Under minimum squared error (MSE) rule, discrete K L transform (DKLT) was given. The 2nd information function, the 2nd information entropy and geometry entropy under DKLT were proposed, by which information characteri...Under minimum squared error (MSE) rule, discrete K L transform (DKLT) was given. The 2nd information function, the 2nd information entropy and geometry entropy under DKLT were proposed, by which information characteristics of DKLT were metricized. Two new concepts of information rate (IR) and accumulated information rate (AIR) were proposed by which the degree of information feature compression of DKLT was illustrated.展开更多
文献[1l提出了分子分母皆为线性函数的多元有理逼近(Rational Approximation with Linear Numerator and Denominator,RALND),满意地求了非线性方程组的解和数学规划最优解,为了克服RALND的不足,使之更好地发挥作用,本文试图改进该逼近:...文献[1l提出了分子分母皆为线性函数的多元有理逼近(Rational Approximation with Linear Numerator and Denominator,RALND),满意地求了非线性方程组的解和数学规划最优解,为了克服RALND的不足,使之更好地发挥作用,本文试图改进该逼近:(1)提出了更合理地筛选有理逼近解的方法;(2)证明了该逼近的单调性;(3)对于原函数在当前点与前次迭代点连线方向上方向导数符号相反的情况,分别提出了迭代求有理逼近和构造在当前点与估算点连线方向上相应的方向导数符号相同的近似有理逼近的方法;(4)提出了一个非单调的有理逼近函数;(5)通过数值计算验证了本文提出的有理逼近是有效和可行的.展开更多
The classification of cancer is a major research topic in bioinformatics. The nature of high dimensionality and small size associated with gene expression data,however,makes the classification quite challenging. Altho...The classification of cancer is a major research topic in bioinformatics. The nature of high dimensionality and small size associated with gene expression data,however,makes the classification quite challenging. Although principal component analysis (PCA) is of particular interest for the high-dimensional data,it may overemphasize some aspects and ignore some other important information contained in the richly complex data,because it displays only the difference in the first twoor three-dimensional PC subspaces. Based on PCA,a principal component accumulation (PCAcc) method was proposed. It employs the information contained in multiple PC subspaces and improves the class separability of cancers. The effectiveness of the present method was evaluated by four commonly used gene expression datasets,and the results show that the method performs well for cancer classification.展开更多
文摘Under minimum squared error (MSE) rule, discrete K L transform (DKLT) was given. The 2nd information function, the 2nd information entropy and geometry entropy under DKLT were proposed, by which information characteristics of DKLT were metricized. Two new concepts of information rate (IR) and accumulated information rate (AIR) were proposed by which the degree of information feature compression of DKLT was illustrated.
文摘文献[1l提出了分子分母皆为线性函数的多元有理逼近(Rational Approximation with Linear Numerator and Denominator,RALND),满意地求了非线性方程组的解和数学规划最优解,为了克服RALND的不足,使之更好地发挥作用,本文试图改进该逼近:(1)提出了更合理地筛选有理逼近解的方法;(2)证明了该逼近的单调性;(3)对于原函数在当前点与前次迭代点连线方向上方向导数符号相反的情况,分别提出了迭代求有理逼近和构造在当前点与估算点连线方向上相应的方向导数符号相同的近似有理逼近的方法;(4)提出了一个非单调的有理逼近函数;(5)通过数值计算验证了本文提出的有理逼近是有效和可行的.
基金supported by the National Natural Science Foundation of China (20835002)International Science and Technology Cooperation Program of the Ministry of Science and Technology (MOST) of China (2008DFA32250)
文摘The classification of cancer is a major research topic in bioinformatics. The nature of high dimensionality and small size associated with gene expression data,however,makes the classification quite challenging. Although principal component analysis (PCA) is of particular interest for the high-dimensional data,it may overemphasize some aspects and ignore some other important information contained in the richly complex data,because it displays only the difference in the first twoor three-dimensional PC subspaces. Based on PCA,a principal component accumulation (PCAcc) method was proposed. It employs the information contained in multiple PC subspaces and improves the class separability of cancers. The effectiveness of the present method was evaluated by four commonly used gene expression datasets,and the results show that the method performs well for cancer classification.
