多變量長期追蹤資料分類問題之研究

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Title:	多變量長期追蹤資料分類問題之研究
Other Titles:	Classification of Multivariate Longitudinal Data
Authors:	李百靈
Contributors:	淡江大學統計學系
Keywords:	分類;分群分析;鑑別分析;多變量長期追蹤資料;Classification,Cluster analysis;Discriminant analysis;Multivariate longitudinal data
Date:	2012-08
Issue Date:	2015-05-12 15:41:59 (UTC+8)
Abstract:	本計畫將探討多變量長期追蹤資料的分類問題。在過去的文獻中，不論是多變量資料分析或是函數型資料分析(functional data analysis, FDA)，大部分的分類方法均以資料的平均結構作為分類的依據，而且較少討論到資料為不規則且稀疏分佈的情況。因此，本計畫想提出能同時將資料在不同時間點的平均趨勢與主要共變異結構作為分群依據的FDA 分類方法，其中並將討論監督式分類(supervised classification)與非監督式分類(unsupervised classification)兩種問題。除此之外，本計畫亦會在不同型態的觀測時間下討論所提出之分類方法的表現，例如，密集觀測時間或是不規則稀疏觀測時點等情形。本計畫期望最後所提出的分類模式能因考慮了不同變量間的相關性而進一步改善只考慮單變量長期追蹤資料之分類方法的表現，並且提供多變量長期追蹤資料另一種可行的分析方式。 In this project, we propose to study the supervised and unsupervised classification problems of multivariate longitudinal data. We will try to propose a new multivariate functional classification model via the functional principal components analysis (FPCA) subspace projection so that the data can be classified based on the mean and covariance structures among groups simultaneously. We will work on the estimation methods of model components under two designs of time points, including the densely collected and sparsely sampled cases. We expect that the classification error rate can be reduced by considering the correlation between the multivariate longitudinal data compared with using the separate univariate models. The proposed method will be evaluated through simulation study and data examples.
Appears in Collections:	[Graduate Institute & Department of Statistics] Research Paper

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