Abstract Effective and concise feature representation is crucial for time series mining. However, traditional time series feature representation approaches are inadequate for Financial Time Series (FTS) due to FTS' complex, highly noisy, dynamic and non- linear characteristics. Thus, we proposed an improved linear segmentation method named MS-BU-GA in this work. The critical data points that can represent financial time series are added to the feature representation result. Specifically, firstly, we propose a division criterion based on the quantile segmentation points. On the basis of this criterion, we perform segmentation of the time series under the constraint of the maximum segment fitting error. Then, a bottom-up mechanism is adopted to merge the above segmentation results under the maximum segment fitting error. Next, we apply Genetic Algorithm (GA) to the merged results for further optimization, which reduced the overall segment representation fitting error and the integrated factor of segment representation error and number of segments. The experimental result shows that the MS-BU-GA has outperformed existing methods in segment number and representation error. The overall average representation error is decreased by 21.73% and the integrated factor of the number of segments and the segment representation error is reduced by 23.14%.

References

[1] Aldabbas H., Albashish D., Khatatneh K., and Amin R., “An Architecture of Iot-Aware Healthcare Smart System By Leveraging Machine Learning,” The International Arab Journal of Information Technology, vol. 19, no. 2, pp. 160- 172, 2022.

[2] Bernardini A. and Sarti A., “Canonical Piecewise- Linear Representation of Curves in the Wave Digital Domain,” in Proceedings of 25th European Signal Processing Conference, Kos, pp. 1125- 1129, 2017.

[3] Buhler J. and Tompa M., “Finding Motifs Using Random Projections,” Journal of Computational Biology, vol. 9, no. 2, pp. 225-242, 2002.

[4] Chang M., Lou Y., and Qiu L., “An Approach for Time Series Similarity Search Based on Lucene,” in Proceedings of 4th International Conference on Cloud Computing and Intelligence Systems, Beijing, pp. 210-214, 2016.

[5] Esling P. and Agon C., “Time-Series Data Mining,” ACM Computing Surveys (CSUR), vol. 45, no. 1, pp. 1-34, 2012.

[6] Hu Y., Ji C., Jing M., Ding Y., Kuai S., and X Li., “A Continuous Segmentation Algorithm For Streaming Time Series,” in Proceedings of International Conference on Collaborative Computing: Networking, Applications and Worksharing Springer, Beijing, pp. 140-151, 2016.

[7] Idrees S., Alam M., and Agarwal P., “A Prediction Approach for Stock Market Volatility Based on Time Series Data,” IEEE Access, vol. 7, pp. 17287-17298, 2019.

[8] Ji C., Liu S., Yang C., Wu L., Pan L., Meng X., “A Piecewise Linear Representation Method Based on Importance Data Points for Time Series Data,” in Proceedings of IEEE 20th International Conference on Computer Supported Cooperative Work in Design, Nanchang, pp. 111-116, 2016.

[9] Keogh E., Chu S., Hart D., Pazzani M., “An Online Algorithm for Segmenting Time Series,” in Proceedings IEEE International Conference on Data Mining, San Josepp, pp. 289-296, 2001.

[10] Liu X., Lin Z., and Wang H., “Novel Online Methods for Time Series Segmentation,” IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 12, pp. 1616-1626, 2008.

[11] Mirjalili S., “Evolutionary Algorithms and Neural Networks,” in Studies in Computational Intelligence, Springer, vol. 780, 2019.

[12] Nayak S., Misra B., and Behera H., “On Developing And Performance Evaluation of Adaptive Second Order Neural Network with Ga- Based Training (Asonn-Ga) for Financial Time Series Prediction,” in Advancements in Applied Metaheuristic Computing, IGI global, pp. 231- 263, 2018.

[13] Pavlidis T., “Waveform Segmentation through Functional Approximation,” IEEE Transactions on Computers, vol. 100, no. 7, pp. 689-697, 1973.

[14] Reinert G., Schbath S., and Waterman M., “Probabilistic and Statistical Properties of Words: An Overview,” Journal of Computational Biology, vol. 7, no. 1-2, pp. 1-46, 2000.

[15] Staden R., “Methods for Discovering Novel Motifs in Nucleic Acid Sequences,” Bioinformatics, vol. 5, no. 4, pp. 293-298, 1989.

[16] Sheta A. and De Jong K., “Time-Series Forecasting Using GA-Tuned Radial Basis Functions,” Information Sciences, vol. 133, no. 3, pp. 221-228, 2001.

[17] Sosiawan A., Nooraeni R., and Sari L., “Implementsation of using HMM-GA in Time Series Data,” Procedia Computer Science, vol. 179, pp. 713-720, 2021.

[18] Temme C., Ebinghaus R., Einax J., Steffen A., Schroeder W., “Time Series Analysis of Long- Term Data Sets of Atmospheric Mercury Concentrations,” Analytical and Bioanalytical Chemistry, vol. 380, no. 3, pp. 493-501, 2004.

[19] Xing Z., Pei J., and Keogh E., “A Brief Survey on Sequence Classification,” ACM Sigkdd Explorations Newsletter, vol. 12, no. 1, pp. 40-48, 2010.

[20] Yi B., and Faloutsos C., “Fast Time Sequence Indexing for Arbitrary LP norms,” in Proceedings of the 26th International Conference on Very Large Databases, Cairo, pp. 297-306, 2000.

[21] Yin J., Si Y., and Gong Z., “Financial Time Series Segmentation Based on Turning Points,” in Proceedings International Conference on System Science and Engineering IEEE, Macau, pp. 394- 399, 2011. An Improved Quantile-Point-Based Evolutionary Segmentation Representation ... 883

[22] Yu P. and Yan X., “Stock Price Prediction Based on Deep Neural Networks,” Neural Computing and Applications, vol. 32, no. 6, pp. 1609-1628, 2020.

[23] Zhan P., Hu Y., Luo W., Xu Y., Zhang Q., and Li X., “Feature-Based Online Segmentation Algorithm for Streaming Time Series (Short Paper),” in Proceedings of the International Conference on Collaborative Computing: Networking, Applications and Worksharing, Shanghai, pp. 477-487, 2018.

[24] Zhu Y., Wu D., and Li S., “A Piecewise Linear Representation Method of Time Series Based on Feature Points,” in Proceedings of the International Conference on Knowledge- Based and Intelligent Information And Engineering Systems, Vietri sul Mare, pp. 1066- 1072, 2007. Lei Liu received the B.S. degree in Information and Computing Science from Sichuan Agricultural University, Ya’an, Sichuan in 2019. He is currently pursuing the master's degree with Xihua University, Chengdu, China. His research interests include machine learning and financial time series analysis. Zheng Pei received the M.S. and Ph.D. degrees from Southwest Jiaotong University, Chengdu, China, in 1999 and 2002, respectively. He is currently a Professor with the School of Science, Xihua University, Chengdu. He has nearly 100 research articles published in academic journals or conference. His research interests include rough set theory, fuzzy set theory, logical reasoning, and linguistic information processing. Peng Chen IEEE member, CCF member, received B.E. degree in computer science and technology from University of Electronic Science and Technology of China, M.Sc. degree in computer software and theory from Peking University and Ph.D. in computer science and technology from Sichuan University. He is currently a full professor of School of Computer and Software Engineering, Xihua University. His research interests include machine learning, service computing and time series analysis. Zhisheng Gao is an professor at the Xihua University. He received his Ph.D. degree in computer science from Sichuan University in 2012. He is the author of more than 50 journal papers. His current research interests include machine learning, image processing, and computer vision. Zhihao Gan received the B.E. degree in Internet of Things Engineering from Xihua University, Chengdu, China in 2020. He is currently pursuing the master's degree with Xihua University, Chengdu, China. His research interests include time series analysis and cloud computing. Kang Feng received the B.E. degree in Communication engineering from Nanjing University of Posts and Telecommunications, Nanjing, China in 2019. He is currently pursuing the master's degree with Xihua University, Chengdu, China. His research interests include financial time series forecasting and decision- making.