The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal...The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal component analysis using this method.Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established.We also provide the convergence rate of the variance estimation of the measurement error.Based on the results,the number of observations within each curve can be of any rate relative to the sample size,which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.展开更多
局部线性嵌入算法采用欧氏距离选择邻域点,这通常会损失数据集本身的非线性特征,造成邻域点选取错误,且仅使用欧氏距离构造权重会导致信息挖掘不充分。针对以上问题,提出基于概率模型与信息熵的局部线性嵌入算法(Probability informatio...局部线性嵌入算法采用欧氏距离选择邻域点,这通常会损失数据集本身的非线性特征,造成邻域点选取错误,且仅使用欧氏距离构造权重会导致信息挖掘不充分。针对以上问题,提出基于概率模型与信息熵的局部线性嵌入算法(Probability information entropy-LLE,PIE-LLE)。首先,为了使邻域点选择更加合理,从数据集的概率分布角度出发,考虑样本点及其邻域的概率分布,为样本点构造符合局部分布的邻域集合。其次,为了充分提取样本的局部结构信息,在权重构造阶段,分别计算样本所属邻域概率以及每个样本的信息熵,融合二者信息重构低维样本。最后,在两个轴承故障数据集上的实验表明,所提方法故障识别准确度最高达到了100%,高于其他对比算法;在邻域点个数5~15范围内,PIE-LLE算法展现出良好的低维可视化效果;在参数敏感性实验中,该算法可以保持Fisher指标较大,有效提高了算法的分类准确度和稳定性。展开更多
基金supported by National Natural Science Foundation of China(project number:11771146,11831008,81530086,11771145)the National Social Science Foundation Key Program(17ZDA091)+2 种基金the 111 Project(B14019)Programof Shanghai Subject Chief Scientist(14XD1401600)supported by the China Postdoctoral Science Foundation(2018M630393).
文摘The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal component analysis using this method.Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established.We also provide the convergence rate of the variance estimation of the measurement error.Based on the results,the number of observations within each curve can be of any rate relative to the sample size,which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.
文摘局部线性嵌入算法采用欧氏距离选择邻域点,这通常会损失数据集本身的非线性特征,造成邻域点选取错误,且仅使用欧氏距离构造权重会导致信息挖掘不充分。针对以上问题,提出基于概率模型与信息熵的局部线性嵌入算法(Probability information entropy-LLE,PIE-LLE)。首先,为了使邻域点选择更加合理,从数据集的概率分布角度出发,考虑样本点及其邻域的概率分布,为样本点构造符合局部分布的邻域集合。其次,为了充分提取样本的局部结构信息,在权重构造阶段,分别计算样本所属邻域概率以及每个样本的信息熵,融合二者信息重构低维样本。最后,在两个轴承故障数据集上的实验表明,所提方法故障识别准确度最高达到了100%,高于其他对比算法;在邻域点个数5~15范围内,PIE-LLE算法展现出良好的低维可视化效果;在参数敏感性实验中,该算法可以保持Fisher指标较大,有效提高了算法的分类准确度和稳定性。
