Classification Using Functional Principal Component Analysis for Curve Data

• Main Authors: Che-Chiu Wang, 王哲秋
• Other Authors: 李百靈
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/51208517560864455260

碩士 === 淡江大學 === 統計學系碩士班 === 98 === 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.