Kwon Heesung, Nasrabadi Nasser M
Army Research Laboratory, AMSRDARL-SE-SE, 2800 Powder Mill Rd., Adelphi, MD 20783, USA.
IEEE Trans Pattern Anal Mach Intell. 2006 Feb;28(2):178-94. doi: 10.1109/TPAMI.2006.39.
In this paper, we present a kernel realization of a matched subspace detector (MSD) that is based on a subspace mixture model defined in a high-dimensional feature space associated with a kernel function. The linear subspace mixture model for the MSD is first reformulated in a high-dimensional feature space and then the corresponding expression for the generalized likelihood ratio test (GLRT) is obtained for this model. The subspace mixture model in the feature space and its corresponding GLRT expression are equivalent to a nonlinear subspace mixture model with a corresponding nonlinear GLRT expression in the original input space. In order to address the intractability of the GLRT in the feature space, we kernelize the GLRT expression using the kernel eigenvector representations as well as the kernel trick where dot products in the feature space are implicitly computed by kernels. The proposed kernel-based nonlinear detector, so-called kernel matched subspace detector (KMSD), is applied to several hyperspectral images to detect targets of interest. KMSD showed superior detection performance over the conventional MSD when tested on several synthetic data and real hyperspectral imagery.
在本文中，我们提出了一种匹配子空间检测器（MSD）的核实现，该检测器基于在与核函数相关联的高维特征空间中定义的子空间混合模型。首先在高维特征空间中重新构建MSD的线性子空间混合模型，然后针对该模型获得广义似然比检验（GLRT）的相应表达式。特征空间中的子空间混合模型及其相应的GLRT表达式等同于原始输入空间中具有相应非线性GLRT表达式的非线性子空间混合模型。为了解决特征空间中GLRT的难处理性问题，我们使用核特征向量表示以及核技巧对GLRT表达式进行核化处理，其中特征空间中的点积由核隐式计算。所提出的基于核的非线性检测器，即所谓的核匹配子空间检测器（KMSD），被应用于多个高光谱图像以检测感兴趣的目标。在多个合成数据和真实高光谱图像上进行测试时，KMSD表现出优于传统MSD的检测性能。
