Dimensionality Reduction for Hyperspectral Data Based on Class-Aware Tensor Neighborhood Graph and Patch Alignment

To take full advantage of hyperspectral information, to avoid data redundancy and to address the curse of dimensionality concern, dimensionality reduction (DR) becomes particularly important to analyze hyperspectral data. Exploring the tensor characteristic of hyperspectral data, a DR algorithm based on class-aware tensor neighborhood graph and patch alignment is proposed here. First, hyperspectral data are represented in the tensor form through a window field to keep the spatial information of each pixel. Second, using a tensor distance criterion, a class-aware tensor neighborhood graph containing discriminating information is obtained. In the third step, employing the patch alignment framework extended to the tensor space, we can obtain global optimal spectral-spatial information. Finally, the solution of the tensor subspace is calculated using an iterative method and low-dimensional projection matrixes for hyperspectral data are obtained accordingly. The proposed method effectively explores the spectral and spatial information in hyperspectral data simultaneously. Experimental results on 3 real hyperspectral datasets show that, compared with some popular vector-and tensor-based DR algorithms, the proposed method can yield better performance with less tensor training samples required.