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核矩阵列相关低秩近似分解算法

, PP. 776-782

Keywords: 核矩阵,不完全Cholesky分解(ICD),低秩近似,列选取

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Abstract:

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。

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