利用函數型資料分析探討穿戴式裝置資料變異來源的處理

Abstract

隨著穿戴式裝置日益普及，其內建感測器所蒐集的資料被廣泛應用於健康監控、運動分析與娛樂等領域，其中以加速度計為核心的資料蒐集方式特別適合應用於手勢辨識任務。這類資料具備連續、可即時追蹤等優勢，然而也同時伴隨來自個體差異、重複測量誤差與感測環境干擾等高變異性與雜訊的挑戰。為了解決穿戴式裝置中手勢資料在辨識任務中常面臨的資料變異的問題，本研究試圖探討透過函數型資料分析方法之資料處理流程，是否能在有限樣本條件下，提升資料品質並壓縮非結構性變異，進而穩定後續手勢分類之進行。研究資料來自48位受試者針對10種手勢進行重複施作所產生的加速度時間序列資料，經過函數平滑化、資料對齊、與函數型主成份分析三道處理流程，依序透過三階B-樣條基底函數建構連續時間函數，再將所有資料統一對齊至首條樣本的時間軌跡以校正相位及振幅差異，最後通過函數型主成份分析提取能解釋90%以上變異的主成份以進行資料函數重構，進一步壓縮資料雜訊。研究最後以總變異、組內變異、組間變異三項指標評估資料於各處理階段的離散情形，結果顯示資料平滑化與主成份分析降維具穩定去噪效果，而對齊步驟在不同手勢上的效果則有所差異，尤其當手勢本質結構差異較大時，對齊反而可能增加資料變異。此外，主成份重構後的曲線保留了關鍵的波峰與轉折訊號，成功去除了局部擾動與高頻干擾，顯示函數型主成份分析方法兼具抑制雜訊與保留訊號的能力。綜合而言，本研究證實在穿戴式手勢資料的資料處理流程上，函數型資料分析在高度變異時間序列資料中具備良好的穩定性與解釋性，未來可進一步應用於樣本有限或跨個體情境下的手勢辨識任務中，作為強化辨識能力與模型穩定性的依據。

With the growing prevalence of wearable devices, data collected from embedded sensors—particularly accelerometers—have been widely applied to health monitoring, sports analytics, and interactive systems. Accelerometer-based data are well-suited for hand gesture recognition due to their continuous and real-time tracking capabilities. However, these data pose challenges such as high variability and noise from individual differences, repeated measurements, and environmental disturbances. This study explores if employing a data processing flow based on functional data analysis (FDA) can enhance data quality and reduce unstructured variation, leading to stabilized gesture classification under limited sample conditions. The dataset comprises time-series accelerometer signals from 48 participants performing 10 hand gestures repeatedly. The pipeline includes functional smoothing using third-order B-spline basis functions, temporal alignment of all curves to the first sample trajectory, and functional principal component analysis (FPCA). Components explaining over 90% of the total variance were retained for reconstructing the signals and compressing noise. To assess the impact of each processing step, the study evaluates total, within-subject, and between-subject variance. Results indicate that smoothing and FPCA consistently reduce noise and improve data structure, while alignment yields mixed effects, especially increasing variation in gestures with greater structural differences. The reconstructed curves preserve key waveform features, such as peaks and turning points, while effectively suppressing local perturbations and high-frequency noise. This FDA-based pipeline demonstrates strong potential for stabilizing high-variability gesture data. It provides a robust and interpretable preprocessing procedure for wearable sensor applications and offers practical value for improving recognition performance in small-sample or cross-subject scenarios.