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Assessment of Schrodinger EigenMaps for Target Detection

机译：评估Schrodinger特征图用于目标检测

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Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term Ⅴ, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term Ⅴ is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.
机译：非线性降维方法因其结构而被广泛应用于高光谱图像，因为信息可以以较低的维数表示而不会丢失信息，并且由于非线性方法在缩小维数的同时保留了数据的局部几何形状。这些方法之一是拉普拉斯特征图（LE），它假设数据位于嵌入高维空间的低维流形上。 LE建立最近的邻居图，计算其拉普拉斯算子并执行拉普拉斯算子的特征分解。这些本征函数构成了保留歧管几何形状的低维空间的基础。除约简问题外，LE还广泛用于分割，聚类和分类等任务。在这方面，开发了一种新的Schrodinger特征图（SE）方法，并将其作为半监督分类方案提出，以提高分类性能并利用标记数据。 SE是一种基于LE的算法，其中以前的Laplacian运算符被Schrodinger运算符代替。薛定inger算子包括一个潜在项Ⅴ，利用附加信息，例如标记数据，可以对相似点进行聚类。在本文中，我们探索了在目标检测中使用SE的想法。这样，我们提出了一个框架，其中势项Ⅴ被定义为势垒势：对角矩阵编码目标的空间位置，并通过使用不同的目标和不同的高光谱场景来评估检测性能。

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