Abstract
In most challenging applications learning algorithms acts in dynamic environments where the data is collected over time. A desirable property of these algorithms is the ability of incremental incorporating new data in the actual decision model. Several incremental learning algorithms have been proposed. However most of them make the assumption that the examples are drawn from a stationary distribution [13]. The aim of this study is to present a detection system (DSKC) for regression problems. The system is modular and works as a post-processor of a regressor. It is composed by a regression predictor, a Kalman filter and a Cumulative Sum of Recursive Residual (CUSUM) change detector. The system continuously monitors the error of the regression model. A significant increase of the error is interpreted as a change in the distribution that generates the examples over time. When a change is detected, the actual regression model is deleted and a new one is constructed. In this paper we tested DSKC with a set of three artificial experiments, and two real-world datasets: a Physiological dataset and a clinic dataset of Sleep Apnoea. Sleep Apnoea is a common disorder characterized by periods of breathing cessation (apnoea) and periods of reduced breathing (hypopnea) [7]. This is a real-application where the goal is to detect changes in the signals that monitor breathing. The experimental results showed that the system detected changes fast and with high probability. The results also showed that the system is robust to false alarms and can be applied with efficiency to problems where the information is available over time.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andre, D., Stone, P.: Physiological data modeling contest. Technical report, University of Texas at Austin (2004)
Basseville, M., Nikiforov, I.: Detection of Abrupt Changes: Theory and Applications. Prentice-Hall, Englewood Cliffs (1993)
Bhattacharyya, G., Johnson, R.: Statistical Concepts and Methods. John Willey & Sons, New York (1977)
Bianchi, G., Tinnirello, I.: Kalman filter estimation of the number of competing terminals in ieee. In: The 22nd Annual Joint Conference of IEEE Computer and Communications (2003)
Cauwenberghs, Gert, Poggio, Tomaso: Incremental and decremental support vector machine learning. Advances in Neural Information Processing Systems, 13 (2001)
Domingos, P., Hulten, G.: Mining high-speed data streams. In: Knowledge Discovery and Data Mining, pp. 71–80 (2000)
Flemons, W.W., Littner, M.R., Rowley, J.A., Gay, W.M.A.P., Hudgel, D.W., McEvoy, R.D., Loube, D.I.: Home diagnosis of sleep apnoeas: A systematic review of the literature. In: Chest, vol. 1543-1579, pp. 211–237 (2003)
Friedman, J.: Multivariate adaptive regression splines. Annals of Statistics 19(1), 1–141 (1991)
Gama, J., Medas, P., Castillo, G.: Learning with drift detection. In: Brazilian AI Conference, pp. 286–295. Springer, Heidelberg (2004)
Grant, E., Leavenworth, R.: Statistical Quality Control. McGraw-Hill, New York (1996)
Guimarães, G., Peter, J.H., Penzel, T., Ultsch, A.: A method for automated temporal knowledge acquisition applied to sleep-related breathing disorders. Artificial Intelligence in Medicine 23, 211–237 (2001)
Higgins, C.M., Goodman, R.M.: Incremental learning using rule-based neural networks. In: International Joint Conference on Neural Networks, Seattle, WA, pp. 875–880 (1991)
Hulten, G., Spencer, L., Domingos, P.: Mining time-changing data streams. In: Proceedings of Knowledge Discovery and Data Mining. ACM Press, New York (2001)
Kalman, R.E.: A new approach to linear filtering and prediction problems. In: Transaction of ASME - Journal of Basic Engineering, 35–45 (1960)
Pang, K.P., Ting, K.M.: Improving the centered CUSUMs statistic for structural break detection in time series. In: Proc. 17th Australian Join Conference on Artificial Intelligence. Springer, Heidelberg (2004)
R Development Core Team. R: A language and environment for statistical computing. In: R Foundation for Statistical Computing, Vienna, Austria (2005) ISBN 3-900051-07-0
Rojas, R.: The Kalman filter. Technical report, Freie University of Berlin (2003)
Welch, G., Bishop, G.: An introduction to the Kalman filter. Technical report, 95-041, Department of Computer Science, University of North Caroline at Chapel Hill (April 2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Severo, M., Gama, J. (2006). Change Detection with Kalman Filter and CUSUM. In: Todorovski, L., Lavrač, N., Jantke, K.P. (eds) Discovery Science. DS 2006. Lecture Notes in Computer Science(), vol 4265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11893318_25
Download citation
DOI: https://doi.org/10.1007/11893318_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46491-4
Online ISBN: 978-3-540-46493-8
eBook Packages: Computer ScienceComputer Science (R0)