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Collaborative coding and dictionary learning for nearest subspace classification

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Abstract

Sparse representation (SR) has been widely studied and successfully applied to many areas of computer science in recent years. However, whether sparsity is essential to improve the classification performance is still an open question. Some studies reveal that it is the collaborative representation (CR) rather than SR that truly improves the classification performance. In this paper, the advantage of CR is further investigated and exploited, and a CR-based coding method is proposed. This method improves the classification performance by applying CR to the traditional nearest subspace (NS) method. Compared to the other NS method which codes the test sample on each class separately, the proposed method employs all samples to code the test sample collaboratively and preserves the subspace structure at the same time. The test sample is then classified to the class with the smallest representation error. Besides, a corresponding dictionary learning algorithm is also proposed so that the coding can be conducted on a dictionary learned from the training dataset. Since analytical solutions for coding and dictionary learning have been derived, our algorithm can be implemented efficiently. Experiments are conducted on seven face databases and the USPS handwritten digit database, and the results show that the proposed algorithm outperforms many state-of-the-art coding methods and dictionary learning methods, which demonstrates the power brought by CR.

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Funding

This work is partially supported by the NSFC under Grant Nos. 61272338 and 61673018.

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Authors and Affiliations

  1. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong, China

    Zhong Zhao, Qi Shen & Guocan Feng

  2. Guangdong Province Key Laboratory of Computational Science, Guangzhou, 510275, Guangdong, China

    Zhong Zhao, Qi Shen & Guocan Feng

  3. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA

    Jiehua Zhu

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  1. Zhong Zhao
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  2. Qi Shen
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  3. Guocan Feng
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  4. Jiehua Zhu
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Contributions

ZZ and QS designed the model and the computational framework. ZZ carried out the implementation and performed the calculations. ZZ and QS wrote the original draft with input from all authors. QS, GCF and JHZ contributed to reviewing and editing.

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Correspondence to Qi Shen.

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Qi Shen: This work is partially supported by the NSFC under Grant Nos. 61272338 and 61673018.

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Zhao, Z., Shen, Q., Feng, G. et al. Collaborative coding and dictionary learning for nearest subspace classification. Soft Comput 25, 7627–7643 (2021). https://doi.org/10.1007/s00500-021-05723-3

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