- 學位論文
以變動掃描視窗檢測平均值偏移之區域範圍
Detecting Clusters with Mean shifts by using variable scan window
摘要
本研究目標為分析空間與時空型態資料，發展空間與時空掃描統計量以偵測資料平均值偏移的區域範圍與發生時間。相較於常見的以圓形固定掃描視窗大小所設計出的空間或時空掃描統計量，本研究方法無需固定掃描半徑，而採用可變動的掃描視窗，透過標準化的過程，判斷資料可能異常的範圍。本研究方法設計更符合解決現實問題中，異常範圍大小往往為未知的難題。研究方法在偵測空間型態資料分為三項方法：（1）同心圓平均法：對各圓形掃描視窗內的觀察值計算平均、（2）同心圓距離層級法：將各圓形掃描視窗內的觀察值依距離層級加權、（3）不規則掃描視窗法：對不規則掃描視窗內的觀察值計算平均，最後再將掃描視窗所對應的掃描統計量取最大值，判斷監控範圍內是否有部分區域其資料平均值異常。在偵測時空型態資料的研究方法，則延伸上述三項方法再分別對時間軸採用指數移動加權平均(Exponentially Weighted Moving Average, EWMA)以累積資料的變異量。本研究發展出同心圓平均之時間加權法、同心圓距離層級之時間加權法、不規則掃描視窗之時間加權法，用以判斷時空型態資料中異常區域的範圍及發生時間。模擬結果顯示，本研究所提出之方法能有效偵測出異常區域，與現有文獻方法相比，各方法對不同異常模式的偵測敏感度各有優劣。文末以新墨西哥(New Mexico)州男性罹患甲狀腺癌之發病情形為例，說明本論文所提之偵測空間分析方法與時空分析方法於實際案例上之運用。
並列摘要
The goal of this research is analyzing spatial and spatiotemporal data. We developed spatial and spatiotemporal scan statistics to detect the regions where the mean values shift and there time of occurrence. Different from the common spatial and spatiotemporal scan statistics that apply circular scan windows with fixed sizes, the proposed method of this research does not require fixed scan radii. Instead, variable scan windows along with standardization were designed to detect the potential abnormal regions. The proposed method is better applicable to the real problems that the size of abnormal region is often unknown. Three methods were developed for spatial analysis: (1) concentric average method: average the observations in each circular scan window, (2) concentric weighted method: weight the observations by distance in each circular scan window, (3) irregular scan window method: average the observations in each irregular scan window. Last, the maximum scan statistics of the scan windows are used to determine whether there exists abnormal region with mean shifts. The three methods are extended to analyzing spatiotemporal data by using the exponentially weighted moving average (EWMA) technique across the temporal axis. Concentric average of the time-weighted method, concentric weighted of the time-weighted method, and irregular scan window method of the time-weighted method were developed to determine the range and time of occurrence of abnormal regions. The simulation results show that the proposed methods can effectively detect the abnormal regions. The proposed methods could be better or worse than the existing methods depending on the pattern of abnormal regions. Last, an implementation of male thyroid cancer in New Mexico is carried out to demonstrate the practicability of the proposed methods.