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.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
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)
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
Principal Component Analysis, Maximum Margin Criterion, Support Vector Machine,Diagonal Block Matrix, Text Visualization
