iccv iccv2013 iccv2013-126 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Bo Wang, Zhuowen Tu, John K. Tsotsos
Abstract: In graph-based semi-supervised learning approaches, the classification rate is highly dependent on the size of the availabel labeled data, as well as the accuracy of the similarity measures. Here, we propose a semi-supervised multi-class/multi-label classification scheme, dynamic label propagation (DLP), which performs transductive learning through propagation in a dynamic process. Existing semi-supervised classification methods often have difficulty in dealing with multi-class/multi-label problems due to the lack in consideration of label correlation; our algorithm instead emphasizes dynamic metric fusion with label information. Significant improvement over the state-of-the-art methods is observed on benchmark datasets for both multiclass and multi-label tasks.
Reference: text
sentIndex sentText sentNum sentScore
1 ca Abstract In graph-based semi-supervised learning approaches, the classification rate is highly dependent on the size of the availabel labeled data, as well as the accuracy of the similarity measures. [sent-7, score-0.357]
2 Here, we propose a semi-supervised multi-class/multi-label classification scheme, dynamic label propagation (DLP), which performs transductive learning through propagation in a dynamic process. [sent-8, score-1.027]
3 Existing semi-supervised classification methods often have difficulty in dealing with multi-class/multi-label problems due to the lack in consideration of label correlation; our algorithm instead emphasizes dynamic metric fusion with label information. [sent-9, score-0.813]
4 Moreover, nice properties enjoyed by graph-based (built on the distance metric) two-class semi-supervised classification [37] become less obvious in the multi-class classification situations [11], due to the correlations of the multiple labels. [sent-13, score-0.239]
5 Supervised metric learning methods often learn a Mahalanobis distance by encouraging small distances among points of the same label while maintaining large distances for points of different labels [30, 29]. [sent-14, score-0.414]
6 Graph-based semisupervised learning frameworks on the other hand utilize a limited amount of labeled data to explore information on a large volume of unlabeled data. [sent-15, score-0.383]
7 Label propagation (LP) [37] specifically assumes that nodes connected by edges of large similarity tend to have the same label through information propagated within the graph. [sent-16, score-0.551]
8 A wide range of applications such as classification, ranking, and retrieval [38] have adopted the label propagation strategy. [sent-17, score-0.455]
9 was at York Uni- view features to help each other by pulling out unlabeled data to re-train and enhance the classifiers. [sent-19, score-0.167]
10 For the multi-class/multilabel case, the label propagation algorithm [37] becomes more problematic, therefore some special care needs to be taken. [sent-21, score-0.455]
11 all approaches is, however, that the correlations among different classes are not fully utilized. [sent-25, score-0.175]
12 In this paper, we propose a new method, dynamic label propagation (DLP), to simultaneously deal with the multiclass and multi-label problem. [sent-27, score-0.618]
13 Our method incorporates the label correlations and instance similarities into a new way of performing label propagation. [sent-28, score-0.668]
14 Our intuition in DLP is to update the similarity measures dynamically by fusing multi-label/multi-class information, which can be understood in a probabilistic framework. [sent-29, score-0.128]
15 The K nearest neighbor (KNN) matrix is used to preserve the intrinsic structure of the input data. [sent-30, score-0.117]
16 Transduction by Laplacian graph [4, 10] is also shown to be able to solve multi-class semi-supervised problems; although these algorithms make use of the relationship between unlabeled and labeled data, their computational complexity is demanding, e. [sent-41, score-0.238]
17 However, there are much fewer attempts to tackle semisupervised multi-label problem, despite there being a rich body of literature about supervised multi-label learning. [sent-44, score-0.11]
18 One popular method is label ranking [8], which learns a ranking function of category labels from the labeled in- stances and classifying each unlabeled instance by thresholding the scores ofthe learned ranking functions. [sent-45, score-0.652]
19 Although being easy to scale up, label ranking fails to exploit the correlations among data categories. [sent-46, score-0.449]
20 Recently, category correlations are given more attention in multi-label learning. [sent-47, score-0.133]
21 A maximum entropy method is employed to model the correlations among categories in [36]. [sent-48, score-0.134]
22 [19] studies a hierarchical structure to handle the correlation information. [sent-49, score-0.114]
23 In [13], a correlated label propagation framework is developed for multi-label learning that explicitly fuses the information of different classes. [sent-50, score-0.567]
24 However, these methods are only for supervised learning, and how to make use of label correlation among unlabeled instances is still unclear. [sent-51, score-0.592]
25 [17] uses constrained non-negative matrix factorization to propagate the label information by enforcing the examples with similar input patterns to share similar sets of class labels. [sent-52, score-0.338]
26 Another semi-supervised multi-label learning technique [7] develops a regularization with two energy terms about smoothness of input instances and label information by solving a Sylvester Equation. [sent-53, score-0.384]
27 Different from these semi-supervised multi-label methods, the proposed method explicitly merges the input data and label correlations. [sent-55, score-0.305]
28 Moreover, by doing projection on the fused manifolds, DLP further takes advantage of the correlations among labeling information of unlabeled data. [sent-56, score-0.347]
29 Our work also differs significantly from a very recent algorithm [14], which emphasizes the learning of fusion parameters for unlabeled data; the focus here is however the dynamic update of the similarity functions from both data and label information. [sent-57, score-0.716]
30 First, the multi-label problem considers the label correlations, but it may lead to a loss in the discrimination power of the multi-class classifiers. [sent-61, score-0.247]
31 The proposed dynamic label propagation method (DLP) aims to solve semi-supervised multiclass and multi-label problem simultaneously by combining the discriminative graph similarities and the label correlations in a dynamic way, while preserving the intrinsic structure of input data. [sent-63, score-1.201]
32 Label Propagation First, a brief introduction of the well-known label propagation algorithm is provided in this section. [sent-66, score-0.455]
33 If ρ is a distance metric defined on the graph, then the similarities matrix can be constructed as follows: W(i,j) = h(ρ(xμiσ,x2j)2), (1) for some function h with exponential decay at infinity. [sent-74, score-0.173]
34 A natural transition matrix on V can be defined by normalizing the weight matrix as: P(i,j) =? [sent-79, score-0.232]
35 , the labels of labeled data must be reset after each iteration. [sent-92, score-0.143]
36 The= =ma Pin algorithm of label propagation is summarized in Fig. [sent-97, score-0.455]
37 Essentially we make the assumption that local similarities (high values) are more reliable than far-away ones; and accordingly local similarities can be propagated to non-local points through a diffusion process on the graph. [sent-110, score-0.419]
38 e full pair-wise similarity information among the data whereas P only encodes the similarity ttioo nearby gda tthae points. [sent-116, score-0.16]
39 hFeo rro cblausr-t ity, we call P the status matrix and P the corresponding KityN,N w me catarlilx. [sent-119, score-0.114]
40 Label Fusion on Diffusion Space One disadvantage of label propagation is that it does not work well on multi-class/multi-label classification problem due to a lack of interplay among labels within different classes. [sent-122, score-0.66]
41 In this paper, we propose a dynamic version of label propagation that aims to improve the effectiveness on multi-class/multi-label classification. [sent-123, score-0.552]
42 Our main idea is to have an improved transition matrix by fusing information of both data features and data labels in each iteration. [sent-124, score-0.325]
43 Given the kernel Pt, where t denotes the number of it- erations, we can define the diffusion distance [15] at time t as: Dt(i, j) =? [sent-125, score-0.321]
44 (5) The diffusion process maps the data space into an ndimensional space Rtn in which each data point is represented by its transition probability to the other data points. [sent-128, score-0.435]
45 It is reasonable to assume that for each data xt ∈ Rtn, we have p(xt) = N(xt |μt, Pt), where μt is unkno∈wn R. [sent-129, score-0.151]
46 Note that the lab)el = =m Natr(ixx Y|μt contains information about class labels, and the correlation of these labels KY = YtYtT can be viewed as the similarity between data points in the label space Qtn, and data points in this label space Qtn have the probability p(yt) = N(yt |0, Kt). [sent-130, score-0.767]
47 The first part of dynamic label propagation is the fusion of the status matrix Pt and the label kernel KY = YtYtT. [sent-132, score-1.073]
48 (6) This operation corresponds to an addition operator in the diffusion spaces: zt = xt + √αyt. [sent-135, score-0.477]
49 (8) This simple fusion technique considers the correlation among the instance label vectors. [sent-137, score-0.469]
50 The underlying assumption is that two instances with high correlated label vectors tend to have high similarity in the input data space. [sent-138, score-0.458]
51 The correlation between label vectors can represent the label dependency among instances, especially for the multi-label/multiclass problem. [sent-139, score-0.635]
52 The advantage of fusing transition kernel and the label correlation is two-fold: On one hand, two instances with high correlated label vectors are likely to have high similarity in input data space, this fusion process therefore enhances the fitness of the kernel matrix for the input manifold. [sent-140, score-1.308]
53 On the other hand, the resulting kernel matrix leads to better label information through next round of label propagation. [sent-141, score-0.657]
54 In this way, we build up a dynamic interaction process between the feature space and label space. [sent-142, score-0.344]
55 However, since the label information is dynamically updated during the propagation process, the resulting label information after the initial several rounds no longer improves the transition matrix, sometimes even makes it worse. [sent-143, score-0.842]
56 Assume P0 is the initial status matrix of the input data calculated using (1) and (2), and P = KNN(P0) by (3) acnaldc (u4la);t Wde u employ th anisd l (in2e)a,r a operator P K tNo Ndo( Pthe projec- tainodn = Pzt + λtε, (9) where ε is white noise, i. [sent-146, score-0.172]
57 (11) The above equation implies that, the essence of dynamic label propagation is to do linear operations on diffusion space iteratively. [sent-158, score-0.794]
58 Note that xt+1 is a point in the diffusion space. [sent-159, score-0.242]
59 Instead of performing linear projection in the original data space, we do projection in the diffusion space. [sent-160, score-0.341]
60 The advantages of projection onto the diffusion space are two-fold: 1) we avoid the need to perform computational expensive sampling procedures in the input space; 2) The resulting variance matrix again is a good diffusion kernel for label propagation. [sent-161, score-0.937]
61 The intuition behind this projection lies in the fact that simple fusion of label correlation in Eqn. [sent-162, score-0.478]
62 (6) would result in a degeneration at the first round when the learned label information of unlabeled data is not accurate enough to infer the similarities in the input space. [sent-163, score-0.536]
63 From (13), we can see that, the diffusion process propagates the similarities through the KNN matrix. [sent-165, score-0.309]
64 In this way, we can adjust the fused kernel matrix to maintain part of the information of the initial structure. [sent-166, score-0.176]
65 The direct reflection of this projection on diffusion space is that , at each iteration, we construct the transition matrix for next iteration to be: Pt+1 = P(Pt + αYtYtT)PT + λtI. [sent-167, score-0.479]
66 (13), we see that only information between dominant neighbours are propagated into the transition matrix of next iteration. [sent-175, score-0.28]
67 An important observation is that if data iand j have common dominant neighbours in both similarity metrics, it is highly possible that they belong to the same class. [sent-176, score-0.145]
68 We summarize the details of dynamic label propagation in Fig. [sent-177, score-0.552]
69 The learned labels can improve the similarity between input instances quickly. [sent-190, score-0.2]
70 A loose theoretical proof of convergence can be constructed based on the spectral analysis of the diffusion projection P. [sent-191, score-0.278]
71 We have − Yt ∝ Y(∞)+[(P)t(P0+αY0Y0T)(PT)t]P0Y0+o(t) (14) where o(t) is an infinitesimal as t approaches infinity, and Y(∞) ∈ Rn×C is a constant label matrix. [sent-193, score-0.247]
72 An easy way to speed up the diffusion process is, first we keep a record of the KNN matrix and then every time we perform the diffusion process, we extract the fixed local structure from the KNN structure and only perform multiplication K times for each pair of data points. [sent-203, score-0.571]
73 Therefore we can update the transition kernel in (12) in time Kn2 +Kn. [sent-204, score-0.191]
74 α is the weight of label correlation, while λ represents the importance of regularization. [sent-216, score-0.247]
75 A Toy Data We first test our dynamic label propagation on a toy data set. [sent-224, score-0.632]
76 We test the effect of the two steps in the dynamic label propagation. [sent-230, score-0.344]
77 First, we omit the first step that fuses the label correlation with the kernel matrix. [sent-232, score-0.5]
78 Second, we do the first step to fuse label correlations but omit the second step of kernel diffusion. [sent-237, score-0.459]
79 Without the label correlation, DLP fails to capture the dependence between different classes; without the kernel diffusion process, the DLP goes wild because the label correlation in the beginning provides a poor guidance for the kernel matrix. [sent-242, score-1.008]
80 Semi-supervised Multi-class Learning We compare our DLP with several popular semisupervised learning methods: 1) Label Propagation (LP) ; 2) A variant of LP on KNN structure(LP+KNN) [23]; 3) Local and Global Consistency (LGC) [35]; 5) Transductive SVM (TSVM) 6) LapRLS [3]. [sent-249, score-0.152]
81 All the datasets have 12 splits each of which has 100 labeled and 1,400 unlabeled instances. [sent-255, score-0.204]
82 To show the effect of fusing label correlation, we especially set α = 0 in our method and denote this special method × as DLP0. [sent-256, score-0.294]
83 We can see that, our method is still capable of performing binary classification but it is especially suitable for the multi-class classification problem, such as in the dataset COIL. [sent-259, score-0.132]
84 05 for DLP, it does not indicate that the label correlation is of little importance. [sent-261, score-0.361]
85 The only reason for small value of α lies in difference of the numerical scale of label correlation and transition probability. [sent-262, score-0.473]
86 (A) is the toy data with only (C) (D) (E) one labeled data (the colored dots) for each class. [sent-305, score-0.171]
87 (B) is the classification result without using label correlations. [sent-306, score-0.313]
88 (C) is the classification result without using diffusion process. [sent-307, score-0.308]
89 These classes are chosen due to the relatively large number of availabel images within the category. [sent-319, score-0.123]
90 We also show the dynamics of label propagation and the proposed methods. [sent-340, score-0.455]
91 However, our method does not suffer from this problem because DLP iteratively update the transition matrix based on local similarity and label information. [sent-347, score-0.472]
92 The second one is based on Constrained Non-negative Matrix Factorization (CNMF) [17], which assumes that two instances tend to have large overlap in their assigned labels if they share high similarity in their input patterns. [sent-377, score-0.2]
93 The third one is Multi-label Informed Latent Semantic Indexing (MISL) [33], which maps the input features into a new feature space which captures the structure of both input data − and label dependency, and then uses SVM on the projected space. [sent-378, score-0.336]
94 , a transductive multi-label classification algorithm via label set propagation [14], which estimates the label sets of the unlabeled instances by utilizing the information from both unlabeled instances and unlabeled data. [sent-381, score-1.378]
95 We can see that our dynamic label propagation can properly capture the inner structure of label correlation and improve the classification accuracy. [sent-387, score-0.979]
96 Number of rtaninig nisatnces = 500 Number of rtaninig nisatnces = 2000 F1oicMr0. [sent-389, score-0.216]
97 Conclusion In this paper, we have proposed a novel classification method named dynamic label propagation (DLP), which improves the discriminative power in multi-class/multilabel problems in the framework of semi-supervised learning. [sent-398, score-0.618]
98 Our method explores the effect of labeled information and local structure in improving the transition matrix in semi-supervised learning. [sent-399, score-0.236]
99 The rendezvous algorithm: multiclass semisupervised lenaring with markov random walks. [sent-413, score-0.176]
100 Distance metric learning for large margin nearest neighbor classification. [sent-608, score-0.114]
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