摘要
矩阵奇异值分解能够实现对高维数据的局部特征提取及维数约减,在智能信息处理和模式识别研究领域具有十分重要的应用价值.首先分析了高维数据处理所面临的困境,并对常用的降维算法进行简单的归纳总结;然后阐述了矩阵奇异值分解的基本原理及其在维数约减和数据压缩中的物理意义;接着通过分析两种建立在奇异值分解基础上的PCA与LSA降维算法的数学导出过程,进一步给出了两者的等价性证明;最后总结了矩阵奇异值分解的优缺点,并且预测了高维数据处理技术未来的发展趋势.
As an important large scale data processing technology, Singular Value Decomposition （SVD） of Matrix can be used to abstract local feature and reduce dimension. In this paper, firstly the dilemma of high dimensional data processing is analyzed and the existing algorithms of dimension reduction is generalized and classified. Secondly, the fundamental principles of SVD and physical significance about dimension reduction and data compression are clarified in detail. Thirdly, by analyzing the mathematical reasoning processes of the PCA and LSA which based on SVD technology, we further prove the equivalence of the two dimension reduction algorithms. Finally, We summarize the strongpoint and shortcoming of SVD and forecast the future development tendency of high dimensional data processing technology.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第15期171-177,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(60703086)
南京邮电大学校科研基金(NY210043
NY210044)
江苏省普通高校研究生科研创新计划(CX10B_195Z)
关键词
奇异值分解
维数约减
主分量分析
隐含语义分析
singular value decomposition
dimension reduction
principal component analy- sis
latent semantic analysis
