對時間序列分類問題而言，測量兩條時間序列的相似度或距離是個很重要的問題。給定兩條時間序列 X 和 Y ，則動態時間校正 (DTW) 演算法可用來測量 X 與 Y 之間的距離。但 DTW 演算法可能會使 X 中的相鄰點與 Y 中相距甚遠的點相互對齊。這個情況會造成只取得高相似性但會失去其所擁有的代表性訊息的對齊方式。在這篇論文中，我們將提出彈性動態時間校正 (FDTW) 的方法用於測量兩條時間序列的相似度。我們的演算法將針對較長的連續一對一對應的片段額外加分。我們還提出不同的投票方案和行為知識空間 (BKS) 方法來建立分類組合。在我們的實驗當中顯示，我們的 FDTW 在提升分類的準確性上，確實是個關鍵的因素。而在分類組合的效能上，無論是投票方案或是BKS方法，都優於單一的方法。

Measuring the similarity or distance between two time series sequences is critical for the classification of a set of time series sequences. Given two time series sequences, X and Y, the dynamic time warping (DTW) algorithm can calculate the distance between X and Y. But the DTW algorithm may align some neighboring points in X to the corresponding points which are far apart in Y. This situation may cause that the alignment gets only a high alignment score, but it may lose its representative information. In this thesis, we propose the flexible dynamic time wrapping (FDTW) method for measuring the similarity of two time series sequences. Our algorithm adds an additional score as the reward for the long contiguous one-to-one segment. We also present the voting schemes and the behavior knowledge space (BKS) methods to construct classifier ensembles. As the experimental results show, our FDTW is indeed a crucial factor for improving the classification accuracy. The performance of a classifier ensemble, built by either voting or BKS, outperforms a single method.

論文審定書 i
DISSERTATION VERIFICATION FORM ii
謝誌 iii
摘要 iv
ABSTRACT v
LIST OF FIGURES viii
LIST OF TABLES x
Chapter 1. Introduction 1
Chapter 2. Preliminaries 5
2.1 The Longest Common Subsequence Problem 5
2.1.1 The Longest Common Subsequence Algorithms 6
2.1.2 The Flexible Longest Common Subsequence Problem 6
2.2 The Time Series Classification Problem 10
2.2.1 The Temporal-Proximity-Based Classification 11
2.2.2 The Representation-Based Classification 12
2.2.3 The Model-Based Classification 13
2.2.4 Other Methods 14
2.3 The Behavior Knowledge Space Method 14
Chapter 3. The Proposed Algorithm 16
Chapter 4. Experimental Results 20
4.1 Comparison with Other Algorithms 21
4.2 The Voting Strategies for Classification 24
4.3 Using Behavior Knowledge Space for Classification 25
Chapter 5. Conclusion 31
BIBLIOGRAPHY 32

H.-Y. Ann, C.-B. Yang, C.-T. Tseng, and C.-Y. Hor, “A fast and simple algorithm for computing the longest common subsequence of run-length encoded strings,” Information Processing Letters, Vol. 108, pp. 360–364, 2008.
P. S. Bidari, R. Manshaei, T. Lohrasebi, A. Feizi, M. A. Malboobi, and J. Alirezaie, “Time series gene expression data clustering and pattern extraction in arabidopsis thaliana phosphatase-encoding genes,” BioInformatics and BioEngineering, 2008. BIBE 2008. 8th IEEE International Conference on, pp. 1–6, Oct 2008.
K. Buza, A. Nanopoulos, and L. Schmidt-Thieme, “Time-series classification based on individualised error prediction,” Computational Science and Engi- neering (CSE), 2010 IEEE 13th International Conference on, pp. 48–54, Dec 2010.
Y. Chen, B. Hu, E. Keogh, and G. E. Batista, “Dtw-d: Time series semi- supervised learning from a single example,” Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, pp. 383–391, 2013.
S. Gao, Y. He, and H. Chen, “Wind speed forecast for wind farms based on arma-arch model,” Sustainable Power Generation and Supply, 2009. SUPER- GEN ’09. International Conference on, pp. 1–4, April 2009.
T. G´orecki, “Using derivatives in a longest common subsequence dissimilarity measure for time series classification,” Pattern Recognition Letters, Vol. 45, No. 0, pp. 99–105, 2014.
Y.-P. Guo, Y.-H. Peng, and C.-B. Yang, “Efficient algorithms for the flexible longest common subsequence problem,” Proceedings of the 31st Workshop on Combinatorial Mathematics and Computation Theory, Taipei, Taiwan, pp. 1–8, 2014.
L. Gupta, D. L. Molfese, R. Tammana, and P. G. Simos, “Nonlinear alignment and averaging for estimating the evoked potential,” Biomedical Engineering, IEEE Transactions on, Vol. 43, No. 4, pp. 348–356, April 1996.
D. S. Hirschberg, “A linear space algorithm for computing maximal common subsequences,” Communications of the ACM, Vol. 18, pp. 341–343, 1975.
C.-Y. Hor, Machine Learning Approaches for the Protein and RNA Sequence Analysis. PhD thesis, National Sun Yat-sen University, Kaohsiung, Taiwan, 2014.
K.-S. Huang, C.-B. Yang, K.-T. Tseng, H.-Y. Ann, and Y.-H. Peng, “Efficient algorithms for finding interleaving relationship between sequences,” Information Processing Letters, Vol. 105(5), pp. 188–193, 2008.
K.-S. Huang, C.-B. Yang, K.-T. Tseng, Y.-H. Peng, and H.-Y. Ann, “Dynamic programming algorithms for the mosaic longest common subsequence problem,” Information Processing Letters, Vol. 102, pp. 99–103, 2007.
X. Huang, H. liang Li, and L. Qiu, “Research on predicting agricultural drought based on fuzzy set and r/s analysis model,” Advanced Computer Theory and Engineering (ICACTE), 2010 3rd International Conference on, Vol. 2, pp. V2– 186–V2–189, Aug 2010.
Y. S. Huang and C. Y. Suen, “The behavior-knowledge space method for combination of multiple classifiers,” Computer Vision and Pattern Recognition, 1993. Proceedings CVPR ’93., 1993 IEEE Computer Society Conference on, pp. 347– 352, Jun 1993.
J. W. Hunt and T. G. Szymanski, “A fast algorithm for computing longest common subsequences,” Communications of the ACM, Vol. 20(5), pp. 350–353, 1977.
F. Itakura, “Minimum prediction residual principle applied to speech recognition,” Acoustics, Speech and Signal Processing, IEEE Transactions on, Vol. 23, No. 1, pp. 67–72, Feb 1975.
Y.-S. Jeong, M. K. Jeong, and O. A. Omitaomu, “Weighted dynamic time warping for time series classification,” Pattern Recognition, Vol. 44, No. 9, pp. 2231
2240, 2011.
D. Jixue, “Data mining of time series based on wave cluster,” Information Technology and Applications, 2009. IFITA ’09. International Forum on, Vol. 1, pp. 697–699, May 2009.
E. Keogh, Q. Zhu, B. Hu, Y. Hao, X. Xi, L. Wei, and C. A. Ratanamahatana, “The UCR time series classification/clustering homepage.” http://www.cs. ucr.edu/~eamonn/time_series_data/, 2011.
E. Keogh and S. Kasetty, “On the need for time series data mining bench- marks: A survey and empirical demonstration,” Data Mining and Knowledge Discovery, Vol. 7, No. 4, pp. 349–371, Oct. 2003.
E. J. Keogh and M. J. Pazzani, “Derivative dynamic time warping,” In First SIAM International Conference on Data Mining, 2001.
B. V. Kini and C. C. Sekhar, “Large margin mixture of ar models for time series classification,” Applied Soft Computing, Vol. 13, No. 1, pp. 361–371, 2013.
H. Kremer, S. Gunnemann, and T. Seidl, “Detecting climate change in multivariate time series data by novel clustering and cluster tracing techniques,” Data Mining Workshops (ICDMW), 2010 IEEE International Conference on, pp. 96–97, Dec 2010.
V. Kurbalija, M. Radovanovi´c, Z. Geler, and M. Ivanovi´c, “The influence of global constraints on dtw and lcs similarity measures for time-series databases,” Third International Conference on Software, Services and Semantic Technologies S3T 2011 (D. Dicheva, Z. Markov, and E. Stefanova, eds.), Vol. 101 of Advances in Intelligent and Soft Computing, pp. 67–74, Springer Berlin Heidel- berg, 2011.
J. Liu and S. Wu, “Research on longest common subsequence fast algorithm,” Consumer Electronics, Communications and Networks (CECNet), 2011 International Conference on, pp. 4338–4341, April 2011.
S. Nanda, B. Mahanty, and M. Tiwari, “Clustering indian stock market data for portfolio management,” Expert Systems with Applications, Vol. 37, No. 12, pp. 8793–8798, 2010.
Y.-H. Peng, C.-B. Yang, K.-S. Huang, C.-T. Tseng, and C.-Y. Hor, “Efficient sparse dynamic programming for the merged LCS problem with block constraints,” International Journal of Innovative Computing, Information and Control, Vol. 6, pp. 1935–1947, 2010.
Y.-H. Peng, C.-B. Yang, K.-S. Huang, and K.-T. Tseng, “An algorithm and applications to sequence alignment with weighted constraints,” International Journal of Foundations of Computer Science, Vol. 21, pp. 51–59, 2010.
T. Rakthanmanon, B. Campana, A. Mueen, G. Batista, B. Westover, Q. Zhu, J. Zakaria, and E. Keogh, “Searching and mining trillions of time series subsequences under dynamic time warping,” Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, pp. 262–270, 2012.
S. Rani and G. Sikka, “Recent techniques of clustering of time series data: A survey,” International Journal of Computer Applications, Vol. 52, No. 15, pp. 1–9, Aug 2012.
C. A. Ratanamahatana and E. Keogh, “Making time-series classification more accurate using learned constraints,” In proc. of SDM Intl Conf, pp. 11–22, 2004.
Sˇ. Raudys and F. Roli, “The behavior knowledge space fusion method: Analysis of generalization error and strategies for performance improvement,” Multiple Classifier Systems (T. Windeatt and F. Roli, eds.), Vol. 2709 of Lecture Notes in Computer Science, pp. 55–64, Springer Berlin Heidelberg, 2003.
H. Sakoe and S. Chiba, “Dynamic programming algorithm optimization for spoken word recognition,” Acoustics, Speech and Signal Processing, IEEE Transactions on, Vol. 26, No. 1, pp. 43–49, Feb 1978.
L. Suyi, Z. Hua, J. Jianping, and L. Bing, “Feature recognition for underwater weld images,” Control Conference (CCC), 2010 29th Chinese, pp. 2729–2734, July 2010.
G. Verdoolaege and Y. Rosseel, “Activation detection in event-related fmri through clustering ofwavelet distributions,” Image Processing (ICIP), 2010 17th IEEE International Conference on, pp. 4393–4396, Sept 2010.
M. Vlachos, J. Lin, E. Keogh, and D. Gunopulos, “A wavelet-based anytime algorithm for k-means clustering of time series,” In Proc. Workshop on Clustering High Dimensionality Data and Its Applications, pp. 23–30, 2003.
Q. Wang, D. Korkin, and Y. Shang, “A fast multiple longest common subsequence (mlcs) algorithm,” Knowledge and Data Engineering, IEEE Transactions on, Vol. 23, No. 3, pp. 321–334, March 2011.
J.-X. Wu and J.-L. Wei, “Combining ica with svr for prediction of finance time series,” Automation and Logistics, 2007 IEEE International Conference on, pp. 95–100, Aug 2007.
X. Xi, E. Keogh, C. Shelton, L. Wei, and C. A. Ratanamahatana, “Fast time series classification using numerosity reduction,” Proceedings of the 23rd International Conference on Machine Learning, ICML ’06, pp. 1033–1040, 2006.
X. Zhang, J. Liu, Y. Du, and T. Lv, “A novel clustering method on time series data,” Expert Systems with Applications, Vol. 38, No. 9, pp. 11891–11900, 2011.