Abstract
The goal of motif discovery algorithms is to efficiently find unknown recurring patterns. In this paper, we focus on motif discovery in time series. Most available algorithms cannot utilize domain knowledge in any way which results in quadratic or at least super-linear time and space complexity. In this paper we define the Constrained Motif Discovery problem which enables utilization of domain knowledge into the motif discovery process. The paper then provides two algorithms called MCFull and MCInc for efficiently solving the constrained motif discovery problem. We also show that most unconstrained motif discovery problems be converted into constrained ones using a change-point detection algorithm. A novel change-point detection algorithm called the Robust Singular Spectrum Transform (RSST) is then introduced and compared to traditional Singular Spectrum Transform using synthetic and real-world data sets. The results show that RSST achieves higher specificity and is more adequate for finding constraints to convert unconstrained motif discovery problems to constrained ones that can be solved using MCFull and MCInc. We then compare the combination of RSST and MCFull or MCInc with two state-of-the-art motif discovery algorithms on a large set of synthetic time series. The results show that the proposed algorithms provided four to ten folds increase in speed compared the unconstrained motif discovery algorithms studied without any loss of accuracy. RSST+MCFull is then used in a real world human-robot interaction experiment to enable the robot to learn free hand gestures, actions, and their associations by watching humans and other robots interacting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chiu, B., Keogh, E. and Lonardi, S., “Probabilistic discovery of time series motifs,” in KDD '03: Proc. of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 493–498, ACM, NY, USA, 2003.
Oates, T., “Peruse: An unsupervised algorithm for finding recurring patterns in time series,” in International Conference on Data Mining, pp. 330–337, 2002.
Jensen, K. L., Styczynxki, M. P., Rigoutsos, I. and Stephanopoulos, G. N., “A generic motif discovery algorithm for sequential data,” BioInformatics, 22, 1, pp. 21–28, 2006.
Lin, J., Keogh, E., Lonardi, S. and Patel, P., “Finding motifs in time series,” in In the 2nd workshop on temporal data mining, at the 8th ACM SIGKDD international, pp. 53–68, 2002.
Minnen, D., Essa, I., Isbell, C. L. and Starner, T., “Detecting subdimensional motifs: An efficient algorithm for generalized multivariate pattern discovery,” in IEEE Int. Conf. on Data Mining (ICDM), 2007.
Tang, H. and Liao, S. S., “Discovering original motifs with different lengths from time series,” Know.-Based Syst., 21, 7, pp. 666–671, 2008.
Keogh, E., Lin, J. and Fu, A., “Hot sax: efficiently finding the most unusual time series subsequence” Data Mining, Fifth IEEE International Conference on, p. 8 2005.
Catalano, J., Armstrong, T. and Oates, T., “Discovering patterns in real-valued time series,” in Knowledge Discovery in Databases: PKDD 2006, pp. 462–469, 2007.
Minnen, D., Starner, T., Essa, I. and Isbell, C. L., “Improving activity discovery with automatic neighborhood estimation,” in Int. Joint Conf. on Artificial Intelligence, 2007.
Basseville, M. and Kikiforov, I., Detection of Abrupt Changes, Printice Hall, Englewood Cliffs, New Jersey, 1993.
Kadambe, S. and Boudreaux-Bartels, G. F., “Application of the wavelet transform for pitch detection of speech signals,” Information Theory, IEEE Transactions on, 38, 2, pp. 917–924, 1992.
Hirano, S. and Tsumoto, S., “Mining similar temporal patterns in long time series data and its application to medicine,” in ICDM '02: Proc. of the 2002 IEEE International Conference on Data Mining (ICDM '02), p. 219, IEEE Computer Society, Washington, DC, USA, 2002.
Gombay, E., “Change detection in autoregressive time series,” J. Multivar. Anal., 99, 3, pp. 451–464, 2008.
Ide, T. and Inoue, K., “Knowledge discovery from heterogeneous dynamic systems using change-point correlations,” in Proc. SIAM Intl. Conf. Data Mining, 2005.
Moskvina, V. and Zhigljavsky, A., “An algorithm based on singular spectrum analysis for change-point detection,” Communications in Statistics — Simulation and Computation, 32, 4, pp.319–352, 2003.
Mohammad, Y., Xu, Y., Matsumura, K. and Nishida, T., “The H3R explanation corpus : human-human and base human-robot interaction dataset,” in The fourth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP2008), 2008.
Buhler, J. and Tompa, M., “Finding motifs using random projections,” in 5th Internatinal Conference on Computational Biology, pp. 69–76, 2001.
Iba, S., Paredis, C. and Khosla, P., “Interactive multimodal robot programming,” International Journal of Robotics Research, 24, 1, pp.83–104, 2005.
Yong Xu, M. G. and Nishida, T., “An experiment study of gesture-based human-robot interface,” in IEEE/ICME International Conference on Complex Medical Engineering-CME 2007, pp. 458–464, 2007.
Mohammad, Y. and Nishida, T., “Human adaptation to a miniature robot: Precursors of mutual adaptation,” in The 17th IEEE International Symposium on Robot and Human Interactive Communication, 2008. RO-MAN 2008, pp. 124–129, 2008.
Ohmura, R., Naya, F., Noma, H. and Kogure, K., “B-pack: a bluetooth-based wearable sensing device for nursing activity recognition,” Wireless Pervasive Computing, 2006 1st International Symposium on, pp. 1686–1693, 2006.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Mohammad, Y., Nishida, T. Constrained Motif Discovery in Time Series. New Gener. Comput. 27, 319–346 (2009). https://doi.org/10.1007/s00354-009-0068-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00354-009-0068-x