Tensor Low-Rank Discriminant Embedding for Hyperspectral Image Dimensionality Reduction

Recently, low-rank embedding (LRE) has yielded satisfactory results in dimensionality reduction (DR), for which low-rank representation and projection learning are integrated into one model to generate robust low-dimensional features. However, LRE requires to convert samples into vectors even if the data naturally appear in high-order form. Furthermore, LRE fails to take the label information into consideration. To address these problems, this paper proposes a novel supervised DR method based on multilinear algebra, i.e., the algebra of tensors. By the motivation of extending LRE into tensor space and simultaneously combining the tensor discriminant analysis, we establish tensor low-rank discriminant embedding (TLRDE) model for hyperspectral image (HSI) DR. The model of TLRDE is solved by an alternative iteration algorithm, whose convergence is also mathematically proven. The proposed TLRDE method employs the tensor representation to preserve the intrinsic geometrical structure, uses low-rank reconstruction to uncover the potential relationship among the data points, and combines label information to enhance the discriminability of features. Moreover, the proposed TLRDE does not suffer from the small sample size problem. The experimental results on three real HSI data sets validate the effectiveness of our proposed TLRDE method.