cvpr cvpr2013 cvpr2013-257 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yangmuzi Zhang, Zhuolin Jiang, Larry S. Davis
Abstract: An approach to learn a structured low-rank representation for image classification is presented. We use a supervised learning method to construct a discriminative and reconstructive dictionary. By introducing an ideal regularization term, we perform low-rank matrix recovery for contaminated training data from all categories simultaneously without losing structural information. A discriminative low-rank representation for images with respect to the constructed dictionary is obtained. With semantic structure information and strong identification capability, this representation is good for classification tasks even using a simple linear multi-classifier. Experimental results demonstrate the effectiveness of our approach.
Reference: text
sentIndex sentText sentNum sentScore
1 By introducing an ideal regularization term, we perform low-rank matrix recovery for contaminated training data from all categories simultaneously without losing structural information. [sent-4, score-0.407]
2 A discriminative low-rank representation for images with respect to the constructed dictionary is obtained. [sent-5, score-0.725]
3 Introduction Recent research has demonstrated that sparse coding (or sparse representation) is a powerful image representation model. [sent-9, score-0.384]
4 The idea is to represent an input signal as a linear combination of a few items from an over-complete dictionary D. [sent-10, score-0.665]
5 The sparse representationbased coding (SRC) algorithm [27] takes the entire training set as dictionary. [sent-13, score-0.272]
6 However, sparse coding with a large dictionary is computationally expensive. [sent-14, score-0.805]
7 The performance of algorithms like image classification is improved dramatically with a well-constructed dictionary and the encoding step is efficient with a compact dictionary. [sent-16, score-0.652]
8 Low-rank matrix recovery, which determines a low-rank data matrix from corrupted input data, has been successfully applied to applications including salient object detection [24], segmentation and grouping [35, 13, 6], background subtraction [7], tracking [34], and 3D visual recovery [13, 3 1]. [sent-24, score-0.282]
9 edu rank matrix recovery to remove noise from the training data class by class. [sent-28, score-0.425]
10 [19] presents a discriminative low-rank dictionary learning for sparse representation (DLRD SR) to learn a low-rank dictionary for sparse representation-based face recognition. [sent-32, score-1.697]
11 A sub-dictionary Di is learned for each class independently; these dictionaries are then combined to form a dictionary D = [D1, D2 , . [sent-33, score-0.763]
12 Label information from training data is incorporated into the dictionary learning process by adding an ideal-code regularization term to the objective function of dictionary learning. [sent-40, score-1.333]
13 Unlike [19], the dictionary learned by our approach has good reconstruction and discrimination capabilities. [sent-41, score-0.632]
14 With this high-quality dictionary, we are able to learn a sparse and structural representation by adding a sparseness criteria into the low-rank objective function. [sent-42, score-0.326]
15 In contrast to the prior work [5, 19] on classification that performs low-rank recovery class by class during training, our method processes all training data simultaneously. [sent-45, score-0.398]
16 Compared to other dictionary learning methods [12, 33, 27, 25] that are very sensitive to noise in training images, our dictionary learning algorithm is robust. [sent-46, score-1.384]
17 Contaminated images can be recovered during our dictionary learning process. [sent-47, score-0.628]
18 The main contributions of this paper are: • We present an approach to learn a structural low-rank aWnde sparse image representation. [sent-48, score-0.265]
19 • We present a supervised training algorithm to construct 6 6 6 7 7 7 64 464 a discriminative and reconstructive dictionary, which is used to obtain a low-rank and sparse representation for images. [sent-51, score-0.395]
20 [26] has shown that sparse representation achieves impressive results on face recognition. [sent-58, score-0.249]
21 One of the most commonly used dictionary learning method is K-SVD [1]. [sent-64, score-0.628]
22 Several algorithms have been developed to make the dictionary more discriminative for sparse coding. [sent-66, score-0.786]
23 In [23], a dictionary is updated iteratively based on the results of a linear predictive classier to include structure information. [sent-67, score-0.604]
24 [12] presents a Label Consistent K-SVD (LC-KSVD) algorithm to learn a compact and discriminative dictionary for sparse coding. [sent-68, score-0.82]
25 [3 1] presents an image classification framework by using non-negative sparse coding, low-rank and sparse matrix decomposition. [sent-82, score-0.326]
26 Compared to previous work, our approach effectively constructs a reconstructive and discriminative dictionary from corrupted training data. [sent-84, score-0.889]
27 Based on this dictionary, structured low-rank and sparse representations are learned for classification. [sent-85, score-0.283]
28 [5] uses this technique to remove noise from training samples class by class; this process is computationally expensive for large numbers of classes. [sent-105, score-0.284]
29 t X = DZ + E where D is a dictionary that linearly spans the data space. [sent-119, score-0.604]
30 [18] employs the whole training set as the dictionary, but this might not be efficient for finding a discriminative representation in classification problems. [sent-121, score-0.24]
31 6 6 6 7 7 7 75 575 [19] tries to learn a structured dictionary by minimizing the rank of each sub-dictionary. [sent-122, score-0.761]
32 Associating label information in the training process, a discriminative dictionary can be learned from all training samples simultaneously. [sent-125, score-0.937]
33 The learned dictionary encourages images from the same class to have similar representations (i. [sent-126, score-0.817]
34 Learning Structured Sparse and Low-rank Representation To better classify images even when training and testing images have been corrupted, we propose a robust supervised algorithm to learn a structured sparse and low-rank representation for images. [sent-131, score-0.433]
35 We construct a discriminative dictionary via explicit utilization of label information from the training data. [sent-132, score-0.765]
36 Based on the dictionary, we learn low- rank and sparse representations for images. [sent-133, score-0.3]
37 As discussed before, low-rank matrix recovery helps to decompose a corrupted matrix X into a low-rank component DZ and a sparse noise component E, i. [sent-143, score-0.549]
38 With respect to a semantic dictionary D, the optimal representation matrix Z for X should be block-diagonal [18]: Z∗? [sent-146, score-0.699]
39 Given a dictionary D, the objective function is formulated as: mZ,Ein||Z||∗ + λ||E||1 + β||Z||1 (4) s. [sent-151, score-0.604]
40 To obtain a low-rank and sparse data representation, D should have discriminative and reconstructive power. [sent-168, score-0.235]
41 Although this decomposition might not result in minimal reconstruction error, low-rank and sparse Q is an optimal representation for classification. [sent-187, score-0.238]
42 With the above definition, we propose to learn a semantic structured dictionary by supervised learning. [sent-188, score-0.722]
43 ur We ein afodrdm aat rieognu linartoiz tahtieo dictionary learning process. [sent-191, score-0.628]
44 A dictionary that encourages Z to be close to Q is preferred. [sent-192, score-0.629]
45 The objective function for dictionary learning is defined as follows: Zm,Ein,D||Z||∗+ λ||E||1 + β||Z||1 + α||Z − Q||2F (5) s. [sent-193, score-0.628]
46 The first subproblem is to compute the optimal Z, E for a given dictionary D. [sent-201, score-0.628]
47 The second subproblem is to solve dictionary D for the given Z, E calculated from the first subproblem. [sent-203, score-0.628]
48 This equation (12) is a quadratic form in variable D, so we can derive an optimal dictionary Dupdate immediately. [sent-222, score-0.626]
49 The dictionary construction process is summarized in Algorithm 2. [sent-224, score-0.604]
50 The input dictionary D0 is initialized by combining all the individual class dictionaries, i. [sent-229, score-0.687]
51 After the dictionary is learned, the low-rank sparse representations Z of 6 6 6 7 7 7 97 797 Algorithm 2 Dictionary Learning via Inexact ALM Input: Data X, and Parameters λ, β, α, γ Output: D, Z Initialize: Initial Dictionary D0, ? [sent-238, score-0.803]
52 Our approach is compared with several other algorithms including the locality-constrained linear coding method (LLC) [25], × SRC [27], LR [5], LR with structural incoherence from [5], DLRD SR [19] and our method without the regularization term | |Z − Q| | (our method without Q). [sent-248, score-0.445]
53 Our trained dictionary has 5 items for each class. [sent-262, score-0.665]
54 We repeat our experiments starting with 32 randomly selected training images and 20 dictionary items per class. [sent-263, score-0.736]
55 We compare our approach with LLC [25], SRC [27], LR [5], and LR with structural incoherence [5]. [sent-273, score-0.336]
56 We evaluate the performance of the SRC algorithm using a full-size dictionary (all training samples). [sent-274, score-0.675]
57 Our method, by taking advantage of structure information, achieves better performance than LLC, LR, LR with structural incoherence and our method without Q. [sent-279, score-0.336]
58 The dictionary contains 50 items (5 for each category). [sent-283, score-0.665]
59 The first line shows the testing images’ representa- tion based on LR and LR with structural incoherence [5]. [sent-284, score-0.397]
60 Figures 3(a) and 3(c) are representations with the full size dictionary (all training sample). [sent-285, score-0.752]
61 Comparison of representations for testing samples from the first ten classes on the Extended YaleB. [sent-287, score-0.277]
62 (a) LR with full-size dictionary; (b) LR with dictionary size 50; (c) LR with structural incoherence with full-size dictionary; (d) LR with structural incoherence with dictionary size 50; (e) SRC; (f) LLC; (g) Our method without Q; (h) Our method. [sent-289, score-1.88]
63 (a) original faces; (b) the low-rank component DZ; (c) the sparse noise component E. [sent-292, score-0.267]
64 Figures 3(e), 3(f) and 3(g) are the representations based on SRC, LLC with the same dictionary size and our method without Q. [sent-295, score-0.681]
65 We also evaluate the computation time of our approach and LR with structural incoherence [5] that trains a model class by class (Figure 5(a)) and uses SRC for classification. [sent-302, score-0.502]
66 Clearly, training over all classes simultaneously is faster than class by class if discriminativeness is preserved for different classes. [sent-305, score-0.311]
67 Our training time is twice as fast and testing is three times faster than LR with structural incoherence. [sent-306, score-0.241]
68 We use seven unobscured images from session 1 and one image with sunglass as training samples for each person, the rest as testing. [sent-328, score-0.546]
69 We use seven unobscured images from session 1 and one image with a scarf as training samples for each person, the remainder as testing. [sent-331, score-0.572]
70 We use seven unobscured images from session 1, one image with sunglasses, and one with a scarf as training samples for each person. [sent-334, score-0.572]
71 Our methods are compared with LLC [25], SRC [27], LR [5], and LR with structural incoherence [5]. [sent-339, score-0.336]
72 Comparison of representations for testing samples from the first ten classes on the AR for the sunglass scenario. [sent-341, score-0.384]
73 (a) LR with full-size dictionary; (b) LR with dictionary size 50; (c) LR with structural incoherence with full-size dictionary; (d) LR with structural incoherence with dictionary size 50; (e) SRC; (f) LLC; (g) Our method without Q; (h) Our method. [sent-343, score-1.88]
74 6 6 6 87 78719 919 (a) original (b) the low-rank gray images component DZ × (c) the sparse noise component E Figure 7. [sent-344, score-0.267]
75 Examples of image decomposition for testing samples from class 4 and 10 on the AR. [sent-345, score-0.272]
76 Our approach achieves the best results and outperforms other approaches with the same dictionary size by more than 3% for the sunglass scenario, 7% for the scarf scenario, and 2% for the mixed scenario. [sent-347, score-0.844]
77 We visualize the representation Z for the first ten classes under the sunglasses scenario. [sent-348, score-0.241]
78 W0 ter use i5n0g as our dictionary ×si 1z0e, i =. [sent-351, score-0.604]
79 Figures 6(a) and 6(c) show the representations of LR and LR method without structural incoherence with a full-size dictionary. [sent-354, score-0.413]
80 In Figures 6(b) and 6(d), we randomly pick 5 dictionary items for each class, and use this reduced dictionary to learn sparse codes. [sent-355, score-1.425]
81 For comparison purposes, we also choose 50 as the dictionary size in LLC and SRC* to learn the representations shown in Figures 6(e) and 6(f). [sent-356, score-0.715]
82 75 In addition, we compare our results with LC-KSVD [12] using the same training samples under the sun and scarf scenarios, using unobscured images for test. [sent-367, score-0.448]
83 Examples of image decomposition for testing samples from class 95 on the AR with 20% uniform noise. [sent-373, score-0.272]
84 (a) corrupted faces; (b) the low-rank component DZ; (c) the sparse noise component E. [sent-374, score-0.368]
85 seven images with illumination and expression variations from session 1 are used for training images, and the other seven images from session 2 are used as testing images. [sent-375, score-0.408]
86 Figure 9 shows the representations of 15 testing samples which are randomly selected from classes 4 ∼ 8. [sent-388, score-0.25]
87 Comparison of representations for testing samples from class 4 to 8 on the Caltech101 . [sent-391, score-0.294]
88 (a) LR with full-size dictionary; (b) LR with dictionary size 55; (c) LR with structural incoherence with full-size dictionary; (d) LR with structural incoherence with dictionary size 55; (e) LLC; (f) Our method without Q; (g) Our method. [sent-393, score-1.88]
89 Discriminative representations are learned via low-rank recovery even for corrupted datasets. [sent-412, score-0.319]
90 The learned representations reveal structural information automatically and can be used for classification directly. [sent-413, score-0.262]
91 Low-rank matrix recovery with structural incoherence for robust face recognition, 2012. [sent-444, score-0.549]
92 Image denoising via sparse and redundant representations over learned dictionaries. [sent-464, score-0.251]
93 Learning a discriminative dictionary for sparse coding via label consistent k-svd, 2011. [sent-491, score-0.895]
94 Sparse representation for face recognition based on discriminative low-rank dictionary learning, 2012. [sent-545, score-0.791]
95 Joint learning and dictionary construction for pattern recognition, 2008. [sent-571, score-0.628]
96 Robust pricipal component analysis: Exact recovery of corrupted low-rank matrices via convex optimization. [sent-593, score-0.301]
97 Gabor feature based sparse representation for face recognition with gabor occlusion dictionary, 2010. [sent-611, score-0.273]
98 Image classification by non-negative sparse coding, low-rank and sparse decomposition, 2011. [sent-627, score-0.292]
99 Online semi-supervised discriminative dictionary learning for sparse representation, 2012. [sent-633, score-0.81]
100 Discriminative k-svd for dictionary learning in face recognition, 2010. [sent-638, score-0.694]
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