Laplacian Sparse Coding, Hypergraph Laplacian Sparse Coding, and Applications
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 L...
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| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence Jg. 35; H. 1; S. 92 - 104 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Los Alamitos, CA
IEEE
01.01.2013
IEEE Computer Society The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0162-8828, 1939-3539, 2160-9292, 1939-3539 |
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| 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. |
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| AbstractList | 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. 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.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. |
| Author | Liang-Tien Chia Shenghua Gao Tsang, Ivor Wai-Hung |
| Author_xml | – sequence: 1 surname: Shenghua Gao fullname: Shenghua Gao email: gaos0004@ntu.edu.sg organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore – sequence: 2 givenname: Ivor Wai-Hung surname: Tsang fullname: Tsang, Ivor Wai-Hung email: ivortsang@ntu.edu.sg organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore – sequence: 3 surname: Liang-Tien Chia fullname: Liang-Tien Chia email: asltchia@ntu.edu.sg organization: Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore |
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| Keywords | Hypergraph Computer vision Image processing Laplacian sparse coding locality preserving Locality Information retrieval Laplacian Bag of words Codebook semi-auto image tagging Signal quantization Tagging hypergraph Laplacian sparse coding Sparse representation Robustness Image classification |
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| SubjectTerms | Algorithms Applied sciences Artificial Intelligence Coding Coding, codes Computer science; control theory; systems Data Compression - methods Data processing. List processing. Character string processing Decision Support Techniques Encoding Exact sciences and technology Graphs hypergraph Laplacian sparse coding Image classification Image coding Image Interpretation, Computer-Assisted - methods Image reconstruction Information retrieval. Graph Information, signal and communications theory Laplace equations Laplacian sparse coding locality preserving Memory organisation. Data processing Pattern analysis Pattern Recognition, Automated - methods Pattern recognition. Digital image processing. Computational geometry Preserves Quantization Representations Robustness semi-auto image tagging Signal and communications theory Similarity Software Sparse matrices Studies Tagging Telecommunications and information theory Theoretical computing |
| Title | Laplacian Sparse Coding, Hypergraph Laplacian Sparse Coding, and Applications |
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