In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and ...In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.展开更多
We prove several inequalies for symmetric postive semidefinite, general Mmatrices and inverse M-matrices which are generalization of the classical Oppenheim's Inequality for symmetric positive semidefinite matrices.
为了降低稀疏主成分分析(Sparse Principal Component Analysis,SPCA)算法对高维数据集的计算复杂度,提出一种改进SPCA(Improved Sparse Principal Component Analysis,ISPCA)算法。该算法将特征选择过程分为两个阶段,第一阶段利用不带...为了降低稀疏主成分分析(Sparse Principal Component Analysis,SPCA)算法对高维数据集的计算复杂度,提出一种改进SPCA(Improved Sparse Principal Component Analysis,ISPCA)算法。该算法将特征选择过程分为两个阶段,第一阶段利用不带低秩惩罚项的SPCA先对数据进行一次特征选择,得到降维数据,采用矩阵的广义逆引理降低算法复杂度。第二阶段在降维数据上执行带低秩惩罚项的SPCA对降维数据再次进行特征选择。对比实验结果表明,ISPCA算法比SPCA算法受参数影响较小,特征选择性能更优,运行速度更快。展开更多
基金This work is supported by National Natural Science Foundation of China （No. 10531080）.
文摘In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.
基金Supported by National Natural Science Foundation of China(60375010).
文摘We prove several inequalies for symmetric postive semidefinite, general Mmatrices and inverse M-matrices which are generalization of the classical Oppenheim's Inequality for symmetric positive semidefinite matrices.
文摘为了降低稀疏主成分分析(Sparse Principal Component Analysis,SPCA)算法对高维数据集的计算复杂度,提出一种改进SPCA(Improved Sparse Principal Component Analysis,ISPCA)算法。该算法将特征选择过程分为两个阶段,第一阶段利用不带低秩惩罚项的SPCA先对数据进行一次特征选择,得到降维数据,采用矩阵的广义逆引理降低算法复杂度。第二阶段在降维数据上执行带低秩惩罚项的SPCA对降维数据再次进行特征选择。对比实验结果表明,ISPCA算法比SPCA算法受参数影响较小,特征选择性能更优,运行速度更快。
