步態相位切割是辨識在一個步態週期中的多個相位之起點與終點的程序，這對於許多基於步態的應用是不可或缺的，像是姿態或疾病的診斷。此研究通常都在受控的臨床環境下完成，亦即是會受限於觀測空間以及觀測日常活動行為的能力。本篇論文提出藉由裝置於受測個體腳部的慣性量測元件(inertial measurement unit)收集步態資訊，並發展出自動步態相位切割的方法，此方法運用了新穎的加權動態時間規整(weighted dynamic time warping)來量測訊號間的距離以及最近鄰居演算法(k-nearest neighbors)來取得步態相位的估計。本篇論文提出的自動步態相位切割的方法能達到相較於傳統恆定百分比例切割的方法較高的F度量(micro f1 score)，0.9378，恆定比例的方法僅達到0.8867。此外，為了避免計算測試資料與全部訓練資料之間的動態時間規整距離(DTW distance)，本篇論文亦提出最近鄰居圖嵌入演算法(k-nearest neighbor graph embedding)，用以將步態訊號投影至能保存動態時間規整距離於歐幾里得空間的低微度向量。此嵌入方法能減少尋找最近鄰居的計算時間並且能估計出高達94%的最近鄰居。

Gait phase segmentation is the process of identifying the start and end points of various phases within a gait cycle, and it is essential to many gait-based applications, e.g., posture or disease diagnosis. This is typically done in a controlled clinical environment, which limits the capture volume and the ability to monitor behavior in daily activities. This work proposes the use of an inertial measurement unit (IMU) mounted on the individual’s foot to gather gait information and develops an automatic gait phase segmentation method utilizing a novel weighted dynamic time warping (DTW) algorithm to measure the distance between signals, and the k-nearest-neighbors algorithm to obtain the gait phase estimates. The proposed automatic gait phase segmentation method achieves a higher micro-F1 score of 0.9378 compared to the conventional constant-percentage segmentation, which achieves only 0.8867. Moreover, to avoid the need for computing the DTW distance between the test signal and all training signals, this work also proposes a k-nearest neighbor graph embedding method that is able to map each gait signal input into a low-dimensional vector that preserves the DTW distance in the Euclidean space. The proposed embedding scheme reduces the computational time of the k-nearest-neighbor search, and achieves a k-nearest-neighbor prediction up to 94% accuracy.

Abstract i
Contents ii
1 Introduction 1
2 Background and Related Works 4
2.1 Background Introduction to Gait Phases . . . . . . . . . . . . . . . . . . . . 4
2.2 Related Works on Gait Phase Segmentation . . . . . . . . . . . . . . . . . . 6
3 System Model 10
4 k-Nearest Neighbors with Weighted Dynamic Time Warping 12
4.1 Weighted Dynamic Time Warping . . . . . . . . . . . . . . . . . . . . . . . . 12
4.2 Weight Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 k-Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5 kNN-DistNet Graph Embedding 19
5.1 Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.3 Alternative Single-Task Embedding Schemes . . . . . . . . . . . . . . . . . . 26
5.3.1 Distance Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3.2 kNN Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 Data Collection and Preprocessing 29
6.1 Hardware Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Measurements and Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6.3 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
6.4 Gait Cycle Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 Experimental Result 35
8 Conclusion 45
Bibliography 46

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