Tensor Low-Rank Discriminant Embedding for Hyperspectral Image Dimensionality Reduction
Tensor Low-Rank Discriminant Embedding for Hyperspectral Image Dimensionality Reduction
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DOI：
10.1109/tgrs.2018.2849085
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发表时间：
2018-07
影响因子：
8.2
通讯作者：
Yangjun Deng;Hengchao Li;Kun Fu;Q. Du;W. Emery
中科院分区：
文献类型：
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作者：
Yangjun Deng;Hengchao Li;Kun Fu;Q. Du;W. Emery
最近，低秩嵌入（LRE）在降维（DR）方面取得了令人满意的结果，其中低秩表示和投影学习集成到一个模型中，以生成鲁棒的低维特征。然而，LRE要求将样本转换为向量，即使数据自然地以高阶形式出现。此外，LRE没有考虑标签信息。针对这些问题，提出了一种基于多线性代数的有监督DR方法，张量的代数将LRE扩展到张量空间，同时结合张量判别分析，建立了高光谱图像DR的张量低秩判别嵌入（TLRDE）模型，采用交替迭代算法求解TLRDE模型，并证明了其收敛性.所提出的TLRDE方法采用张量表示来保持固有的几何结构，使用低秩重建来揭示数据点之间的潜在关系，并结合标签信息来增强特征的可区分性。此外，拟议的TLRDE不受样本量小的问题。在三个真实的HSI数据集上的实验结果验证了该方法的有效性。
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.