基于PCA扩展的判别性特征融合  

Discriminative Feature Fusion Based on Extensions of PCA

作　　者：檀敬东[1,2,3] 苏雅茹[2,3] 王儒敬[2,3] 

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]中国科学院合肥智能机械研究所智能决策实验室,合肥230031 [3]中国科学技术大学自动化系,合肥230027

出　　处：《模式识别与人工智能》2012年第2期305-312,共8页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金资助项目(No.60774096)

摘　　要：提出两个判别性的特征融合方法——主成分判别性分析和核主成分判别性分析.基于主成份分析和最大间隔准则理论,构造一个多目标规划模型作为特征融合的目标.随后,该模型被转化成一个单目标规划问题并通过特征分解的方法求解.此外,将一个近似分块对角核矩阵K分成c(c为数据集中的类别数)个小矩阵,并求出它们的特征值和特征向量.在此基础上,通过向量代数处理得到一个映射矩阵α,当核矩阵K投影到α上,同类样本的相似信息能最大程度地得到保持.本文中的实验证实两种方法的有效性.Two methods for dimensionality reduction, principal component discriminative analysis and kernel principal component discriminative analysis, are proposed. Based on the theory of principal component analysis and maximum margin criterion, a multi-objective project model is constructed to formalize the goals for feature fusion. Then, it is transformed into a single-objective cost function for the projection, and the optimal linear mapping is obtained through optimizing this cost function. Additionally, the nearly diagonal block kernel matrix is divided into c kernel matrixes （ c is the number of classes in dataset）, and eigen-decomposition method is used to solve their d principal vectors. Through the process of vector algebra, a combined mapping α is obtained. When the original kernel matrix K is projected on α, the inner-class information is optimally preserved. The experimental results show their validity.

关 键 词：主成份分析 最大间隔准则 支持向量机 分块对角阵 文本可视化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]