Generalized robust graph-Laplacian PCA and underwater image recognition
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ORIGINAL ARTICLE
Generalized robust graph-Laplacian PCA and underwater image recognition Pengfei Bi1 • Jian Xu1 • Xue Du1 • Juan Li1 Received: 14 December 2019 / Accepted: 6 April 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
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 l2;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. Keywords Graph-Laplacian principal component analysis (gLPCA) Distance metric Robust Underwater image recognition
1 Introduction Currently, with the rapid development of underwater optical technology, increasing numbers of underwater optical images can be obtained with underwater acquisition equipment, such as underwater cameras [1, 2]. However, how to find an effective recognition method based on the characteristics of underwater images (such as high-dimension [3], insufficient samples available [4], proneness & Jian Xu [email protected] Pengfei Bi [email protected] Xue Du [email protected] Juan Li [email protected] 1
College of Automation, Harbin Engineering University, Harbin 150001, Heilongjiang, China
to occlusion [5] and low-quality [6, 7]) becomes very important. Over the last few decades, matrix-based subspace learning has been considered by many scholars to be a popular and effective dimensionality reduction technology that has been widely used in image recognition and image retrieval, and it has achieved various successes. Among these methods, principal component analysis (PCA) [8, 9], independent component analysis (ICA) [10] and linear discriminant analysis (LDA) [11] are the most representative subspace learning technologies. PCA seeks a projection matrix that maximizes the variance of the projected data. ICA can extract independent components based on higher-order statistics. LDA sol
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