KCRC-LCD: Discriminative kernel collaborative representation with locality constrained dictionary for visual categorization

• Propose a generalized KCRC-LCD framework with good performance and scalability.
• LCD can be nicely incorporated under the framework of KCRC through kernelization.
• A unified similarity measurement framework is considered to reduce metric biases.
• Conducted comprehensive experiments and analysis.
• The proposed framework is comparable or outperforms state-of-the-art methods.

We consider the image classification problem via kernel collaborative representation classification with locality constrained dictionary (KCRC-LCD). Specifically, we propose a kernel collaborative representation classification (KCRC) approach in which kernel method is used to improve the discrimination ability of collaborative representation classification (CRC). We then measure the similarities between the query and atoms in the global dictionary in order to construct a locality constrained dictionary (LCD) for KCRC. In addition, we discuss several similarity measure approaches in LCD and further present a simple yet effective unified similarity measure whose superiority is validated in experiments. There are several appealing aspects associated with LCD. First, LCD can be nicely incorporated under the framework of KCRC. The LCD similarity measure can be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. Example shows that KCRC is able to perfectly classify data with certain distribution, while conventional CRC fails completely. Comprehensive experiments on widely used public datasets also show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches.