函數型迴歸分析於曲線資料分類之應用

淡江大學機構典藏 > 商管學院 > 統計學系暨研究所 > 研究報告 > Item 987654321/76309

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题名:	函數型迴歸分析於曲線資料分類之應用
其它题名:	Curve Data Classification via Functional Regression Analysis
作者:	李百靈
贡献者:	淡江大學統計學系
关键词:	Classification;Curve data;Discriminant analysis;Functional data analysis;Functional principal components analysis;Functional regression;Stochastic process
日期:	2011
上传时间:	2012-05-07 13:41:48 (UTC+8)
摘要:	本計畫將討論曲線資料(curve data)的分類(classification)問題，尤其是當存在有與分類相關的解釋變數(covariates)時，探討如何將這些解釋變數有用之訊息有效加入函數型分類方法中。我們將曲線資料視為隨機過程的實際觀測值，並假設在多個已知分類下，各類隨機函數的平均函數與共變異函數均可能相異。在給定相關解釋變數的訊息下，我們將利用條件函數型主成份分析 (conditional functional principal components)建立適當的曲線分類模式與規則。本計畫將透過實際資料與模擬驗證的方式來比較所提出之方法與其他已發展之函數型分類方法的表現，期望加入解釋變數相關訊息的分類方法可以提高分類正確率。 We propose a new functional classification method for classifying the curve data with accommodating additional covariate information. The data are viewed as realizations of a mixture of stochastic processes and each sub-process corresponds to a known class. We assume that all the sub-processes have different mean and covariance functions, and both the mean and covariance functions depend on the covariates. The curve data of each class are represented by various conditional functional principal components analysis (FPCA) models. We expect that the classification error rate can be reduced by considering the related covariates. The proposed method will be evaluated and compared with other previous functional classification approaches through simulation study and data examples
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