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.
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.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2011年第6期776-782,共7页
Pattern Recognition and Artificial Intelligence
基金
国家自然科学基金资助项目(No.61070137
60702063
60933009)
