【作者】 刘笑嶂；

【导师】 冯国灿；

【作者基本信息】 中山大学 ， 信息计算科学， 2010， 博士

【摘要】 核方法作为一种非线性方法，对于非线性模式分类问题，具有坚实的理论支撑和强大的应用潜力。它具有两个显著的特点：首先是在线性与非线性之间架设起一座桥梁，其次是通过巧妙地引入核函数，避免了维数灾难，也没有增加计算复杂度。目前，支持向量机样本约简、核函数构造以及多重核学习都是核方法研究的重要方向。在支持向量机样本约简方面，一些研究致力于开发基于核聚类的样本约简方法；在核函数构造方面，利用数据的特性构造高效的专用核在很多应用领域尚未实现；在多重核学习方面，目前的多重核学习是在支持向量机的框架下提出并发展起来的，迄今还极少见到基于多重核的子空间分析方法的报告。本文的主要工作包括以下三个方面。提出了一种“自顶向下”的层次核聚类方法一核二分K一均值聚类算法(KBK)，该方法能够在核特征空间中快速产生规模相近的簇；在此基础上，提出了支持向量机样本约简的KBK—SR算法，它将一个经过改造的KBK聚类过程与一个样本移除过程相结合，作为支持向量机训练的预处理过程。理论分析和实验都表明，KBK—SR算法能够在保持较高测试精度的同时，快速有效地进行支持向量机样本约简。针对人脸图像的光照变化，为基于核的LDA识别方法提出了一种系统的核学习方法。该方法从朗伯假设出发，通过最大化类内和类间相似度的差来学习核矩阵，进而使用散乱数据插值技术将核矩阵推广为被我们称作ILLUM核的核函数。在可变光照条件下的人睑图像集上的实验表明，我们的ILLUM核能够使基于核的LDA方法很好地处理人脸图像识别中的光照问题，在这个意义下，ILLUM核显著优于线性核和高斯径向基核等常用核。提出了多重核线性判别分析(MKDA)方法，首先针对基于核的LDA给出了一种多重核的构造方法，继而通过使用拉格朗日乘子法优化最大边缘准则，在基于核的LDA的框架下导出了MKDA权值优化的迭代算法。在实验部分，一方面，优化权值后的MKDA在几个UCI标准数据集上显示了高于单个核KDDA的鉴别性能；另一方面，将MKDA的权值优化算法用于核选择，为人脸图像识别有效地选取出了鉴别能力最强的核。更多还原

【Abstract】 As a nonlinear approach, kernel methods possess a sound foundation and anextensive application potential for nonlinear pattern classification tasks. They are char-acterized by two merits. First, they build a bridge between linearity and nonlinearity;next, they introduce a kernel function to avoid the curse of dimensionality withoutincreasing computational complexity. At present, sample reduction for support vectormachines (SVMs), kernel construction and multiple kernel learning are all key researchtopics in the field of kernel methods. In terms of SVM sample reduction, some re-searches aim at developing sample reduction approaches based on kernel clustering.In terms of kernel construction, few kernels are successfully constructed for given datafrom specific application backgrounds. In terms of multiple kernel learning, it wasdeveloped under the framework of SVMs, and so far, there have hardly been reportson multiple kernel learning for subspace analysis methods.The contributions of this dissertation include the following three aspects.Atop-downhierarchicalkernelclusteringapproachnamedkernelbisectingk-means(KBK) clustering algorithm is proposed, which tends to quickly produce balancedclusters of similar sizes in the kernel feature space. On this basis, we present theKBK-SR algorithm for SVM sample reduction, which integrates a modified versionof KBK with a subsequent sample removal procedure as a sampling preprocess-ing part for SVM training to improve the scalability. Theoretical analysis and experimental results both show that, with very short sampling time, our algorithmdramatically accelerates SVM training while maintaining high test accuracy.A systematic method to construct a new kernel for the kernel-based LDA meth-ods is proposed, which is good for handling illumination problem. The proposedmethod first learns a kernel matrix by maximizing the di?erence between inter-class and intra-class similarities under the Lambertian model, and then generalizesthe kernel matrix to our proposed ILLUM kernel using the scattered data interpo-lation technique. Experiments on face images under varying illumination showthat, the kernel-based LDA methods with our ILLUM kernel deal with the illumi-nation problem well in face image recognition. And in this sense, ILLUM kerneloutperforms popular kernels such as the linear kernel and the Gaussian RBF kernel.Multiple kernel discriminant analysis (MKDA) is proposed. We first present amultiple kernel construction method for kernel-based LDA, then through opti-mizing the maximum margin criterion (MMC) using the Lagrangian multipliermethod, deduce the weight optimization scheme for MKDA. In the experiments,on one hand, MKDA with optimized weights shows superior discriminant powerto KDDA with individual kernels on several UCI benchmark datasets; on the otherhand, the weight optimization scheme for MKDA is used to e?ectively select thekernel with the most discriminant power for recognition of face images.更多还原