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日本冈山理工大学Yuichi Mori教授学术报告

时间:2019-12-16 16:03      来源:新皇冠体育

报告题目:Nonlinear principal component analysis and its applications

报 告 人:冈山理工大学Yuichi Mori教授

报告时间:20191219日(周四)上午1030

报告地点:清水河主楼A1-513

邀 请 人:夏应存 教授


报告摘要:

Principal components analysis (PCA) is a commonly used descriptive multivariate method for handling numerical data and can be extended to deal with mixed measurement level data. The extended PCA with such a mixture of categorical (nominal and ordinal) and numerical variables is referred to as nonlinear PCA. Nonlinear PCA (NLPCA) alternates between estimating the parameters of PCA and quantifying categorical data, and uses the alternating least squares (ALS) algorithm as the algorithm to find least squares solutions.

   Here we show three topics on NLPCA, variable selection in NLPCA, reduced k-means clustering with NLPCA, and acceleration of ALS algorithm.

NLPCA allows us to deal with any measurement level multivariate data uniformly as numerical data. This means that all variables in the data can be analyzed as numerical variables, and we can therefore solve the variable

selection problem for mixed measurement level data using any existing variable selection method such as the modified PCA, which finds a subset of numerical variables that represents all variables as far as possible. We discuss variable selection in NLPCA for mixed measurement level data using criteria in the modified PCA.

   Reduced k-means clustering (RKM) is a useful tool to find clusters from data with a large number of numerical variables, which applies the dimension reduction method (PCA) and the k-means clustering simultaneously. For mixed level measurement data, we can perform RKM to such data by replacing PCA by NLPCA in the dimension reduction part of RKM. A numerical experiment demonstrates that RKM with NLPCA find reasonable clusters from categorical data.

ALS algorithm may require many iterations and significant computation time to converge, because its speed of convergence is linear. In order to accelerate the convergence, we propose a new iterative algorithm using the vector epsilon algorithm to generate a faster linear convergent sequence. Numerical experiments for a large number of variables with a variety of mixing rates of categorical and numerical variables and for variable selection problem in NLPCA demonstrate that the speed of convergence of the proposed acceleration algorithm is significantly faster than that of the ordinary ALS algorithm.


报告人简介:

Yuichi Mori,日本冈山理工大学管理学院管理系教授,1995年博士毕业于冈山大学统计系。目前研究方向:计算统计(包括变量选择,统计计算加速,非线性多元方法以及基于网络的统计系统研究)和统计教育。现任WIREs (Wiley Interdisciplinary Reviews) Computational Statistics的组稿编辑,Bulletin of Data Analysis of Japanese Classification Society等多个期刊副主编。


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