基于核方法和流形学习的雷达目标距离像识别研究
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摘要
雷达目标识别是现代雷达发展的重要方向之一,具有广泛的军事和民用价值。高分辨距离像包含了较多的目标结构信息,从而为我们提供了一种可靠的目标识别手段。核方法是目前模式识别领域研究的一个焦点,它对于解决非线性问题具有许多独特优势;流形学习是近年来出现的一种新型的机器学习理论,其旨在发现高维数据集分布的内在规律性。
本文对以上两种机器学习理论进行研究,针对已有算法的不足进行推广和改进,并应用于基于高分辨距离像的雷达目标识别。论文的主要工作和创新之处概括如下:
1.在对核鉴别分析(Kernel Discriminant Analysis,KDA)及其变形算法进行深入研究的基础上,提出一种最优核鉴别分析(Optimal Kernel DiscriminantAnalysis,OKDA)算法用于雷达目标距离像特征提取。实验结果表明,OKDA具有较好的识别性能以及良好的类内聚合性。
2.研究基于核不相关鉴别分析的雷达目标距离像特征提取。通过对统计不相关特性进一步分析并引入核函数,推导出核不相关Fisher准则,并提出两种核不相关鉴别分析算法——直接核不相关鉴别分析(Direct Kernel UncorrelatedDiscriminant Analysis,DKUDA)和基于广义奇异值分解的核不相关鉴别分析(Kernel Uncorrelated Discriminant Analysis Based on Generalized Singular ValueDecomposition,KUDA/GSVD),用于从雷达目标距离像中提取统计不相关的鉴别特征。与不相关鉴别分析(Uncorrelated Discriminant Analysis,UDA)和核不相关鉴别分析(Kernel Uncorrelated Discriminant Analysis,KUDA)相比,这两种算法大大减少了运算量,而且能有效解决奇异性问题。
3.研究基于流形学习理论的雷达目标距离像特征提取。在对几种经典的流形学习算法进行分析总结的基础上,提出一种有监督的非线性流形学习算法——监督核近邻保持投影(Supervised Kernel Neighborhood Preserving Projections,SKNPP),用于对雷达目标距离像进行特征提取。SKNPP在近邻保持投影(Neighborhood Preserving Projections,NPP)的基础上引入样本的类别信息,并利用核函数将其推广到非线性形式而得到。该算法不但保留了高维空间中类内样本之间的几何结构,而且可以获得对数据流形的非线性逼近。
4.提出了基于核不相关鉴别近邻嵌入(Kernel Uncorrelated DiscriminativeNeighborhood Embedding,KUDNE)和核不相关鉴别局部保持投影(KernelUncorrelated Discriminative Locality Preserving Projections,KUDLPP)的雷达目标距离像特征提取方法。KUDNE和KUDLPP是在统计不相关约束条件下,分别将监督核近邻保持投影(SKNPP)和监督核局部保持投影(Supervised Kernel LocalityPreserving Projections,SKLPP)与核鉴别分析(KDA)相结合而得到的。这两种算法在保留类内样本之间固有几何关系的同时,使投影后样本的类间散射最大,而且使生成的特征空间具有最小的冗余度。
5.研究基于核非线性分类器的雷达目标识别方法。对支持向量机(SupportVector Machine,SVM)、KND(Kernel-Based Nonlinear Discriminator)以及KNR(Kernel-Based Nonlinear Representor)的分类原理及学习过程进行了深入研究和比较,并将其应用于雷达目标距离像分类。KND和KNR是两种新型的核非线性分类器,与SVM相比,它们不但能提高雷达目标识别速度,而且能得到满意的识别精度。
Radar target recognition plays an important role in modern radar, and finds its ways to wide military and civilian applications. High resolution range profiles contain more structural information of a target, and are easy to obtain and process, and thus provide us with a more reliable tool for target recognition. Currently, kernel method and manifold learning, among other methods, become two focuses in the field of pattern recognition and machine learning. Kernel method shows many advantages as to solve nonlinear problems, while manifold learning aims to discover the intrinsic characteristics of high-dimensional data.
In this dissertation, the above two methods are studied, and in order to overcome the weakness of existing methods, several generalized and improved algorithms are proposed and applied to radar target recognition using range profiles. The main contents and innovations of this dissertation are summarized as follows.
1. Kernel discriminant analysis and its variants are studied intensively, and an optimal kernel discriminant analysis (OKDA) is given and adopted to extract nonlinear discriminative features from range profiles. Experimental results show the good recognition performance of OKDA.
2. Kernel uncorrelated discriminant analysis is studied for feature extraction from range profiles. By analyzing the statistically uncorrelated property further and introducing a kernel function, a kernel uncorrelated Fisher criterion is derived, and two equivalent algorithms, called direct kernel uncorrelated discriminant analysis (DKUDA) and kernel uncorrelated discriminant analysis based on generalized singular value decomposition (KUDA/GSVD), are proposed to extract statistically uncorrelated discriminative features from range profiles. As compared with uncorrelated discriminant analysis (UDA) and kernel uncorrelated discriminant analysis (KUDA), DKUDA and KUDA/GSVD can reduce large amount of computation. Moreover, the singularity problem is resolved effectively.
3. Manifold learning is studied for feature extraction from range profiles. Based on the analysis of several classical manifold learning methods, a supervised nonlinear manifold learning algorithm, named supervised kernel neighborhood preserving projections (SKNPP), is proposed to extract nonlinear features from range profiles. SKNPP is obtained by modifying NPP with class label information and furtherextending it to nonlinear form by utilizing kernel function. It can not only preserve the within-class neighboring geometry in high-dimensional space, but also gain a perfect nonlinear approximation of data manifold.
4. Two novel nonlinear manifold learning algorithms, called kernel uncorrelated discriminative neighborhood embedding (KUDNE) and kernel uncorrelated discriminative locality preserving projections (KUDLPP), are proposed to extract features from range profiles. They are obtained by combing supervised kernel neighborhood preserving projections (SKNPP) and supervised kernel locality preserving projections (SKLPP) with kernel discriminant analysis (KDA), respectively, under the statistically uncorrelated constraint. The two algorithms can not only preserve the within-class geometry, but also maximizing the between-class scatter of projected samples. Moreover, the extracted feature space contains minimum redundancy.
5. Three kernel-based nonlinear classifiers, including support vector machine (SVM), kernel-based nonlinear discriminator (KND) and kernel-based nonlinear representor (KNR) are studied and compared in detail, and applied for radar target recognition with range profiles. Especially, KND and KNR are two novel kernel-based nonlinear classifiers, which can achieve satisfactory recognition performance, in terms of both recognition accuracy and recognition speed, as compared with SVM.
本文对以上两种机器学习理论进行研究,针对已有算法的不足进行推广和改进,并应用于基于高分辨距离像的雷达目标识别。论文的主要工作和创新之处概括如下:
1.在对核鉴别分析(Kernel Discriminant Analysis,KDA)及其变形算法进行深入研究的基础上,提出一种最优核鉴别分析(Optimal Kernel DiscriminantAnalysis,OKDA)算法用于雷达目标距离像特征提取。实验结果表明,OKDA具有较好的识别性能以及良好的类内聚合性。
2.研究基于核不相关鉴别分析的雷达目标距离像特征提取。通过对统计不相关特性进一步分析并引入核函数,推导出核不相关Fisher准则,并提出两种核不相关鉴别分析算法——直接核不相关鉴别分析(Direct Kernel UncorrelatedDiscriminant Analysis,DKUDA)和基于广义奇异值分解的核不相关鉴别分析(Kernel Uncorrelated Discriminant Analysis Based on Generalized Singular ValueDecomposition,KUDA/GSVD),用于从雷达目标距离像中提取统计不相关的鉴别特征。与不相关鉴别分析(Uncorrelated Discriminant Analysis,UDA)和核不相关鉴别分析(Kernel Uncorrelated Discriminant Analysis,KUDA)相比,这两种算法大大减少了运算量,而且能有效解决奇异性问题。
3.研究基于流形学习理论的雷达目标距离像特征提取。在对几种经典的流形学习算法进行分析总结的基础上,提出一种有监督的非线性流形学习算法——监督核近邻保持投影(Supervised Kernel Neighborhood Preserving Projections,SKNPP),用于对雷达目标距离像进行特征提取。SKNPP在近邻保持投影(Neighborhood Preserving Projections,NPP)的基础上引入样本的类别信息,并利用核函数将其推广到非线性形式而得到。该算法不但保留了高维空间中类内样本之间的几何结构,而且可以获得对数据流形的非线性逼近。
4.提出了基于核不相关鉴别近邻嵌入(Kernel Uncorrelated DiscriminativeNeighborhood Embedding,KUDNE)和核不相关鉴别局部保持投影(KernelUncorrelated Discriminative Locality Preserving Projections,KUDLPP)的雷达目标距离像特征提取方法。KUDNE和KUDLPP是在统计不相关约束条件下,分别将监督核近邻保持投影(SKNPP)和监督核局部保持投影(Supervised Kernel LocalityPreserving Projections,SKLPP)与核鉴别分析(KDA)相结合而得到的。这两种算法在保留类内样本之间固有几何关系的同时,使投影后样本的类间散射最大,而且使生成的特征空间具有最小的冗余度。
5.研究基于核非线性分类器的雷达目标识别方法。对支持向量机(SupportVector Machine,SVM)、KND(Kernel-Based Nonlinear Discriminator)以及KNR(Kernel-Based Nonlinear Representor)的分类原理及学习过程进行了深入研究和比较,并将其应用于雷达目标距离像分类。KND和KNR是两种新型的核非线性分类器,与SVM相比,它们不但能提高雷达目标识别速度,而且能得到满意的识别精度。
Radar target recognition plays an important role in modern radar, and finds its ways to wide military and civilian applications. High resolution range profiles contain more structural information of a target, and are easy to obtain and process, and thus provide us with a more reliable tool for target recognition. Currently, kernel method and manifold learning, among other methods, become two focuses in the field of pattern recognition and machine learning. Kernel method shows many advantages as to solve nonlinear problems, while manifold learning aims to discover the intrinsic characteristics of high-dimensional data.
In this dissertation, the above two methods are studied, and in order to overcome the weakness of existing methods, several generalized and improved algorithms are proposed and applied to radar target recognition using range profiles. The main contents and innovations of this dissertation are summarized as follows.
1. Kernel discriminant analysis and its variants are studied intensively, and an optimal kernel discriminant analysis (OKDA) is given and adopted to extract nonlinear discriminative features from range profiles. Experimental results show the good recognition performance of OKDA.
2. Kernel uncorrelated discriminant analysis is studied for feature extraction from range profiles. By analyzing the statistically uncorrelated property further and introducing a kernel function, a kernel uncorrelated Fisher criterion is derived, and two equivalent algorithms, called direct kernel uncorrelated discriminant analysis (DKUDA) and kernel uncorrelated discriminant analysis based on generalized singular value decomposition (KUDA/GSVD), are proposed to extract statistically uncorrelated discriminative features from range profiles. As compared with uncorrelated discriminant analysis (UDA) and kernel uncorrelated discriminant analysis (KUDA), DKUDA and KUDA/GSVD can reduce large amount of computation. Moreover, the singularity problem is resolved effectively.
3. Manifold learning is studied for feature extraction from range profiles. Based on the analysis of several classical manifold learning methods, a supervised nonlinear manifold learning algorithm, named supervised kernel neighborhood preserving projections (SKNPP), is proposed to extract nonlinear features from range profiles. SKNPP is obtained by modifying NPP with class label information and furtherextending it to nonlinear form by utilizing kernel function. It can not only preserve the within-class neighboring geometry in high-dimensional space, but also gain a perfect nonlinear approximation of data manifold.
4. Two novel nonlinear manifold learning algorithms, called kernel uncorrelated discriminative neighborhood embedding (KUDNE) and kernel uncorrelated discriminative locality preserving projections (KUDLPP), are proposed to extract features from range profiles. They are obtained by combing supervised kernel neighborhood preserving projections (SKNPP) and supervised kernel locality preserving projections (SKLPP) with kernel discriminant analysis (KDA), respectively, under the statistically uncorrelated constraint. The two algorithms can not only preserve the within-class geometry, but also maximizing the between-class scatter of projected samples. Moreover, the extracted feature space contains minimum redundancy.
5. Three kernel-based nonlinear classifiers, including support vector machine (SVM), kernel-based nonlinear discriminator (KND) and kernel-based nonlinear representor (KNR) are studied and compared in detail, and applied for radar target recognition with range profiles. Especially, KND and KNR are two novel kernel-based nonlinear classifiers, which can achieve satisfactory recognition performance, in terms of both recognition accuracy and recognition speed, as compared with SVM.
引文
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