In this section, we applied Riemannian manifold to characterize the hyperspectral image and proposed the dimensionality reduction framework to learn local Riemannian embedding. The procedures of proposed method are summarized in following Figure. In our proposed framework, we first divide the hyperspectral image into multi spectral groups based on band clustering. Then, we learn the low dimensional local Riemannian embedding for each spectral group.
The summary of group local Riemannian embedding (GLRE) algorithm. The low dimensional embedding is learned from the high dimensional hyperspectral image by following step. 1) dividing all spectral bands into multi groups; 2) constructing the region covariance matrix for each groups; 3) learning local Riemannian embedding for each groups; 4) merging all the embedding of groups into a final embedding.
To assess and discuss the proposed methods, we designed an experiment in the following. We first presented the performance of all studied methods.
kNN classification maps for Indian Pines using data transformed by different dimensionality reduction methods. (a) Ground truth; (b) Original; © LPP; (d) LDA; (e) MPCA; (f) TLPP; (g) IPD-TLPP; (h) MTLPP; (i) GLRE.
The classification results of each classes of hyperspectral image are summarized in the following table. It is clearly that the proposed GLRE outperformed other methods.
