Sparse Representation With Kernels

Recent research has shown the initial success of sparse coding (Sc) in solving many computer vision tasks. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which helps in finding a sparse representation of nonlinear features, we propose kernel sparse represen...

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Bibliographic Details
Published inIEEE transactions on image processing Vol. 22; no. 2; pp. 423 - 434
Main Authors Shenghua Gao, Tsang, I. W., Liang-Tien Chia
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.02.2013
Institute of Electrical and Electronics Engineers
Subjects
Algorithms
Applied sciences
Approximation methods
Artificial intelligence
Biometric Identification - methods
Coding, codes
Computer science; control theory; systems
Databases, Factual
Encoding
Exact sciences and technology
Face recognition
Female
Humans
image classification
Image coding
Image processing
Image Processing, Computer-Assisted - methods
Image representation
Information, signal and communications theory
Kernel
kernel matrix approximation
kernel sparse representation
Male
nonlinear mapping
Pattern recognition
Pattern recognition. Digital image processing. Computational geometry
Signal and communications theory
Signal processing
sparse coding
Sparse matrices
Telecommunications and information theory
Biometrics
Performance evaluation
kernel matrix approximation
Histogram
Phase measurement
Image recognition
Similarity
Image processing
Mapping
Learning
Accuracy
Coding
Signal quantization
Sparse representation
Robustness
kernel sparse representation
Computer vision
nonlinear mapping
Discriminant analysis
Face recognition
Pattern recognition
sparse coding
Kernel method
Automatic recognition
Artificial intelligence
Image classification
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Summary:Recent research has shown the initial success of sparse coding (Sc) in solving many computer vision tasks. Motivated by the fact that kernel trick can capture the nonlinear similarity of features, which helps in finding a sparse representation of nonlinear features, we propose kernel sparse representation (KSR). Essentially, KSR is a sparse coding technique in a high dimensional feature space mapped by an implicit mapping function. We apply KSR to feature coding in image classification, face recognition, and kernel matrix approximation. More specifically, by incorporating KSR into spatial pyramid matching (SPM), we develop KSRSPM, which achieves a good performance for image classification. Moreover, KSR-based feature coding can be shown as a generalization of efficient match kernel and an extension of Sc-based SPM. We further show that our proposed KSR using a histogram intersection kernel (HIK) can be considered a soft assignment extension of HIK-based feature quantization in the feature coding process. Besides feature coding, comparing with sparse coding, KSR can learn more discriminative sparse codes and achieve higher accuracy for face recognition. Moreover, KSR can also be applied to kernel matrix approximation in large scale learning tasks, and it demonstrates its robustness to kernel matrix approximation, especially when a small fraction of the data is used. Extensive experimental results demonstrate promising results of KSR in image classification, face recognition, and kernel matrix approximation. All these applications prove the effectiveness of KSR in computer vision and machine learning tasks.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2012.2215620