On the other hand, PPM has been popularly used for feature point correspondence with unsupervised learning [26, 34]. [sent-93, score-0.067]
56 Our method in this paper is essentially motivated by these pioneering works. [sent-94, score-0.032]
57 However, with a new formulation of lowrank matrices and PPM constraints, we show that our proposed method fits well for the ambiguous learning task. [sent-95, score-0.278]
58 The proposed framework We formally define the problem of learning from ambiguously labeled images as follows. [sent-97, score-0.523]
59 Each image has different , lneucmtiobenr o off N samples f Iro,m· ·d·i s,tIinctive classes, and there are K¯ classes in total. [sent-99, score-0.18]
60 More precisely, we assume there are Kn samples from the nth image, and they are from different classes. [sent-100, score-0.247]
61 Hence, the nth image is represented as Fn = [f1n, ··· , fnKn] ∈ Rd×Kn. [sent-102, score-0.067]
62 Associated with the nth image is a binary ve]ct ∈or Rtn ∈ {0, 1}K¯ representing the labels appearing in the caption o {f0 t,h1e} nth image: tn (i) = 1 if the label of the ith class appears in the image caption, and 0 otherwise. [sent-103, score-0.581]
63 In the following, we first introduce how the low-rank assumption of the matrix formed by the samples from the same class can be used to simultaneously optimize a set of PPMs for assigning labels to the samples in the ambiguously labeled training images. [sent-105, score-1.108]
64 Low-rank assumption same class for samples from the Face images of the same individual are commonly assumed to reside in a low-dimensional subspace [28, 10]. [sent-108, score-0.29]
65 Put it in another way, if we place sufficient face samples from the same class into a matrix, this matrix should be approximately low-rank. [sent-109, score-0.316]
66 Denote F¯i = ··· ,¯fini] ∈ Rd×ni as the matrix containing ni samples f,r·o·m· the i ∈th class, i∈ {1, . [sent-110, score-0.209]
67 When these samples are human faces, then iF¯i ∈ s h{1ou,. [sent-114, score-0.18]
68 a rHeo hwumevaenr, tahcee sd,i tshtrein- [f¯i1, × bution and ground-truth labels of these ni samples in the N training images are unknown. [sent-118, score-0.342]
69 In our ambiguous learning tasks, we show next how this low-rank assumption can be used to seek the sample-label correspondences. [sent-119, score-0.313]
70 Sample-label correspondences via PPM Given N training images, our first objective is to find the sample-label correspondences for all samples from K¯ classes. [sent-122, score-0.254]
71 In this work, we use partial permutation matrix (PPM) [26, 3 1, 34] to model such correspondences. [sent-123, score-0.059]
72 The first row in (1) enforces that only labels appearing in the caption can be assigned to samples in the image In. [sent-133, score-0.509]
73 The second row in (1) is designed ptloe satisfy t ihme non-redundancy and uniqueness constraints. [sent-134, score-0.14]
74 { PNote∈ thPat }PPM has been used in [3 1] for ambiguous learning. [sent-136, score-0.245]
75 However, their work did not enforce the uniqueness constraint when using PMMs. [sent-137, score-0.138]
76 Given {Fn}nN=1, there exist the PPMs such that samples of the same c}lass can be identified and columnly corresponded in {FnPn ∈ or equivalently, the K¯ sub matrices {LF1, . [sent-138, score-0.209]
77 , LTK¯]T are rank deficient, where vec(·) is an operator that vectoriazrees a nmka tdreixfi by concatenating ·it)s cso alunm opn evreacttoorr tsh. [sent-145, score-0.067]
78 aBta vseecdt on our low-rank assumption for samples from the same class, the sample-label correspondence problem can be formulated as the following problem: ? [sent-146, score-0.278]
79 Considering intra-class variations and inevitable data noise or corruption, the above low-rank assumption is likely to be violated. [sent-153, score-0.035]
80 1 is the l1norm and λ > 0 is a trade-off parameter twhahte rbea ? [sent-168, score-0.032]
81 Modeling for the background samples In practical ambiguously labeled images from Internet, there are many irrelevant or background samples that cooccur with the samples we are interested in. [sent-173, score-1.03]
82 In line with the convention in ambiguous learning [24, 18], we call these background samples as samples of null class. [sent-174, score-0.84]
83 Without loss of generality, we let the K¯th class be the null class. [sent-175, score-0.289]
84 Note that enforcing low-rank and sparse constraints on samples of the null class is inappropriate. [sent-176, score-0.45]
85 In addition, there might be no true labels appearing in image captions for samples from the null class, we again take the convention to set tn (K¯) = 0. [sent-177, score-0.639]
86 Moreover, to avoid the trivial solution that all samples are assigned to the null class, we assume that at least one sample per image is not associated with the null class. [sent-178, score-0.496]
87 Similar to the PPM definition in (s1 a), ct h×e cfi irsdte row imn (t2ri)x prohibits our hmee PthPoMd from choosing a label not appeared in the image caption except the null class. [sent-187, score-0.455]
88 The second row enforces that at least one label from the caption must be chosen to avoid the trivial solution that assigning all the samples to the null class. [sent-188, score-0.576]
89 The third and forth rows in (2) enforce the uniqueness and non-redundancy constraints respectively. [sent-189, score-0.145]
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