時間序列分類問題的研究已有數十年，動態時間校正 (DTW) 演算法提供了強大的方法用於測量兩條時間序列的距離，但是DTW演算法並非適合所有種類的時間序列問題。

2014年，彭永興博士和楊昌彪教授定義可變間隔最長共同子序列 (VGLCS)問題，VGLCS是最長共同子序列 (LCS) 的變形並加入間隔 (gap) 的限制，而我們改造VGLCS演算法提出了可變間隔最長共同子序列相似性測量 (VGS) 演算法，將VGLCS演算法應用於測量兩條由實數所組成的時間序列之間的相似度，另外，我們提出了一個訓練方法來獲得合適的間隔限制及參數用於VGS演算法，然後，我們用VGS演算法來處理時間序列分類問題，除此之外，為了降低錯誤率，我們應用行為知識空間 (BKS)方法來結合三個分類器的結果，包括DDTW (微分動態時間校正)、DTWW (彎曲窗口動態時間校正)、LCS/VGS，建立出一個分類器。在實驗中，我們使用UCR網站所提供的資料集進行實驗，實驗結果顯示，相較於先前知名的DTWW方法，對於較小的資料集，BKS方法改進錯誤率的幅度大約21%~22%，對於較大的資料集，BKS方法改進錯誤率的幅度大約17%。

The time series classification problem has been studied for decades. The dynamic time warping (DTW) algorithm provides a powerful way to measure the distance between two time series. However, the DTW algorithm may not be suitable for all time series of various types.

In 2014, Peng and Yang defined the variable gap longest common subsequence (VGLCS) problem, which is a variant of the longest common subsequence (LCS) problem with gap constraints. With slight modification on the VGLCS algorithm, we propose an algorithm of the variable gap LCS similarity measurement (VGS) for measuring the similarity of two time series consisting of real numbers. We propose a training approach to get proper gap constraints and the parameters for the VGS algorithm. Then, we use the VGS algorithm for solving the time series classification problems. In addition, to reduce the error rates, we apply the behavior knowledge space (BKS) method to build ensemble classifiers by combining three classifiers, including DDTW (derivative dynamic time warping), DTWW (DTW with warping window) and LCS/VGS. The datasets for experiments are obtained from the UCR web site. The experimental results show that the BKS method improves the error rate about 21%~22% on small datasets, and about 17% on large datasets, over the previously best-known DTWW method.

論文審定書 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
THESIS VERIFICATION FORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
謝辭 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . v
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 The Longest Common Subsequence Problem . . . . . . . . . . . . . . 5
2.2 The Variable Gap Longest Common Subsequence Problem . . . . . . 6
2.3 Time Series Classification . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 The Temporal-Proximity-Based Classification . . . . . . . . . 7
2.3.2 The Representation-Based Classification . . . . . . . . . . . . 10
2.3.3 The Model-Based Classification . . . . . . . . . . . . . . . . . 10
2.3.4 Other Classification Methods . . . . . . . . . . . . . . . . . . 11
2.4 The Behavior Knowledge Space Method . . . . . . . . . . . . . . . . 11
Chapter 3. The Proposed Algorithm . . . . . . . . . . . . . . . . . . . . 13
3.1 The Variable Gap LCS Similarity Measurement Algorithm . . . . . . 13
3.2 Training Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 4. Experimental Results . . . . . . . . . . . . . . . . . . . . . . 22
4.1 Performance Comparison of Various Algorithms . . . . . . . . . . . . 25
4.2 Classification with Behavior Knowledge Space . . . . . . . . . . . . . 37
Chapter 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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