Dimensionality Reduction And Classification Of Hyperspectral Images Under Riemann Manifolds

Feature extraction of hyperspectral images and feature classification and identification technology are the key processing technologies for decoding and analyzing hyperspectral images,which can be used for effective and accurate material analysis and judgment of geology,mineral deposits,forest,water conservancy,ocean,agriculture and other resources by satellite remote sensing technology.However,in practical applications,(1)there is the phenomenon of "same object with different spectrum" and "different object with same spectrum",and it is difficult to distinguish different features by using spectral features only.(2)The number of hyperspectral image bands is large,which is high-dimensional data and can easily lead to dimensional disaster.(3)The correlation between bands is large and there is much redundant information.(4)Hyperspectral images have obvious nonlinear characteristics due to bidirectional reflection distribution function effect,multiple scattering and heterogeneity of pixel components,showing a nonlinear manifold structure,and it is difficult for traditional linear models to extract nonlinear features effectively.In this paper,to address the above problems in hyperspectral image dimensionality reduction and classification,Riemann manifold method is introduced to investigate the use of the nonlinear representation capability of manifold geometry to extract the implicit features of hyperspectral images,combined with metric learning methods to obtain discriminative low-dimensional embedded features.The main research work in this paper includes the following:(1)In this paper,a hyperspectral image dimensionality reduction and classification algorithm under Gaussian manifold is designed.First,the spatial neighborhood pixel sets of hyperspectral image pixels are extracted,and then their corresponding mean and covariance statistics are calculated to estimate the Gaussian model.Second,the Gaussian Riemann kernel function derived from Gaussian manifold geometry is used to better measure the inter-sample similarity.By performing metric learning in the tangent space of the Gaussian manifold,the geometric properties of the data are preserved by using the non-negative reconstruction coefficients to build a similarity map between samples.Finally,an explicit and nonlinear dimensionality reduction result is obtained using the tangent space projection matrix.Experiments on real hyperspectral classification datasets confirm that the algorithm can combine the spatial-spectral information of hyperspectral images and better exploit and preserve the nonlinear features embedded in hyperspectral images to achieve high classification accuracy.(2)In this paper,a hyperspectral image dimensionality reduction and classification algorithm with multiple manifold metrics is proposed.First,for the spatial neighborhood pixel sets of hyperspectral image pixels,the proposed model calculates their linear subspace structures and Gaussian distributions,respectively,to map the samples to Grassmann and Gaussian manifolds,respectively.Then,the Grassmann Riemannian kernel function derived for the Grassmann manifold geometry is linearly combined with the Gaussian kernel function to form a combinatorial multinuclear function to achieve the complementarity of different manifold structures.Among them,Fisher’s criterion is used to find a combination coefficient that increases the inter-class distance and decreases the intra-class distance.Finally,for the combinatorial Riemannian kernel function,the corresponding combinatorial Riemannian manifold tangent space can be derived,and by performing metric learning in this combinatorial tangent space while using the convex combinatorial reconstruction coefficients to achieve the Riemann graph embedding between samples,the complementary data nonlinear feature mining capability is enhanced.Deriving the corresponding projection matrix in the combinatorial tangent space allows explicit and nonlinear dimensionality reduction of the original hyperspectral images.Experiments on three real hyperspectral datasets validate the effectiveness of the proposed algorithm for extracting nonlinear discriminative features.