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Generalized robust graph-Laplacian PCA and underwater image recognition

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Abstract

Recently, given the importance of the structure-preserving ability of features, many principal component analysis (PCA) methods based on manifold learning theory, such as graph-Laplacian PCA (gLPCA), have been developed to protect the geometrical structure of the original data space. However, many methods do not best minimize the reconstruction error, which is great significance for underwater image recognition and representation. To alleviate this deficiency, a novel idea for gLPCA—generalized robust graph-Laplacian PCA (GRgLPCA)—was proposed. GRgLPCA not only employs the \(l_{2,p}\)-norm on regarding the correlation between the reconstruction error and variance in the projection data to suppress the influence of underwater noise, but it also employs it regarding the graph-Laplacian regularization term to better protect the intrinsic geometric information embedded in the data. Moreover, GRgLPCA preserves the rotational invariance well, and the solution of the model is related to image covariance matrix, which are the two desired properties of PCA-based method. Finally, we design a fast and effective non-greedy iterative algorithm to obtain the GRgLPCA solution. A series of experiments on several underwater image databases and one face image extension database illustrated the effectiveness of our proposed method.

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Acknowledgements

This work is supported by the Best Sea Assembly and the Control Technology Institute. The authors would like to thank Xue Du and Juan Li for providing assistance with the underwater experiments. This work is also supported in part by the National Natural Science Foundation of China Under Grants 51609046 and 51709062 and in part by Research Funds for the Underwater Vehicle Technology Key Laboratory of China Under Grants 614221502061701 and 6142215180107.

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  1. College of Automation, Harbin Engineering University, Harbin, 150001, Heilongjiang, China

    Pengfei Bi, Jian Xu, Xue Du & Juan Li

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  1. Pengfei Bi
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  2. Jian Xu
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  3. Xue Du
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  4. Juan Li
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Correspondence to Jian Xu.

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Bi, P., Xu, J., Du, X. et al. Generalized robust graph-Laplacian PCA and underwater image recognition. Neural Comput & Applic 32, 16993–17010 (2020). https://doi.org/10.1007/s00521-020-04927-2

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