時間序列集群演算法在許多科學領域得到了廣泛的研究，特別是對於過去十年的交通流量預測問題。最近，在2015年提出了一種稱為TADPole的基於密度的時間序列集群演算法，其性能優於所有其他方法。既使TADPole在大多數測試用例中表現良好，但其輸出分群結果的精準度仍有改進空間以及其選定為群中心的品質。
在本研究中，我們提出了一種快速且準確的時間序列集群演算法，Density Peak via Center Selection (DPCS)，我們透過更精準的群心選擇來保留各群的特性在這些群心中。此外，我們根據所需的各資料分佈的屬性構建輸出集群。實驗結果表明DPCS對於大量集群具有高度有效性，即使在處理群集之間具有明顯不同密度時也是如此。特別地，我們顯示DPCS在輸出群集和集群中心都比TADPole更準確，同時保持了與TADPole類似的運行時間。從實務的角度，我們提出的DPCS演算法可以很好的處理時間序列預測問題的應用。

Time series clustering algorithms have been widely studied in many scientific areas, especially for the traffic flow prediction problem in past decade. Very recently, a density-based time series clustering algorithm, called TADPole, which outperforms all the other approaches, was proposed in 2015. Although TADPole performs well in most of the test cases, there is still room for improvement in precision of its output clusters and the quality of the selected centers.
　In this study, we propose a fast and more accurate time series clustering algorithm,
Density Peak via Center Selection (DPCS), which selects centers that can hold features of the cluster data. Moreover, we construct the output clusters according to the required properties. Experimental results demonstrate the effectiveness of DPCS for a large number of clusters, even when dealing with clusters with significantly different densities. In particular, we show that DPCS is more accurate than TADPole in both output clusters and cluster centers while maintaining similar running time of TAD-Pole. From a practical perspective, the proposed DPCS algorithm can obviously find many applications of time series forecasting problems.

Contents
摘要 I
Abstract II
誌謝 III
Contents IV
List of Figures and Tables V
1 Introduction 1
1.1 Motivation 1
1.2 Prior work 2
1.2 Our contribution 3
2 DTW and TADPole Revisited 6
2.1 Multi-dimensional DTW 6
2.2 Lower bound of multi-dimensional DTW 7
2.3 Procedures of TADPole 8
3 DPCS: Density Peak via Center Selection 12
3.1 Algorithm 12
3.2 Comparison with the TADPole algorithm 14
3.3 Assignment strategies 17
4 Experimental Evaluation 19
4.1 Evaluation of the algorithm 19
4.2 Cluster centers evaluation 25
4.3 Parameter sensitivity of DPCS 26
4.4 Discussion 27
5 Real-world Case Study: Traffic Network 28
5.1 Similar time series patterns 28
5.2 Correlation between pattern and traffic situation 31
6 Conclusion 33
Reference 33

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