Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(...Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).展开更多
线性判别分析(Linear discriminant analysis,LDA)作为一种有监督的降维方法,已经广泛应用于各个领域。然而,传统的LDA存在以下缺点:1)LDA假设数据是高斯分布和单一模态的;2)LDA对异常值和噪声十分敏感;3)LDA的判别投影方向对特征的可...线性判别分析(Linear discriminant analysis,LDA)作为一种有监督的降维方法,已经广泛应用于各个领域。然而,传统的LDA存在以下缺点:1)LDA假设数据是高斯分布和单一模态的;2)LDA对异常值和噪声十分敏感;3)LDA的判别投影方向对特征的可解释性低且对降维数较为敏感。为克服以上问题,提出了基于信息熵的鲁棒稀疏子类判别分析(Robust sparse subclass discriminant analysis based on information entropy,RSSDAIE)新方法。具体而言,对每个类别划分不同数量的子类后,重新定义类内散射矩阵和类间散射矩阵,使其更适应现实数据。另外,引入L_(21)范数、稀疏矩阵和正交重构矩阵以确保RSSDAIE具有更高的鲁棒性、更好的可解释性和更低的维度敏感性。同时采用交替方向乘子法对目标函数求解,避免类内散射矩阵不可逆的情形。在多个数据集上进行了对比实验,证明了RSSDAIE在数据适用类型、降低噪声影响、减少降维数影响等方面更有优越性,分类准确率更高。展开更多
Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We dis...Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.展开更多
基金Supported by the National Natural Sciences Foundation of P.R.China(No.10371029)the Natural Sciences Foundation of Hebei Province(No.103144)the Doctoral Foundation of Hebei Normal University(No.103257)
文摘Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).
文摘线性判别分析(Linear discriminant analysis,LDA)作为一种有监督的降维方法,已经广泛应用于各个领域。然而,传统的LDA存在以下缺点:1)LDA假设数据是高斯分布和单一模态的;2)LDA对异常值和噪声十分敏感;3)LDA的判别投影方向对特征的可解释性低且对降维数较为敏感。为克服以上问题,提出了基于信息熵的鲁棒稀疏子类判别分析(Robust sparse subclass discriminant analysis based on information entropy,RSSDAIE)新方法。具体而言,对每个类别划分不同数量的子类后,重新定义类内散射矩阵和类间散射矩阵,使其更适应现实数据。另外,引入L_(21)范数、稀疏矩阵和正交重构矩阵以确保RSSDAIE具有更高的鲁棒性、更好的可解释性和更低的维度敏感性。同时采用交替方向乘子法对目标函数求解,避免类内散射矩阵不可逆的情形。在多个数据集上进行了对比实验,证明了RSSDAIE在数据适用类型、降低噪声影响、减少降维数影响等方面更有优越性,分类准确率更高。
文摘Objectives: We introduce a special form of the Generalized Poisson Distribution. The distribution has one parameter, yet it has a variance that is larger than the mean a phenomenon known as “over dispersion”. We discuss potential applications of the distribution as a model of counts, and under the assumption of independence we will perform statistical inference on the ratio of two means, with generalization to testing the homogeneity of several means. Methods: Bayesian methods depend on the choice of the prior distributions of the population parameters. In this paper, we describe a Bayesian approach for estimation and inference on the parameters of several independent Inflated Poisson (IPD) distributions with two possible priors, the first is the reciprocal of the square root of the Poisson parameter and the other is a conjugate Gamma prior. The parameters of Gamma distribution are estimated in the empirical Bayesian framework using the maximum likelihood (ML) solution using nonlinear mixed model (NLMIXED) in SAS. With these priors we construct the highest posterior confidence intervals on the ratio of two IPD parameters and test the homogeneity of several populations. Results: We encountered convergence problem in estimating the hyperparameters of the posterior distribution using the NLMIXED. However, direct maximization of the predictive density produced solutions to the maximum likelihood equations. We apply the methodologies to RNA-SEQ read count data of gene expression values.
