Abstract
Due to the high dimensionality and high data redundancy of hyperspectral remote sensing images, it is difficult to maintain the nonlinear structural relationship in the dimensionality reduction representation of hyperspectral data. In this paper, a feature representation method based on high order contractive auto-encoder with nuclear norm constraint (CAE-HNC) is proposed. By introducing Jacobian matrix in the CAE of the nuclear norm constraint, the nuclear norm has better sparsity than the Frobenius norm and can better describe the local low dimension of the data manifold. At the same time, a second-order penalty term is added, which is the Frobenius norm of the Hessian matrix expressed in the hidden layer of the input, encouraging a smoother low-dimensional manifold geometry of the data. The experiment of hyperspectral remote sensing image shows that CAE-HNC proposed in this paper is a compact and robust feature representation method, which provides effective help for the ground object classification and target recognition of hyperspectral remote sensing image.
Highlights
In order to verify the effectiveness of the proposed algorithm, experimental simulation analysis was carried out on three groups of hyperspectral images, and feature extraction and representation of different algorithms were performed using hyperspectral data such as Contractive Auto-encoder (CAE), CAE-H, stacked contractive auto-encoder (SCAE), denoising-contractive auto-encoder (DCAE), and contractive auto-encoder with nuclear norm constraint (CAE-HNC), classification comparison was conducted to verify the robustness of the proposed method
In order to test the robustness of the proposed algorithm, 5% and 10% of the hyperspectral data were selected as training samples, and CAE-HNC method was used for data feature extraction
Contractive Auto-encoder (SCAE) and Denoising Contractive Auto-encoder (DCAE).The experimental results were measured by the Overall Accuracies (OA) A and Kappa coefficient (R) of ground object classification in hyperspectral images
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In order to overcome the disadvantage of local generalization, Reference [23] suggested neural network algorithm of Contractive Auto-encoder (CAE), the method by changing the main singular vectors of the Jacobian matrix, captured every input point around the local manifold structure, the corresponding singular value specified in related to the corresponding singular vectors direction how many local changes are credible, and keep in high density area of the input space. Starting from the effective characterization of the nonlinear manifold structure of hyperspectral image data in low-dimensional space, this paper analyzes the Jacobian matrix Frobenius norm approximation of CAE, the geometric interpretation of CAE and the Hession matrix Frobenius norm approximation of CAE-H, and proposes a feature representation method of Higher Order Contractive Auto-Encoders With Nuclear Norm. A second-order penalty term is added, which is the Frobenius norm of the Hessian matrix expressed in the hidden layer of the input, encouraging a smoother low-dimensional manifold geometry of the data
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