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| 矩阵奇异值分解及其在高维数据处理中的应用 | |
| 引用本文： | 尹芳黎,杨雁莹,王传栋,王士鹏.矩阵奇异值分解及其在高维数据处理中的应用[J].数学的实践与认识,2011,41(15). |
| 作者姓名： | 尹芳黎 杨雁莹 王传栋 王士鹏 |
| 作者单位： | 1. 南京下关中等专业学校数学教研组,江苏南京,210011 2. 南京森林警察学院信息技术系,江苏南京,210046 3. 南京邮电大学计算机学院,江苏南京,210003 4. 中国电子科技集团公司第十四研究所,江苏南京,210039 |
| 基金项目： | 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) |
| 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. |
| 关 键 词： | 奇异值分解 维数约减 主分量分析 隐含语义分析 |
Research on the Advances of Singular Value Decomposition and Its Application in the High Dimensional Data Mining |
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| YIN Fang-li,YANG Yan-ying,WANG Chuan-dong,WANG Shi-peng.Research on the Advances of Singular Value Decomposition and Its Application in the High Dimensional Data Mining[J].Mathematics in Practice and Theory,2011,41(15). | |
| Authors: | YIN Fang-li YANG Yan-ying WANG Chuan-dong WANG Shi-peng |
| Institution: | YIN Fang-li~1,YANG Yan-ying~2,WANG Chuan-dong~3,WANG Shi-peng~4 (1.Department of Mathematics,Xiaguan Middle Vocational School,Nanjing 210011,China) (2.Department of Information and Technology,Nanjing College of Forestry Police,Nanjing 210046,China) (3.College of Computer,Nanjing University of Posts & Telecommunications,Nanjing 210003,China) (4.The 14th Research Institute,CETC,Nanjing 210039,China) |
| Abstract: | 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 pr... |
| Keywords: | singular value decomposition dimension reduction principal component analysis latent semantic analysis |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |