论文部分内容阅读
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.
This paper proposes a low-rank approximation decomposition method for nuclear matrix.Firstly, in view of the assumption that the traditional kernel matrix decomposes columns and categories independently, the relations between columns are studied, and the column selection strategy of the core matrix is designed in combination with the classification.On this basis, The decomposition is divided into two stages. Compared with the traditional decomposition algorithm which considers only the diagonal elements, the Cholesky factor obtained by the relationship between the columns of the kernel matrix and the column is decomposed and the base vector is expanded to the entire space Finally, the expected value of the approximate error bound is given.The algorithm does not need the hypothesis that the columns are independent of the categories, the columns are associated with the categories, the discriminant submatrices can be extracted and the eigenvalue decomposition operation of the whole nuclear matrix can be avoided , Which can effectively reduce the computational cost.The experiment and analysis of multiple data sets verify the rationality and effectiveness of the algorithm.