Dimension reduction (DR) addresses the problem known as the curse of dimensionality in myriad hyperspectral imagery applications. Although the spatial pattern may assist in the distinction between different land covers that have close spectral signatures, it is often neglected by the current DR methods. In order to overcome this defect, two solutions: patch-based and tensor-patch-based, are studied in this article for a group of graph-based DR methods. To date, only a few attempts have been made in the patch- and tensor-patch-based variations for the graph-based DR methods. This article proposed two weight modified tensor-patch-based methods, namely weight modified tensor locality preserving projections and weight modified tensor neighborhood preserving embedding. Specifically, as graph-based DR methods heavily rely on the construction of adjacency graphs, this paper proposes a new use of the weighted region covariance matrix in the calculation of adjacency graphs. We found that the two proposed tensor-patch methods outperform the up-to-date methods.

中文翻译：

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使用基于权重修正张量补丁的方法进行高光谱图像降维

降维 (DR) 解决了在无数高光谱图像应用中被称为维度灾难的问题。尽管空间模式可能有助于区分具有紧密光谱特征的不同土地覆盖，但当前的 DR 方法经常忽略它。为了克服这个缺陷，本文针对一组基于图的DR方法研究了两种解决方案：patch-based和ten​​sor-patch-based。迄今为止，对于基于图的 DR 方法，仅在基于补丁和基于张量补丁的变体中进行了几次尝试。本文提出了两种基于权重修正张量补丁的方法，即权重修正张量局部保持投影和权重修正张量邻域保持嵌入。具体来说，由于基于图的 DR 方法严重依赖于邻接图的构建，本文提出了加权区域协方差矩阵在邻接图计算中的新用途。我们发现提出的两种张量补丁方法优于最新方法。