iccv iccv2013 iccv2013-290 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Xiao Cai, Feiping Nie, Weidong Cai, Heng Huang
Abstract: In multi-label image annotations, because each image is associated to multiple categories, the semantic terms (label classes) are not mutually exclusive. Previous research showed that such label correlations can largely boost the annotation accuracy. However, all existing methods only directly apply the label correlation matrix to enhance the label inference and assignment without further learning the structural information among classes. In this paper, we model the label correlations using the relational graph, and propose a novel graph structured sparse learning model to incorporate the topological constraints of relation graph in multi-label classifications. As a result, our new method will capture and utilize the hidden class structures in relational graph to improve the annotation results. In proposed objective, a large number of structured sparsity-inducing norms are utilized, thus the optimization becomes difficult. To solve this problem, we derive an efficient optimization algorithm with proved convergence. We perform extensive experiments on six multi-label image annotation benchmark data sets. In all empirical results, our new method shows better annotation results than the state-of-the-art approaches.
Reference: text
sentIndex sentText sentNum sentScore
1 Previous research showed that such label correlations can largely boost the annotation accuracy. [sent-6, score-0.494]
2 However, all existing methods only directly apply the label correlation matrix to enhance the label inference and assignment without further learning the structural information among classes. [sent-7, score-0.383]
3 In this paper, we model the label correlations using the relational graph, and propose a novel graph structured sparse learning model to incorporate the topological constraints of relation graph in multi-label classifications. [sent-8, score-1.246]
4 As a result, our new method will capture and utilize the hidden class structures in relational graph to improve the annotation results. [sent-9, score-0.829]
5 In proposed objective, a large number of structured sparsity-inducing norms are utilized, thus the optimization becomes difficult. [sent-10, score-0.246]
6 We perform extensive experiments on six multi-label image annotation benchmark data sets. [sent-12, score-0.194]
7 In all empirical results, our new method shows better annotation results than the state-of-the-art approaches. [sent-13, score-0.194]
8 An example of label correlations for class membership inference. [sent-30, score-0.306]
9 Different to traditional single-label multi-class image classifications, in image annotation, each image or video clip is often associated with more than one semantic label, which poses so-called multi-label multi-class classification problem. [sent-34, score-0.216]
10 The multi-label multi-class classifications have many applications, such as document classification, protein function prediction, and music annotation. [sent-38, score-0.118]
11 An important difference between single-label classification and multi-label classification is that, the annotation classes in single-label classification are mutually exclusive, but the annotation terms in multi-label classification are correlated to each other. [sent-39, score-1.035]
12 Thus, in multi-label classification, researchers can utilize such annotation label correlations to infer the class memberships from one to another. [sent-40, score-0.552]
13 However, from the training visual data, we can learn the high correlations between “sky” and “plane”, and between “ocean” and “ship”. [sent-43, score-0.16]
14 Many previous multi-label image annotation methods explore such label correlations to improve the classification accuracy [3, 17, 11, 12, 13]. [sent-48, score-0.562]
15 However, all previous methods enhance the multi-label classifications by directly multiplying a label correlation matrix C ∈ ? [sent-49, score-0.405]
16 c×c (which can be calculated by the normalmizeatdr icxo Csine ∈ similarity between classes and c is the number of classes) on the label matrix or coefficient matrix to improve the label propagation or label assignment. [sent-50, score-0.579]
17 None of them explores the structures of classes under the label correlations. [sent-51, score-0.256]
18 Beyond straightforwardly applying the label correlation matrix, in this work, we propose to utilize the class relational graph to model the underlying structures existing in multi-label classes. [sent-52, score-0.803]
19 The label correlations indeed can be modeled as a class relational graph. [sent-53, score-0.6]
20 For example, using PASCAL 2006 data set, we can model the correlations among annotation term as a relational graph G = {V, E} in Fig. [sent-54, score-0.846]
21 2, where nodes ains Va are tiohen aaln gnroatpathio Gn c =las {seVs, Ean}d weights ,o fw edges oind eEs are the correlation values between classes (nodes). [sent-55, score-0.247]
22 Some classes, such as “Cat”, “Cow”, “Sheep”, have very small correlations with the rest classes shown in the left panel of Fig. [sent-56, score-0.347]
23 Such a relational graph model can capture the underlying structural interrelations between classes. [sent-61, score-0.492]
24 How to utilize this relational graph with discovering the hidden classes structures to enhance multi-label classification is computationally challenging. [sent-62, score-0.88]
25 In this paper, we will propose the novel structured sparsity-inducing norm regularization to incorporate the relational graph information into multi-label classification model. [sent-63, score-0.893]
26 Different to previous methods, which directly use the label correlation values to enhance the classification results, our new method will impose the correlated classes to share the common space, such that the input data relevant to both classes will learn jointly. [sent-64, score-0.662]
27 Our new class relational graph regularization will include a large number of non-smooth structured sparsity-inducing norms, such that the objective function optimization becomes difficult. [sent-65, score-0.892]
28 We will introduce new optimization algorithms to solve the proposed non-smooth convex objective with convergence proof. [sent-66, score-0.21]
29 We perform our new method on six multi-label classification benchmark data sets and compare the results with eight state-of-the-art multi-label classification methods. [sent-67, score-0.224]
30 Multi-Label Classification Using Graph Structured Sparse Learning Model The existing multi-label learning models cannot incorporate the semantic terms relational graph to enhance the annotation results. [sent-69, score-0.905]
31 To study the feature or class structural re- lations, many structured sparse learning methods have been proposed in recent research and shown promising results [18, 6, 4, 8, 1, 14, 15, 7]. [sent-70, score-0.247]
32 However, these approaches also cannot incorporate the label relational graph into the classification models. [sent-71, score-0.751]
33 To address this challenging problem, we propose new graph structured sparsity-inducing norms, which learn the correlated classes in a common space under the relational graph structure. [sent-72, score-1.05]
34 n×c for c classes, the structured sparsityinducing norm ∈ba ? [sent-76, score-0.222]
35 a nTdh eL regularization term Ω(W) is the structured sparsity-inducing norm, which usually uses the mixed norms to capture the features and classes structural relations for enhancing the classification tasks. [sent-81, score-0.554]
36 In multi-label annotations, we have the label (semantic terms) relational graph G = {V, E} (e. [sent-82, score-0.588]
37 the class relationtael graph claotniosntarulc gteradp ihn G Fig. [sent-84, score-0.248]
38 If we correctly incorporate such label relational graph into multi-label classifi- cation model, the performance can definitely be boosted. [sent-88, score-0.639]
39 Thus, the structured sparsity-inducing norm Ω(W) is expected to model the label relational graph. [sent-89, score-0.551]
40 However, it is challenging to model such graph structured sparsity by the convex norm. [sent-91, score-0.447]
41 We propose a new graph structured sparsity model to capture the graph structures using the structured sparsityinducing norms. [sent-92, score-0.859]
42 Our new graph structured sparse multilabel classification model is to solve: mW,inbL(X,W,b;Y ) + γE? [sent-93, score-0.601]
43 Our regularization terms go through all edges in E to include all topological constraints by the structured sparsity-inducing norms. [sent-104, score-0.29]
44 id=1 880022 graph, where nodes are labels and weights of edges are correlation values between classes. [sent-106, score-0.128]
45 Meanwhile, our regularization terms are also convex norms which guarantee the globally optimal results. [sent-108, score-0.211]
46 Because the weight aij of the edge connecting nodes Vi and Vj represents the correlation level of these two classes, we also use the weights values to scale the regularization terms. [sent-109, score-0.26]
47 As a result, the highly correlated classes will get large weight in the joint sparsity regularization. [sent-110, score-0.238]
48 2,1-norm minimization problem, based on which we will further derive the algorithm to solve the main objective in (4). [sent-140, score-0.161]
49 ion Tr(GiT(X)DiGi (X)), where Di is a diagonal matrix with the k-th diagonal element as 2? [sent-154, score-0.239]
50 In the following, we will prove that this algorithm will converge and converge to a local or global solution to the problem in (5), when the problem in (5) is non-convex or convex. [sent-159, score-0.191]
51 Algorithm Convergence Analysis To prove the convergence of our Algorithm 1, first we introduce the following lemma: Lemma 1 Suppose D is a diagonal matrix, where the k-th diagonal element is 2? [sent-163, score-0.221]
52 i Thus the Algorithm 1monotonically decreases the value of objective function in (5) or remains the objective function value unchanged in each iteration t. [sent-295, score-0.224]
53 The following theorem guarantees that the Algorithm 1 will converge to a local or global solution to the problem (5). [sent-299, score-0.154]
54 Theorem 2 The Algorithm 1will converge to a local optimal solution of the objective in (5), and will converge to a global solution if the objective in (5) is a convex function. [sent-300, score-0.463]
55 i2γiDiGi(X) −∂h∂(XX,Λ) = 0, (11) where D is a diagonal matrix, and the k-th diagonal element is Suppose the Algorithm 1 converges to a solution X∗, from Step 2 in Algorithm 1, we have: 2? [sent-311, score-0.22]
56 iγiTr(GiT(X)(D∗)iGi(X)), (12) where D is a diagonal matrix with the k-th diagonal element as 2? [sent-315, score-0.239]
57 Therefore, the converged solution X∗ is a local solution of the objective in (5). [sent-324, score-0.234]
58 Moreover, if the objective in (5) is a convex function, then the converged solution X∗ is a global solution of the objective in (5) ? [sent-325, score-0.395]
59 In the next section, we will derive the algorithm to solve the objective in (4) based on Algorithm 1. [sent-326, score-0.161]
60 Algorithm to Solve Objective in (4) According to Algorithm 1, the key step to solve the objective in (4) is to solve the following problem: γmWi? [sent-328, score-0.21]
61 matrix with the k-th diagonal ele- ment We simplify the second term in Eq. [sent-335, score-0.147]
62 (17) Therefore, we get the optimal solution of the problem (16) as: wi = (XHXT + γMi)−1XHyi . [sent-420, score-0.144]
63 (18) Based on the above derivation, the detailed algorithm to solve the objective in (4) is summarized in Algorithm 2. [sent-421, score-0.161]
64 Because the objective in (4) is a convex problem, according to Theorem 2, we can obtain the global solution with Algorithm 2. [sent-422, score-0.197]
65 Experiment Data In this section, we will briefly introduce the multi-label image data sets that we used to evaluation the proposed graph structured sparse multi-label learning model. [sent-426, score-0.395]
66 Note that multiple objects from multiple classes may be present in the same image. [sent-440, score-0.119]
67 It has 25000 images with 38 classes downloaded from the social photography site Flickr through its public API. [sent-463, score-0.119]
68 colors, seasons and place names, the average number of annotation per image is 8. [sent-466, score-0.194]
69 Experiment Settings In our experment, we used the following way to build the graph structure for the annotations. [sent-472, score-0.198]
70 mDi affnedre 0nt o fhreormw sceo,n ∀vie n=tio 1n,2a,l single-label classification learning in which classes are mutual exclusive, the annotations are interrelated with one another in multi-label problem. [sent-477, score-0.343]
71 We utilize the following cosine similarity to calculate the annotation affinity matrix A(i,j) = cos(yi,yj) =(| j| ) (19) where yi and yj are the i-th and j-th column of the indicator matrix of the labeled data Y ∈ Rl respectively. [sent-478, score-0.356]
72 Thus, a graph G = (V, E) is induced∈, w Rhere V = A and E ⊆ V V . [sent-479, score-0.198]
73 d Wucheadt by mthoer eo,u itnlie orr ddearta to or imneovvitea tbhlee ”innaocicsyu”rate annotation information of the training data, we set up a filter to set those entries of A in Eq. [sent-481, score-0.194]
74 We will use the above calculated annotation graph structure as input for both our method and the comparison approaches. [sent-483, score-0.392]
75 Moreover, we compare our proposed method with the following state-of-art multi-label classification methods: K Nearest Neighbor (KNN), where we set K as 1(1NN) for its simple and intuitive interpretation, that is, we predict the annotations of the testing data as the ones of its nearest neighbor. [sent-499, score-0.262]
76 the rest strategy to predict the annotations one by one, where we chose the linear kernel and set C as 1. [sent-503, score-0.15]
77 Multi-Label Informed Latent Semantic Indexing (MLSI) [17] is an approach to extend unsupervised latent semantic indexing (LSI) to utilize the provided supervision information. [sent-506, score-0.156]
78 However, the way that MLLS takes advantage of the annotation information is different with our proposed method. [sent-509, score-0.194]
79 o Itnati [o3n], i infd wicea tdoern moteatr tihxe as tYa m∈a Rtrinx× acs, tXhen ∈ M RLLaSn explores tthioen l iinnedairc atonrno mtaattiroinx ainsf Yorm ∈at iRon by calculating XY YTX only without the graph information. [sent-511, score-0.198]
80 What is more, with the development of feature selection methods, more and more filter methods or their variations can be used to reduce the dimension of feature and further boost the multi-label classification performance. [sent-512, score-0.156]
81 In addition, they used 1NN as the classifier to evaluate the multi-label classification performance on 10% to 70% selected features and reported the best multilabel classification result based on a certain number of selected features. [sent-515, score-0.318]
82 Multi-Label Classification Results Two standard multi-label classification performance metrics precision and F1 score are used to evaluate image annotation performances. [sent-518, score-0.306]
83 In our experiment, we report both macro and micro results in Table. [sent-519, score-0.147]
84 As can be observed from the table, first of all, correlations between annotations can indeed boost the classification performance compared with the methods that consider annotation classification independently, like SVM. [sent-521, score-0.734]
85 Moreover, given the same graph structure, our proposed graph structured sparse multi-label learning method can consistently beat those dimension reduction methods as well as feature selection methods invented for multi-label classification on most data sets. [sent-522, score-0.705]
86 Therefore, although the precision of our method is higher, we get a less macro and micro F1 score. [sent-524, score-0.147]
87 Given an image having “Chairs”, “Dinning table”, “Person” inside, the annotation affinity matrix shows the correlation values between these semantic terms. [sent-529, score-0.425]
88 Because semantic terms “Chairs” and “Dinning table” often appear together and have large correlations, the weight of edge connecting them in the label relational graph G is large. [sent-530, score-0.692]
89 Thus, their regularization term has large contribution in training process (in right-bottom panel), such that the learned coefficient matrix W∗ showing these correlations. [sent-531, score-0.194]
90 2,1-norm with the help of pairwise annotation correlation information, which is shown in the top panel. [sent-534, score-0.266]
91 Obviously two semantic terms show similar weight coefficient structures, i. [sent-536, score-0.166]
92 The existing methods didn’t consider the shared structure between correlated semantic terms, hence they predict “Dinning table”, but miss “Chairs” in the prediction. [sent-540, score-0.222]
93 Our graph structured sparse multi-label learning model can correctly predict both labels due to the shared similar weight structures in W∗ . [sent-541, score-0.474]
94 Conclusion In this paper, we model the label correlations using the relational graph, and propose a novel graph structured s880077 ? [sent-543, score-0.909]
95 2,1-norm will shrink the coefficient matrix based on different weight values. [sent-544, score-0.117]
96 And the higher weight will boost the multi-label classification via graph structured sparse learning. [sent-545, score-0.551]
97 parse learning model to incorporate the topological constraints of relation graph to tackle multi-label classifications problem. [sent-546, score-0.419]
98 Moreover, it is a general method to incorporate graph structure information to the supervised learning. [sent-547, score-0.249]
99 Compared with multiple state-of-art multi-label classification methods, our method consistently achieves superior classification result with respect to both precision and F1 score in macro as well as micro cases. [sent-550, score-0.371]
100 Image annotation using birelational graph ofimages and semantic labels. [sent-635, score-0.496]
wordName wordTfidf (topN-words)
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