| Summary: | Sparse coding is attracting more and more researchers’ attention in computer vision area because of its good performance in feature reconstruction based applications. In this thesis, we further improve the ability of sparse coding by leveraging the Hypergraph, kernel and structure, and propose four advanced sparse coding techniques, i.e., Laplacian sparse coding and Hypergraph Laplacian sparse coding, weighted sparse coding, kernel sparse representation, and Multi-layer group sparse coding. Specifically,
1. Given lots of features to be encoded, traditional sparse coding suffers from the instability because of the overcomplete or sufficient codebook. To improve the robustness
of sparse coding and encode the similarity and locality information among the features in the sparse coding process, we propose a Laplacian sparse coding by
introducing a Laplacian regularizer to the objective function of sparse coding. Such graph regularized Laplacian sparse coding is applied to image classification. We also extend the Laplacian sparse coding to Hypergraph case and propose the Hypergraph
Laplacian sparse coding, which preserves the similarity among the features within the same hyperedge. Such Hypergraph Laplacian sparse coding is applied to solving semi-auto image tagging task.
2. We propose a weighted sparse coding formulation, which can encode the features constrained by a hypergraph where each hyperedge only contains one feature with certain weight to distinguish its importance. Our weighted sparse coding can learn a discriminative codebook which favors to reduce the information loss for those more important features. We apply our weighted sparse coding to feature coding in object recognition, where the features corresponding to the object usually are more visually salient and therefore should have a larger contribution for image presentation.
3. Motivated by the success of kernel trick in many machine learning applications, we propose a kernel sparse representation, which is the sparse coding in Reproducing Kernel Hilbert Space (RKHS). Another motivation of our kernel sparse representation
comes from the good performance of sparse coding in feature coding and Histogram Intersection Kernel based feature quantization which is the hard assignment feature coding in RKHS. Therefore we manage to combine them together to
further improve the feature coding in image classification and arrive at the kernel sparse representation. Kernel sparse representation is also applied to face recognition.
4. Motivated by the close relationship between image classification and image annotation, we propose a multi-layer group sparse coding framework. By imposing the sparsity penalties on the groups defined as each instance in instance layer, instances with the same class label in class group layer and instances with both the same class label and similar tags distribution in tags-based group layer respectively, we can concurrently cope with the image classification and image annotation.
We evaluate the proposed methods on some publicly available datasets, experimental results demonstrate the good performance and effectiveness of our proposed advanced sparse coding techniques in their respective applications.
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