本計畫將探討函數型資料(functional data)或曲線資料(curve data)之分類 (classification)問題。實際資料將被視為隨機過程的觀測值，而且資料可分為多 個已知的分類。在假設各分類之資料的平均函數與特徵空間等結構相異的情況 下，我們將提出一個新的函數型分類方法。本計畫將透過實際資料與模擬驗證 的方式來比較計畫所提出之方法與其他已發展之函數型分類方法的表現。此 外，本計畫的另一個目的是想探討當存在有與分類相關的解釋變數(covariates) 時，如何將這些解釋變數有用的訊息加入目前已有的函數型分類方法之中。我 們將討論如何在此情況下建立適當的分類模式，並進一步做理論探討與數值資 料之分析，期望加入解釋變數後的分類方法可以提高分類正確率。 This project will focus on classification of functional data or curve data. The data are viewed as realizations of a mixture of stochastic processes and each sub-process corresponds to a known class. Under an assumption that all the sub-processes have different mean functions and eigenspaces, we propose a novel functional classification method. The proposed method will be evaluated and compared with other previous functional classification approaches through simulation study and data examples. In addition, we will also discuss how to combine the information of important covariates into functional classification. We expect that the classification error rate can be reduced by considering the related covariates.
