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Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)Phát hiện chuỗi bất thường trên dữ liệu chuỗi thời gian (Luận văn thạc sĩ)
HỌC VIỆN CƠNG NGHỆ BƯU CHÍNH VIỄN THƠNG - Huỳnh Cẩm PHÁT HIỆN CHUỖI BẤT THƯỜNG TRÊN DỮ LIỆU CHUỖI THỜI GIAN LUẬN VĂN THẠC SĨ KỸ THUẬT (Theo định hướng ứng dụng) THÀNH PHỐ HỒ CHÍ MINH – 2018 HỌC VIỆN CƠNG NGHỆ BƯU CHÍNH VIỄN THƠNG - Huỳnh Cẩm PHÁT HIỆN CHUỖI BẤT THƯỜNG TRÊN DỮ LIỆU CHUỖI THỜI GIAN CHUYÊN NGÀNH : HỆ THỐNG THÔNG TIN MÃ SỐ : 8480104 LUẬN VĂN THẠC SĨ KỸ THUẬT (Theo định hướng ứng dụng) NGƯỜI HƯỚNG DẪN KHOA HỌC TS DƯƠNG THỊ THÙY VÂN THÀNH PHỐ HỒ CHÍ MINH – 2018 i LỜI CAM ĐOAN Tơi cam đoan cơng trình nghiên cứu riêng Các số liệu, kết nêu luận văn trung thực chưa cơng bố cơng trình khác Việc tham khảo từ cơng trình, nguồn tài liệu khác trích dẫn yêu cầu Tp Hồ Chí Minh, ngày 16 tháng 05 năm 2018 Học viên thực luận văn Huỳnh Cẩm ii LỜI CẢM ƠN Tôi xin gởi lời cảm ơn chân thành sâu sắc đến TS Dương Thị Thuỳ Vân tận tình hướng dẫn, động viên, giúp đỡ tơi nhiều suốt q trình thực luận văn, Cơ đóng góp ý kiến tạo điều kiện tốt để tơi hồn thành luận văn Tơi xin cảm ơn quý Thầy, Cô trường Học Viện Công Nghệ Bưu Chính Viễn Thơng sở Tp.Hồ Chí Minh dạy dỗ, truyền đạt nhiều kiến thức cần thiết q trình học tập Tơi xin cảm ơn Cha, Mẹ, gia đình, bạn bè đồng nghiệp ln động viên, khích lệ tạo điều kiện thuận lợi giúp tơi hồn thành luận văn Mặc dù cố gắng song luận văn không tránh khỏi thiếu sót Tơi mong nhận ý kiến đóng góp Thầy Cơ để tơi hồn thiện đề tài Xin trân trọng cảm ơn Tp Hồ Chí Minh, ngày 16 tháng 05 năm 2018 Học viên thực luận văn Huỳnh Cẩm iii MỤC LỤC CHƯƠNG – TỔNG QUAN .4 1.1 Giới thiệu 1.1.1 Dữ liệu chuỗi thời gian 1.1.2 Các loại liệu chuỗi thời gian 1.1.3 Các toán liệu chuỗi thời gian 1.2 Tổng quan toán phát chuỗi bất thường 1.3 Những khó khăn thách thức 10 1.3.1 Những thách thức nghiên cứu liệu chuỗi thời gian .10 1.3.2 Những thách thức toán phát chuỗi bất thường 10 1.4 Mục tiêu nghiên cứu 11 1.5 Đối tượng phạm vi nghiên cứu 11 1.5.1 Đối tượng nghiên cứu: 11 1.5.2 Phạm vi nghiên cứu: 11 1.6 Phương pháp nghiên cứu 12 CHƯƠNG - CƠ SỞ LÝ THUYẾT 13 2.1 Thu giảm số chiều chuỗi thời gian .13 2.2 Rời rạc hóa chuỗi thời gian 14 2.3 Các kỹ thuật phát bất thường 16 2.3.1 Dựa vào cửa sổ trượt (Window based) 16 2.3.2 Dựa vào tương tự (Proximity based) 19 2.3.3 Dựa vào dự đoán 20 2.3.4 Dựa vào mơ hình Markov ẩn 21 2.3.5 Dựa vào phân đoạn 22 2.4 Một số khái niệm 23 iv 2.4.1 Chuỗi thời gian (Time series) .23 2.4.2 Chuỗi (Subsequence) 23 2.4.3 Cửa sổ trượt (Slide windows) .24 2.4.4 Trùng khớp (Match) 24 2.4.5 Trùng khớp không tầm thường (Non-Self Match) 24 2.4.6 Mật độ có trọng số (weighted density) 24 2.5 Giải thuật phát chuỗi bất thường 25 2.5.1 Giải thuật Brute force 25 2.5.2 Giải thuật phát chuỗi bất thường Heuristic 26 CHƯƠNG – GIẢI THUẬT VÀ THỰC NGHIỆM .28 3.1 Đặt vấn đề 28 3.2 Hướng giải vấn đề 29 3.2.1 Thu giảm số chiều theo phép biến đổi PAA 29 3.2.2 Rời rạc hóa liệu theo phép biến đổi SAX 29 3.2.3 Xây dựng giải thuật đề xuất dựa giải thuật HOTSAX 29 3.3 Dữ liệu thực nghiệm 32 3.4 Thiết lập thực nghiệm .33 3.5 Kết thực nghiệm đánh giá .34 KẾT LUẬN VÀ HƯỚNG PHÁT TRIỂN 44 DANH MỤC TÀI LIỆU THAM KHẢO 46 PHỤ LỤC – BÀI BÁO KHOA HỌC ĐÃ CÔNG BỐ 50 PHỤ LỤC – TẬP DỮ LIỆU ECG 58 v DANH SÁCH BẢNG Bảng 2.1: Giá trị hop thay đổi, kích thước cửa sổ cố định 17 Bảng 2.2: Thuật tốn tìm chuỗi bất thường Brute force 26 Bảng 2.3: Giải thuật phát chuỗi bất thường Heuristic .26 Bảng 3.1: Tính mật độ có trọng số cho chuỗi .30 Bảng 3.2: Giải thuật phát chuỗi bất thường dựa Heuristics .31 Bảng 3.3: Đặc điểm tập liệu thực nghiệm .32 Bảng 3.4: Cố định giá trị w = 5, thay đổi giá trị a tập liệu VIDEO 35 Bảng 3.5: Cố định giá trị w=5, thay đổi giá trị a tập liệu ECG 36 Bảng 3.6: Cố định giá trị w=5, thay đổi giá trị a tập liệu POWER 37 Bảng 3.7: Cố định giá trị w=5 thay đổi giá trị a tập liệu PATIENT 38 Bảng 3.8: Cố định giá trị w=10, thay đổi giá trị a tập liệu SpaceShuttle .39 Bảng 3.9: Cố định giá trị a, thay đổi giá trị w tập liệu VIDEO 40 Bảng 3.10: Cố định giá trị a, thay đổi giá trị w tập liệu ECG 40 Bảng 3.11: Cố định giá trị a, thay đổi giá trị w tập liệu POWER 41 Bảng 3.12: Cố định giá trị a, thay đổi giá trị w tập liệu PATIENT 41 Bảng 3.13: Cố định giá trị a, thay đổi giá trị w tập liệu SpaceShuttle 42 vi DANH SÁCH HÌNH VẼ Hình 1.1: Đường biểu diễn chuỗi thời gian Hình 1.2: Chuỗi thời gian tuần hồn – đồng Hình 1.3: Chuỗi thời gian khơng tuần hồn – đồng .5 Hình 1.4: Chuỗi thời gian tuần hồn – khơng đồng .6 Hình 1.5: Chuỗi thời gian khơng tuần hồn – khơng đồng Hình 2.1: Phương pháp biểu diễn PAA với N = 128, m = ([31]) 14 Hình 2.2: Hình minh hoạ phương pháp SAX với a = 15 Hình 2.3: Một chuỗi thời gian bất thường (màu đỏ), chuỗi thời gian bình thường (màu xanh) Chuỗi bất thường bỏ qua chu kỳ cuối (vùng bất thường) 19 Hình 3.1: Hướng giải vấn đề 29 Hình 3.2: Chuỗi bất thường tập liệu VIDEO 35 Hình 3.3: Chuỗi bất thường tập liệu ECG 36 Hình 3.4: Chuỗi bất thường tập liệu POWER 37 Hình 3.5: Chuỗi bất thường tập liệu PATIENT .38 Hình 3.6: Chuỗi bất thường tập liệu SpaceShuttle 39 MỞ ĐẦU Dữ liệu chuỗi thời gian liệu đo đạc cách theo thời gian Có nhiều loại liệu có yếu tố thời gian vậy, ví dụ liệu điện tâm đồ, liệu thiên văn, thời tiết, mực nước, liệu tài chính, giá chứng khốn, … Một nghiên cứu khảo sát hướng nghiên cứu quan trọng thách thức lĩnh vực khai phá liệu học máy thực vào năm 2006 Yang Wu [1] cho kết 10 hướng nghiên cứu Trong đó, hướng nghiên cứu khai phá liệu chuỗi thời gian xếp thứ 10 hướng nghiên cứu quan trọng thách thức Do đó, việc khai phá liệu chuỗi thời gian thu hút nhiều quan tâm nghiên cứu giới Các tốn điển hình khai phá liệu chuỗi thời gian bao gồm: Lập mục (Indexing), Gom cụm (Clustering), Phân lớp (Classificaition), Tổng hợp (Summarization), Phát Motif (Motif detection), Phát chuỗi bất thường (Anomaly detection) Khai phá liệu chuỗi thời gian ứng dụng rộng rãi nhiều lĩnh vực y học, kinh tế, tài chính, chứng khốn, quản lý mạng truyền thông, … Các lĩnh vực nghiên cứu y học dịch vụ tài chính, … thường cần độ xác cao Trong đó, chuỗi bất thường liệu chuỗi thời gian thường ảnh hưởng nhiều đến kết khai phá liệu Vì việc xác định chuỗi bất thường liệu chuỗi thời gian đóng vai trò quan trọng thường dùng bước tiền xử lý cho toán khai phá liệu chuỗi thời gian Sau số ứng dụng quan trọng toán phát chuỗi bất thường liệu chuỗi thời gian [2]: - Phát bất thường xung nhịp tim liệu điện tim ECG [3], [4]: thông thường liệu điện tim ECG chuỗi thời gian tuần hoàn ghi lại biến thiên điện lực tim phát hoạt động co Một bất thường liệu mẫu khơng phù hợp (nonconforming pattern) mặt chu kỳ biên độ, điều có vấn đề sức khỏe - Phát công hệ thống tư vấn (recommender system): công Shilling, kẻ cơng đưa xếp hạng, đánh giá có thiên vị để ảnh hưởng đến tư vấn, gợi ý tương lai [5] - Phát bất thường chuyến bay sử dụng liệu cảm biến từ máy báy: hành vi hệ thống chuyến bay thể liệu cảm biến thông qua thông số khác Các thông số có giá trị thay đổi suốt trình bay Nếu liệu cảm biến có chuỗi bất thường hành vi hệ thống chuyến bay có sai lệch, cần cảnh báo [6] - Phát bất thường hình dạng: Tìm hình dạng khác biệt với hình dạng khác, với hình dạng chuyển thành chuỗi thời gian [7], [8], [9] Trong lĩnh vực khai phá liệu y học, cho hình dạng số chủng loại, hình dạng khác với hình dạng lại cho thấy bất thường biến đổi gen tạo - Phát đường cong ánh sáng bất thường danh mục có độ sáng biến đổi tuần hồn: phát bất thường ngơi có độ sáng biến đổi tuần hoàn Các bất thường tương ứng với số khác biệt vật lý bên trong, chẳng hạn thay đổi chu kỳ biên độ, thể qua độ nhiễu đường cong ánh sáng [10], [11] - Phát thay đổi hệ sinh thái cách sử dụng liệu khoa học trái đất sinh trưởng thực vật hay nhiệt độ [12] Với phân tích trên, tốn phát chuỗi bất thường thu hút quan tâm đáng kể cộng đồng nghiên cứu từ thập niên 1980 Các nhóm nghiên cứu [13], [14], [1], [15], [16], [17], [3], [4] định nghĩa nhiều loại chuỗi bất thường khác outlier, anomaly, unusual, discord, … đề xuất nhiều phương pháp phát chuỗi bất thường Trong đó, phương pháp phát chuỗi bất thường discord (discord discovery) Keogh et al [14] giới thiệu từ năm 2005 gần nhóm [18], [19], [20], [17], [21] tập trung nghiên cứu Luận văn tập trung nghiên cứu phương pháp phát chuỗi bất thường liệu chuỗi thời gian Từ đó, luận văn đề xuất phương pháp phát chuỗi bất thường discord dựa vào cửa sổ trượt (Window) 56 SpaceShuttle dataset VIDEO dataset ECG dataset POWER dataset PATIENT dataset Figure 3: Running time (on vertical axis) of each algorithm on each dataset: Keep alphabet size a unchanged and increase the word size w (on horizontal axis) VIDEO dataset ECG dataset POWER dataset PATIENT dataset SpaceShuttle dataset Figure 4: Number distance function calls (on vertical axis) of each algorithm on each dataset: Keep alphabet size a unchanged and increase the word size w (on horizontal axis) The results shown above in Group suggest that the proposed algorithm has much more efficient runtime than the HOT SAX algorithm, especially when w is small As the w increases, the running time of our algorithm increases, too According to line and in Table 2, our algorithm’s running cost depends on w, the smaller the value of w is, the more efficient our algorithm is Unlike our method, the running time of the HOT SAX does not linearly increase when w rises In terms of memory cost, our algorithm is more efficient than HOT SAX As presented in Table 2, our algorithm just uses four arrays to store the computed value for E(Ci), W(Ci), DenCj(xi) and WDen(xi) to make heuristic for the next step Three of them have size of w and the other has size of (m-n+1) which is the number of subsequences When w is small, most of space we need for preprocessing is nearly an array of (m-n+1), whereas HOT SAX is much more expensive due to using an array and a trie for considering subsequences in two nested loops General formula to compute space for HOT SAX is (m-n+1)*w Therefore, our algorithm reduces space to one wth times compared to HOT SAX Conclusion and Future Works In this work, we propose an information theory-based approach to solving the problem of discord discovery in time series with detailed analysis of its efficiency for the metrics of running time, the number of calls to distance function and the memory cost compared to HOT SAX Our method is evaluated more efficient on both running cost and memory cost than HOT SAX while guaranteeing to produce identical results even though our number of calls to distance function are a bit higher than HOT SAX in some cases Furthermore, the parameter selection in our algorithm is easier due to the simplicity and the data independence of the method In the future, we are working in the extension of our algorithm in many directions Firstly, we will apply some other time series discretization methods in our algorithm that is free-parameter in order to make it more efficiently Secondly, we may modify the formula of weighted density to make better heuristic for two nested loops Finally yet importantly, we will extend our work on data streams, which is the most challenging problem recently REFERENCES [1] D Hawkins, Identification of Outliers, Chapman and Hall, London, 1980 57 [2] V Chandola, A Banerjee and V Kumar, Outlier Detection: A Survey, Technical Report 07-017, University of Minnesota, 2007 [3] Z Y He, S C Deng and X F Xu, An optimization model for outlier detection in categorical data, Proc of 2005 International Conference on Advances in Intelligent Computing, Hefei, pp.400-409, 2005 [4] Z Y He, S C Deng and X F Xu, A fast greedy algorithm for outlier mining, Proc of 10th Pacific Asia Conference on Knowledge and Data Discovery, pp.567-576, 2006 [5] S Wu and S Wang, Information-Theoretic Outlier Detection for Large-Scale Categorical Data, IEEE Transactions on Knowledge Engineering and Data Engineering, vol.25, no.3, pp.589-602, 2013 [6] X W Zhao, J Y Liang and F Y Cao, A simple and effective outlier detection algorithm for categorical data, International Journal of Machine Learning Cybernet, vol.5, no.3, pp.469-477, 2014 [7] E Keogh, J Lin and A Fu, HOT SAX: Efficiently Finding the Most Unusual Time Series Subsequence, Proc of 5th IEEE International Conference on Data Mining (ICDM), pp.226-233, 2005 [8] E Keogh, J Lin and H V Herle, Finding unusual medical time-series subsequences: algorithms and applications, IEEE Transactions on Information Technology in Biomedicine, vol.10, no.3, pp.429-439, 2006 [9] E Keogh et al., Finding the most unusual time series subsequence: algorithms and applications Knowledge and Information Systems, vol.11, no.1, pp.1-27, 2007 [10] N H Kha, D T Anh, From cluster-based outlier detection to time series discord discovery, Trends and Applications in Knowledge Discovery and Data Mining, pp.16-28, 2015 [11] Y Bu et al., WAT: finding Top-K discords in time series database, Proc of the 2007 SIAM International Conference on Data Mining, Minneapolis, USA, 2007 [12] L V Q Anh et al., Vector Quantization: A Discretization Technique for Fast Time Series Discord Discovery, The NAFOSTED Conference on Information and Computer Science 2015 (NICS’15), 2015 [13] J Lin et al., A symbolic representation of time series with implications for streaming algorithms, Proc.of 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discover (DMKD 2003), pp.2-11, 2003 [14] E Keogh, www.cs.ucr.edu/~eamonn/discords/ (accessed on December, 2017) 58 PHỤ LỤC – TẬP DỮ LIỆU ECG 4.88E+00 4.89E+00 4.87E+00 4.85E+00 4.84E+00 4.91E+00 5.01E+00 4.80E+00 4.49E+00 4.35E+00 4.69E+00 4.90E+00 4.93E+00 4.96E+00 4.94E+00 4.97E+00 4.99E+00 5.00E+00 5.08E+00 5.07E+00 5.08E+00 5.08E+00 5.06E+00 4.98E+00 4.97E+00 4.95E+00 4.93E+00 4.94E+00 4.88E+00 4.94E+00 4.88E+00 4.86E+00 4.83E+00 4.80E+00 4.82E+00 4.82E+00 4.84E+00 4.87E+00 4.84E+00 4.80E+00 4.87E+00 4.87E+00 4.85E+00 4.85E+00 4.86E+00 4.84E+00 4.92E+00 4.88E+00 4.92E+00 4.95E+00 5.06E+00 5.04E+00 4.82E+00 4.81E+00 4.85E+00 4.89E+00 4.86E+00 4.85E+00 4.86E+00 4.89E+00 4.87E+00 4.96E+00 4.78E+00 4.41E+00 4.39E+00 4.76E+00 4.91E+00 4.90E+00 4.94E+00 4.94E+00 4.99E+00 5.00E+00 5.02E+00 5.04E+00 5.07E+00 5.07E+00 5.09E+00 5.08E+00 4.97E+00 4.95E+00 4.96E+00 4.95E+00 4.93E+00 4.89E+00 4.97E+00 4.85E+00 4.85E+00 4.82E+00 4.80E+00 4.81E+00 4.82E+00 4.85E+00 4.89E+00 4.84E+00 4.80E+00 4.86E+00 4.87E+00 4.83E+00 4.88E+00 4.86E+00 4.84E+00 4.93E+00 4.88E+00 4.92E+00 4.98E+00 5.05E+00 5.03E+00 4.80E+00 4.82E+00 4.83E+00 4.88E+00 4.86E+00 4.87E+00 4.89E+00 4.89E+00 4.81E+00 4.88E+00 4.72E+00 4.37E+00 4.46E+00 4.87E+00 4.90E+00 4.89E+00 4.92E+00 4.93E+00 4.98E+00 4.99E+00 5.00E+00 5.03E+00 5.07E+00 5.07E+00 5.10E+00 5.04E+00 4.98E+00 4.94E+00 4.94E+00 4.97E+00 4.93E+00 4.88E+00 4.95E+00 4.85E+00 4.84E+00 4.82E+00 4.82E+00 4.81E+00 4.82E+00 4.85E+00 4.88E+00 4.84E+00 4.85E+00 4.84E+00 4.84E+00 4.83E+00 4.89E+00 4.88E+00 4.84E+00 4.90E+00 4.86E+00 4.90E+00 5.04E+00 5.09E+00 5.00E+00 4.82E+00 4.80E+00 4.82E+00 4.86E+00 4.86E+00 4.91E+00 4.88E+00 4.86E+00 4.80E+00 4.83E+00 4.66E+00 4.34E+00 4.51E+00 4.94E+00 4.90E+00 4.89E+00 4.91E+00 4.95E+00 4.97E+00 4.99E+00 4.98E+00 5.02E+00 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4.74E+00 4.84E+00 4.77E+00 4.78E+00 4.76E+00 4.80E+00 4.79E+00 4.82E+00 4.81E+00 4.80E+00 4.79E+00 4.84E+00 4.82E+00 5.01E+00 5.03E+00 4.86E+00 4.77E+00 4.72E+00 4.77E+00 4.79E+00 4.77E+00 4.76E+00 4.82E+00 4.62E+00 4.42E+00 4.22E+00 4.54E+00 4.78E+00 4.82E+00 4.87E+00 4.89E+00 4.88E+00 4.90E+00 4.91E+00 4.93E+00 4.95E+00 5.00E+00 5.01E+00 4.99E+00 4.95E+00 4.94E+00 4.92E+00 4.92E+00 4.87E+00 4.97E+00 4.94E+00 4.91E+00 4.87E+00 4.87E+00 4.83E+00 4.86E+00 4.84E+00 4.81E+00 4.76E+00 4.76E+00 4.78E+00 4.76E+00 4.75E+00 4.79E+00 4.79E+00 4.77E+00 4.79E+00 4.82E+00 4.78E+00 4.80E+00 4.81E+00 4.81E+00 4.81E+00 4.89E+00 4.84E+00 5.00E+00 5.03E+00 4.82E+00 4.79E+00 4.77E+00 4.77E+00 4.79E+00 4.75E+00 4.76E+00 4.83E+00 4.61E+00 4.35E+00 4.24E+00 4.56E+00 4.78E+00 4.84E+00 4.88E+00 4.89E+00 4.86E+00 4.91E+00 4.88E+00 4.93E+00 4.97E+00 5.00E+00 5.00E+00 4.99E+00 4.93E+00 4.93E+00 4.92E+00 4.92E+00 4.86E+00 4.94E+00 4.93E+00 4.90E+00 4.89E+00 4.86E+00 4.84E+00 4.86E+00 4.84E+00 4.78E+00 4.75E+00 4.78E+00 4.79E+00 4.75E+00 4.78E+00 4.76E+00 4.80E+00 4.78E+00 4.81E+00 4.82E+00 4.78E+00 4.76E+00 4.81E+00 4.83E+00 4.84E+00 4.93E+00 4.88E+00 4.99E+00 5.02E+00 4.80E+00 4.79E+00 4.79E+00 4.76E+00 4.77E+00 4.74E+00 4.77E+00 4.79E+00 4.62E+00 4.29E+00 4.26E+00 4.60E+00 4.81E+00 4.85E+00 4.86E+00 4.86E+00 4.87E+00 4.92E+00 4.91E+00 4.95E+00 5.00E+00 5.01E+00 4.99E+00 4.99E+00 4.96E+00 4.93E+00 4.92E+00 4.91E+00 4.84E+00 4.90E+00 4.91E+00 4.89E+00 4.89E+00 4.86E+00 4.86E+00 4.85E+00 4.83E+00 4.80E+00 4.77E+00 4.79E+00 4.77E+00 4.74E+00 4.80E+00 4.76E+00 4.81E+00 4.79E+00 4.81E+00 4.80E+00 4.78E+00 4.75E+00 4.82E+00 4.82E+00 4.83E+00 4.94E+00 4.90E+00 4.98E+00 5.01E+00 4.79E+00 4.76E+00 4.80E+00 4.75E+00 4.76E+00 4.73E+00 4.79E+00 4.71E+00 4.57E+00 4.25E+00 4.30E+00 4.65E+00 4.84E+00 4.87E+00 4.85E+00 4.86E+00 4.86E+00 4.94E+00 4.92E+00 4.96E+00 5.00E+00 5.01E+00 4.97E+00 5.01E+00 5.00E+00 4.94E+00 4.89E+00 4.90E+00 4.83E+00 4.90E+00 4.87E+00 4.89E+00 4.91E+00 4.89E+00 4.86E+00 4.83E+00 4.81E+00 4.81E+00 4.79E+00 4.78E+00 4.78E+00 4.74E+00 4.80E+00 4.78E+00 4.83E+00 4.78E+00 4.79E+00 4.78E+00 4.79E+00 4.78E+00 4.80E+00 4.80E+00 4.79E+00 4.90E+00 4.93E+00 4.99E+00 5.00E+00 4.77E+00 4.73E+00 4.77E+00 4.74E+00 4.76E+00 4.74E+00 4.83E+00 4.64E+00 4.50E+00 4.23E+00 4.34E+00 4.72E+00 4.85E+00 4.87E+00 4.85E+00 4.88E+00 4.86E+00 4.96E+00 4.95E+00 4.97E+00 5.00E+00 5.00E+00 4.97E+00 5.02E+00 5.00E+00 4.93E+00 4.87E+00 4.89E+00 4.83E+00 70 4.84E+00 4.88E+00 4.89E+00 4.82E+00 4.92E+00 4.92E+00 5.65E+00 6.13E+00 5.28E+00 4.85E+00 4.63E+00 4.58E+00 4.58E+00 4.52E+00 4.47E+00 4.43E+00 4.39E+00 4.40E+00 4.35E+00 4.43E+00 4.47E+00 4.52E+00 4.66E+00 4.83E+00 4.91E+00 5.02E+00 4.82E+00 4.78E+00 4.81E+00 4.81E+00 4.84E+00 4.84E+00 4.85E+00 4.86E+00 4.88E+00 4.88E+00 4.81E+00 4.92E+00 4.95E+00 5.81E+00 6.08E+00 5.20E+00 4.78E+00 4.56E+00 4.60E+00 4.57E+00 4.51E+00 4.47E+00 4.43E+00 4.40E+00 4.39E+00 4.34E+00 4.42E+00 4.47E+00 4.55E+00 4.70E+00 4.84E+00 4.91E+00 5.00E+00 4.78E+00 4.76E+00 4.83E+00 4.83E+00 4.83E+00 4.83E+00 4.87E+00 4.86E+00 4.87E+00 4.88E+00 4.82E+00 4.94E+00 5.02E+00 5.96E+00 6.07E+00 5.16E+00 4.68E+00 4.50E+00 4.59E+00 4.56E+00 4.49E+00 4.45E+00 4.44E+00 4.40E+00 4.38E+00 4.35E+00 4.42E+00 4.48E+00 4.58E+00 4.72E+00 4.88E+00 4.91E+00 4.93E+00 4.75E+00 4.77E+00 4.84E+00 4.82E+00 4.82E+00 4.83E+00 4.87E+00 4.85E+00 4.87E+00 4.82E+00 4.92E+00 5.07E+00 6.08E+00 5.99E+00 5.15E+00 4.62E+00 4.50E+00 4.58E+00 4.54E+00 4.49E+00 4.46E+00 4.46E+00 4.39E+00 4.37E+00 4.37E+00 4.42E+00 4.50E+00 4.60E+00 4.75E+00 4.88E+00 4.93E+00 4.90E+00 4.76E+00 4.78E+00 4.83E+00 4.80E+00 4.83E+00 4.83E+00 4.86E+00 4.85E+00 4.88E+00 4.84E+00 4.90E+00 5.17E+00 6.16E+00 5.86E+00 5.10E+00 4.62E+00 4.52E+00 4.57E+00 4.53E+00 4.50E+00 4.46E+00 4.43E+00 4.38E+00 4.37E+00 4.38E+00 4.43E+00 4.51E+00 4.60E+00 4.78E+00 4.85E+00 4.96E+00 4.89E+00 4.78E+00 4.77E+00 4.79E+00 4.81E+00 4.82E+00 4.86E+00 4.86E+00 4.87E+00 4.86E+00 4.87E+00 4.89E+00 5.28E+00 6.20E+00 5.65E+00 4.99E+00 4.67E+00 4.55E+00 4.57E+00 4.53E+00 4.50E+00 4.46E+00 4.42E+00 4.38E+00 4.37E+00 4.40E+00 4.45E+00 4.51E+00 4.62E+00 4.79E+00 4.87E+00 4.98E+00 4.89E+00 4.78E+00 4.78E+00 4.79E+00 4.81E+00 4.83E+00 4.87E+00 4.87E+00 4.89E+00 4.84E+00 4.91E+00 4.89E+00 5.46E+00 6.17E+00 5.44E+00 4.91E+00 4.68E+00 4.56E+00 4.58E+00 4.54E+00 4.48E+00 4.44E+00 4.40E+00 4.39E+00 4.36E+00 4.41E+00 4.46E+00 4.53E+00 4.63E+00 4.80E+00 4.89E+00 5.01E+00 4.86E+00 4.78E+00 4.79E+00 4.79E+00 4.83E+00 4.84E+00 4.87E+00 ... phát chuỗi thời gian bất thường chuỗi bất thường chuỗi thời gian Vì tồn chuỗi thời gian chia thành chuỗi nhỏ nên dễ dàng xác định có chuỗi bất thường Nếu toàn chuỗi thời gian bất thường tất chuỗi. .. lượng hành vi bất thường quan sát chuỗi thời gian nên phát tất loại bất thường: quan sát bất thường chuỗi thời gian, chuỗi bất thường chuỗi thời gian hay toàn chuỗi thời gian bất thường 2.3.5... hóa chuỗi thời gian, kỹ thuật phát chuỗi bất thường liệu chuỗi thời gian giải thuật phát chuỗi bất thường 2.1 Thu giảm số chiều chuỗi thời gian Các chuỗi thời gian thực tế thường có số điểm liệu