Tensor Subspace Learning and Classification: Tensor Local Discriminant Embedding for Hyperspectral Image

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Hyperspectral image (HSI) has shown promising results in many fields because of its high spectral resolution. However, the redundancy of spectral dimension seriously affects the classification of HSI. Therefore, many popular dimension reduction (DR) algorithms are proposed and subspace learning algorithm is a typical one. In HSI, cube data is traditionally flatted into 1-D vector, so spatial information is completely ignored in most dimension reduction algorithms. The tensor representation for HSI considers both the spatial information and cubic properties simultaneously, so that tensor subspace learning can be naturally introduced into DR for HSI. In this paper, a tensor local discriminant embedding (TLDE) is proposed for DR and classification of HSI. TLDE can take full advantage of spatial structure and spectral information and map a high dimensional space into a low dimensional space by three projection matrices trained. TLDE can be more discriminative by calculating an intrinsic graph and a penalty graph. The experimental results on two real datasets demonstrate that TLDE is effective and works well even when the training samples are small.