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Issue No.01 - Jan. (2013 vol.35)
pp: 92-104
Shenghua Gao , Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
Ivor Wai-Hung Tsang , Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
Liang-Tien Chia , Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
ABSTRACT
Sparse coding exhibits good performance in many computer vision applications. However, due to the overcomplete codebook and the independent coding process, the locality and the similarity among the instances to be encoded are lost. To preserve such locality and similarity information, we propose a Laplacian sparse coding (LSc) framework. By incorporating the similarity preserving term into the objective of sparse coding, our proposed Laplacian sparse coding can alleviate the instability of sparse codes. Furthermore, we propose a Hypergraph Laplacian sparse coding (HLSc), which extends our Laplacian sparse coding to the case where the similarity among the instances defined by a hypergraph. Specifically, this HLSc captures the similarity among the instances within the same hyperedge simultaneously, and also makes the sparse codes of them be similar to each other. Both Laplacian sparse coding and Hypergraph Laplacian sparse coding enhance the robustness of sparse coding. We apply the Laplacian sparse coding to feature quantization in Bag-of-Words image representation, and it outperforms sparse coding and achieves good performance in solving the image classification problem. The Hypergraph Laplacian sparse coding is also successfully used to solve the semi-auto image tagging problem. The good performance of these applications demonstrates the effectiveness of our proposed formulations in locality and similarity preservation.
INDEX TERMS
Encoding, Image coding, Laplace equations, Image reconstruction, Sparse matrices, Tagging, Quantization,locality preserving, Laplacian sparse coding, hypergraph Laplacian sparse coding, image classification, semi-auto image tagging
CITATION
Shenghua Gao, Ivor Wai-Hung Tsang, Liang-Tien Chia, "Laplacian Sparse Coding, Hypergraph Laplacian Sparse Coding, and Applications", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 1, pp. 92-104, Jan. 2013, doi:10.1109/TPAMI.2012.63
REFERENCES
 [1] D. Donoho, "For Most Large Underdetermined Systems of Linear Equations, the Minimal l1-Norm Solution Is Also the Sparsest Solution," technical report, Stanford Univ., 2004. [2] D. Donoho, "For Most Large Underdetermined Systems of Linear Equations, the Minimal l1-Norm Near-Solution Approximates the Sparsest Near-Solution," technical report, Stanford Univ., 2004. [3] E. Candès, J. Romberg, and T. Tao, "Stable Signal Recovery from Incomplete and Inaccurate Measurements," Comm. Pure and Applied Math., vol. 59, no. 8, pp. 1207-1223, 2006. [4] A. Eriksson and A. van den Hengel, "Efficient Computation of Robust Low-Rank Matrix Approximations in the Presence of Missing Data Using the $l_1$ Norm," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010. [5] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, "Non-Local Sparse Models for Image Restoration," Proc. IEEE Int'l Conf. Computer Vision, 2009. [6] M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation," IEEE Trans. Signal Processing, vol. 54, no. 11, pp. 4311-4322, Nov. 2006. [7] M. Aharon and M. Elad, "Image Denoising via Sparse and Redundant Representations over Learned Dictionaries," IEEE Trans. Image Processing, vol. 15, no. 12, pp. 3736-3745, Dec. 2006. [8] J. Yang, K. Yu, Y. Gong, and T. Huang, "Linear Spatial Pyramid Matching Using Sparse Coding for Image Classification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009. [9] S. Gao, I.W. Tsang, and L.-T. Chia, "Kernel Sparse Representation for Image Classification and Face Recognition," Proc. European Conf. Computer Vision, 2010. [10] J. Wright, A.Y. Yang, A. Ganesh, S.S. Sastry, and Y. Ma, "Robust Face Recognition via Sparse Representation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 31, no. 2, pp. 210-227, Feb. 2009. [11] C. Wang, S. Yan, L. Zhang, and H.-J. Zhang, "Multi-Label Sparse Coding for Automatic Image Annotation," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009. [12] H. Cheng, Z. Liu, and J. Yang, "Sparsity Induced Similarity Measure for Label Propagation," Proc. IEEE Int'l Conf. Computer Vision, 2009. [13] J. Mairal, F. Bach, J. Ponce, G. Sapiro, and A. Zisserman, "Supervised Dictionary Learning," Proc. Advances in Neural Information Processing Systems, 2008. [14] J. Wang, J. Yang, K. Yu, F. Lv, and Y. Gong, "Locality-Constrained Linear Coding for Image Classification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010. [15] S. Gao, I.W. Tsang, L.-T. Chia, and P. Zhao, "Local Features Are Not Lonely-Laplacian Sparse Coding for Image Classification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010. [16] M. Yuan and Y. Lin, "Model Selection and Estimation in Regression with Grouped Variables," J. Royal Statistical Soc.: Series B (Statistical Methodology), vol. 68, pp. 49-67, Feb. 2006. [17] S. Bengio, F. Pereira, Y. Singer, and D. Strelow, "Group Sparse Coding," Proc. Advances in Neural Information Processing Systems, 2009. [18] J. Friedman, T. Hastie, and R. Tibshiraniz, "A Note on the Group Lasso and a Sparse Group Lasso," technical report, arXiv:1001.0736v1, 2010. [19] S. Mosci, S. Villa, A. Verri, and L. Rosasco, "A Primal-Dual Algorithm for Group Sparse Regularization with Overlapping Groups," Proc. Advances in Neural Information Processing Systems, 2010. [20] L. Jacob, G. Obozinski, and J.-P. Vert, "Group Lasso with Overlap and Graph Lasso," Proc. Int'l Conf. Machine Learning, 2009. [21] S. Kim and E.P. Xing, "Tree-Guided Group Lasso for Multi-Task Regression with Structured Sparsity," Proc. Int'l Conf. Machine Learning, 2010. [22] X. Chen, Q. Lin, S. Kim, J. Peña, J.G. Carbonell, and E.P. Xing, "An Efficient Proximal-Gradient Method for Single and Multi-Task Regression with Structured Sparsity," technical report, arXiv:1005.4717, 2010. [23] J. Sivic and A. Zisserman, "Video Google: A Text Retrieval Approach to Object Matching in Videos," Proc. IEEE Int'l Conf. Computer Vision, 2003. [24] J. Wu and J.M. Rehg, "Beyond the Euclidean Distance: Creating Effective Visual Codebooks Using the Histogram Intersection Kernel," Proc. IEEE Int'l Conf. Computer Vision, 2009. [25] O. Boiman, E. Shechtman, and M. Irani, "In Defense of Nearest-Neighbor Based Image Classification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2008. [26] J. Philbin, O. Chum, M. Isard, J. Sivic, and A. Zisserman, "Object Retrieval with Large Vocabularies and Fast Spatial Matching," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007. [27] S. Lazebnik, C. Schmid, and J. Ponce, "Beyond Bags of Features: Spatial Pyramid Matching for Recognizing Natural Scene Categories," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2006. [28] K. Grauman and T. Darrell, "The Pyramid Match Kernel: Discriminative Classification with Sets of Image Features," Proc. IEEE Int'l Conf. Computer Vision, 2005. [29] Y. Liu, D. Xu, I.W. Tsang, and J. Luo, "Textual Query of Consumer Photos Facilitated by Large-Scale Web Data," IEEE Trans. Pattern Analysis and Machine Intelligence, to appear. [30] G. Wang, D. Hoiem, and D.A. Forsyth, "Building Text Features for Object Image Classification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009. [31] S. Gao, Z. Wang, L.-T. Chia, and I.W.-H. Tsang, "Automatic Image Tagging via Category Label and Web Data," Proc. ACM Int'l Conf. Multimedia, 2010. [32] B. Sigurbjörnsson and R. van Zwol, "Flickr Tag Recommendation Based on Collective Knowledge," Proc. 17th Int'l Conf. World Wide Web, 2008. [33] Y. Song, Z. Zhuang, H. Li, Q. Zhao, J. Li, W.-C. Lee, and C.L. Giles, "Real-Time Automatic Tag Recommendation," Proc. Ann. Int'l ACM SIGIR Conf. Research and Development in Information Retrieval, 2008. [34] H. Lee, A. Battle, R. Raina, and A.Y. Ng, "Efficient Sparse Coding Algorithms," Proc. Advances in Neural Information Processing Systems, 2006. [35] U. von Luxburg, "A Tutorial on Spectral Clustering," Statistics and Computing, vol. 14, no. 7, pp. 395-416, 2007. [36] B.A. Olshausen and D.J. Fieldt, "Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by v1," Vision Research, vol. 37, pp. 3311-3325, 1997. [37] D. Zhou, J. Huang, and B. Schölkopf, "Learning with Hypergraphs: Clustering, Classification, and Embedding," Proc. Advances in Neural Information Processing Systems, 2006. [38] S. Agarwal, K. Branson, and S. Belongie, "Higher Order Learning with Graphs," Proc. Int'l Conf. Machine Learning, 2006. [39] J. Mairal, F. Bach, J. Ponce, and G. Sapiro, "Online Learning for Matrix Factorization and Sparse Coding," J. Machine Learning Research, vol. 11, pp. 19-60, Mar. 2010. [40] Y.-L. Boureau, J. Ponce, and Y. LeCun, "A Theoretical Analysis of Feature Pooling in Visual Recognition," Proc. Int'l Conf. Machine Learning, 2010. [41] Y.-L. Boureau, F. Bach, Y. LeCun, and J. Ponce, "Learning Mid-Level Features for Recognition," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010. [42] D.G. Lowe, "Distinctive Image Features from Scale-Invariant Keypoints," Int'l J. Computer Vision, vol. 60, no. 2, pp. 91-110, 2004. [43] G. Griffin, A. Holub, and P. Perona, "Caltech-256 Object Category Data Set," technical report, California Inst. of Tech nology, 2007. [44] J.C. van Gemert, J.M. Geusebroek, C.J. Veenman, and A.W.M. Smeulders, "Kernel Codebooks for Scene Categorization," Proc. European Conf. Computer Vision, 2008. [45] L.-J. Li and L. Fei-Fei, "What, Where and Who? Classifying Events by Scene and Object Recognition," Proc. IEEE Int'l Conf. Computer Vision, 2007. [46] Z. Lu and H.H. Ip, "Image Categorization with Spatial Mismatch Kernels," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009. [47] Z. Lu and H.H. Ip, "Image Categorization by Learning with Context and Consistency," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2009. [48] K. Kavukcuoglu, M. Ranzato, and Y. Lecun, "Fast Inference in Sparse Coding Algorithms with Applications to Object Recognition," technical report, arXiv:1010.3467v1, 2008. [49] T.-S. Chua, J. Tang, R. Hong, H. Li, Z. Luo, and Y.-T. Zheng, "Nus-Wide: A Real-World Web Image Database from National University of Singapore," Proc. ACM Int'l Conf. Image and Video Retrieval, 2009. [50] M. Ameesh, P. Vladimir, and K. Sanjiv, "A New Baseline for Image Annotation," Proc. European Conf. Computer Vision, 2008. [51] M. Ameesh, P. Vladimir, and K. Sanjiv, "A New Baseline for Image Annotation," Int'l J. Computer Vision, vol. 90, pp. 88-105, 2010. [52] X. Liu, S. Yan, J. Luo, J. Tang, Z. Huang, and H. Jin, "Nonparametric Label-to-Region by Search," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2010. [53] C. Wang, S. Yan, and H.-J. Zhang, "Large Scale Natural Image Classification by Sparsity Exploration," Proc. IEEE Int'l Conf. Acoustics, Speech, and Signal Processing, 2009. [54] Y. Chen, M. Welling, and A. Smola, "Super-Samples from Kernel Herding," Proc. Conf. Uncertainty in Artificial Intelligence, 2010.