Generalized robust graph-Laplacian PCA and underwater image recognition

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.