函數型主成份分析於曲線資料分類問題之應用

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Title:	函數型主成份分析於曲線資料分類問題之應用
Other Titles:	Classification using functional principal component analysis for curve data
Authors:	王哲秋;Wang, Che-chiu
Contributors:	淡江大學統計學系碩士班李百靈
Keywords:	分類;曲線資料;函數型主成份分析;classification;Curve Data;Functional Principal Components Analysis
Date:	2010
Issue Date:	2010-09-23 16:41:36 (UTC+8)
Abstract:	本文提出一最佳預測曲線分類準則來分析曲線資料，在假設不同類別之隨機曲線的平均函數與特徵函數是相異的情況下，利用函數型主成份分析建立各類曲線的模式。對某一特定的觀測曲線，最佳預測曲線分類準則是以此觀測曲線與根據各類別模式所得之配適曲線的最小距離決定此曲線的最佳分類。本文以數值模擬研究與一組實際資料做為新方法的驗證，所分析的實際資料則是由美國范德堡大學癌症生物統計中心所提供的介質輔助雷射脫附游離(Matrix Assisted Laser Desorption, MALDI) 資料。從數值模擬研究與實際資料可以發現, 當各類別的特徵函數不同時，最佳預測曲線分類準則其結果是較其他方法有優勢的。此外，函數型分類方法於曲線分類之表現較多變量分類方法好，而利用函數型主成份分析有助於曲線資料的分類。 We propose a best predicted curve (BPC) classification criterion for classifying the curve data. The data are viewed as realizations of a mixture of stochastic processes and each sub-process corresponds to a known class. Under the assumption that all the subprocesses have different mean functions and eigenspaces, an observed curve is classified into the best predicted class by minimizing the distance between the observed and predicted curves via subspace projection among all classes based on the functional principal component analysis (FPCA) model.The BPC approach accounts for both the means and the modes of variation differentials among classes while other classical functional classification methods consider the differences in mean functions only. Practical performance of the proposed method is demonstrated through simulation studies and a real data example of matrix assisted laser desorption (MALDI) mass spectrometry data provided by Dr. Yu Shyr of Vanderbilt University. The proposed method is also compared with other previous functional classification approaches. Overall, the BPC method outperforms the other methods when the eigenspaces among classes are significantly distinct.For classifying the MALDI mass spectrometry data, we found that functional classification methods perform better then multivariate data approaches and applying the FPCA for dimension reduction is advantageous to improving the accuracy of classification.
Appears in Collections:	[Graduate Institute & Department of Statistics] Thesis

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