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核矩阵列相关低秩近似分解算法
  • ISSN号：1003-6059
  • 期刊名称：模式识别与人工智能
  • 时间：2011
  • 页码：776-782
  • 分类：TP391[自动化与计算机技术—计算机应用技术;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]西安电子科技大学计算机学院,西安710071, [2]兰州大学交叉学科研究中心,兰州730000, [3]中国科学院物理研究所凝聚态理论与材料计算实验室,北京100170
  • 相关基金：国家自然科学基金资助项目（No.61070137,60702063,60933009）
  • 相关项目：原因学习：理论及在全基因组关联分析中的应用
作者： 刘松华|张军英|丁彩英|
关键词： 核矩阵, 不完全Cholesky分解(ICD), 低秩近似, 列选取, Kernel Matrix, Incomplete Cholesky Decomposition（ICD）, Low-Rank Approximation, Column Selection
中文摘要：

提出一种核矩阵低秩近似分解方法．首先针对传统核矩阵分解列与类别独立的假设，研究列之间的关系，结合类别设计核矩阵的列选取策略．在此基础上，将核矩阵的分解分为两个阶段，与传统分解算法只考虑对角元素占优不同，利用核矩阵列之间以及列与类别之间的关系获取的Cholesky因子进行分解，并将其基向量扩展到整个空间．最后给出近似误差界的期望值．该算法不需要列之间或列与类别独立的假设，将列与类别关联，能提取有判别能力的子矩阵，并避免对核矩阵整体进行特征值分解运算，有效降低计算量．多个数据集的实验和分析验证该算法的合理性和有效性．

英文摘要：

An effective method of low-rank approximation and decomposition for kernel matrix is proposed . Firstly, aiming at the assumption that column of the kernel matrix is independent from its class label, the correlation of columns is studied and a strategy for column selection is designed. Secondly, the kernel matrix is decomposed into two stages： low-rank matrix decomposition and extension. Then an expectation of low-rank approximation error bound is given. The proposed algorithm extracts discriminative sub-matrix without independent assumption. In this way, it avoids the decomposition of the entire kernel matrix and effectively reduces the computational complexity. Finally, the experimental results show that the proposed method is effective and reasonable.

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期刊信息
  • 《模式识别与人工智能》
  • 中国科技核心期刊
  • 主管单位:中国科学技术协会 中国自动化学会
  • 主办单位:国家智能计算机研究开发中心 中国科学院合肥智能机械研究所
  • 主编：郑南宁
  • 地址：安徽省合肥市蜀山湖路350号中国科学院合肥智能机械研究所
  • 邮编：230031
  • 邮箱：bjb@iim.cas.cn
  • 电话：0551-5591176
  • 国际标准刊号：ISSN：1003-6059
  • 国内统一刊号：ISSN：34-1089/TP
  • 邮发代号:26-69
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:10169