Mining multivariate time series with mixed sampling rates

ABSTRACT

Fitting sensors to humans and physical structures is becoming more and more common. These developments provide many opportunities for ubiquitous computing, as well as challenges for analyzing the resulting sensor data. From these challenges, an underappreciated problem arises: modeling multivariate time series with mixed sampling rates. Although mentioned in several application papers using sensor systems, this problem has been left almost unexplored, often hidden in a preprocessing step or solved manually as a one-pass procedure (feature extraction/construction). This leaves an opportunity to formalize and develop methods that address mixed sampling rates in an automatic fashion.

We approach the problem of dealing with multiple sampling rates from an aggregation perspective. We propose Accordion, a new embedded method that constructs and selects aggregate features iteratively, in a memory-conscious fashion. Our algorithms work on both classification and regression problems. We describe three experiments on real-world time series datasets, with satisfying results.

References

1. Angelini, E., Henry, J., and Marcellino, M. Interpolation and backdating with a large information set. Journal of Economic Dynamics and Control 30, 12 (Dec. 2006), 2693--2724.
2. Armesto, M. Forecasting with mixed frequencies. Federal Reserve Bank of St. Louis (2010), 521--536.
3. Bao, L., and Intille, S. Activity recognition from user-annotated acceleration data. Pervasive Computing (2004), 1--17.
4. Brush, A., Krumm, J., Scott, J., and Saponas, T. Recognizing Activities from Mobile Sensor Data: Challenges and Opportunities. In Proceedings Ubicomp' 11 (2011).
5. Figo, D., Diniz, P. C., Ferreira, D. R., and Cardoso, J. a. M. P. Preprocessing techniques for context recognition from accelerometer data. Personal and Ubiquitous Computing 14, 7 (Mar. 2010), 645--662.
6. Friedman, J., Hastie, T., and Tibshirani, R. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software (2010).
7. Ghysels, E., Santa-Clara, P., and Valkanov, R. Predicting volatility: getting the most out of return data sampled at different frequencies. Journal of Econometrics (2006).
8. Gujarati, D. Basic econometrics, fourth ed. McGraw Hill, 2003.
9. Hastie, T., Tibshirany, R., and Friedman, J. The Elements of Statistical Learning Data Mining, Inference, and Prediction, second ed. Springer, 2009.
10. Hobson, J. A. Rem sleep and dreaming: towards a theory of protoconsciousness. Nature Reviews Neuroscience 10, 11 (2009), 803--813.
11. Huynh, T., and Schiele, B. Analyzing features for activity recognition. In Smart objects and ambient intelligence: innovative context-aware services: usages and technologies, no. 10 (2005).
12. John, G., Kohavi, R., and Pfleger, K. Irrelevant features and the subset selection problem. In Machine Learning (1994), 121--129.
13. Keogh, E., and Kasetty, S. On the need for time series data mining benchmarks: a survey and empirical demonstration. Data Mining and Knowledge Discovery (2002), 349--371.
14. Kuzin, V., Marcellino, M., and Schumacher, C. MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area. International Journal of Forecasting 27, 2 (Apr. 2011), 529--542.
15. Kwapisz, J., Weiss, G., and Moore, S. Activity recognition using cell phone accelerometers. ACM SIGKDD Explorations Newsletter (2011).
16. Lin, J., Keogh, E., Lonardi, S., and Chiu, B. A symbolic representation of time series, with implications for streaming algorithms. Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery - DMKD '03 (2003), 2.
17. Makridakis, S., Wheelwright, S. C., and Hyndman, R. J. Forecasting methods and applications. John Wiley & Sons, 1998.
18. Miluzzo, E., Lane, N., and Fodor, K. Sensing meets mobile social networks: the design, implementation and evaluation of the CenceMe application. In Proceedings of Embedded network sensor systems (2008), 337--350.
19. Park, J.-g., Patel, A., Curtis, D., Teller, S., and Ledlie, J. Online pose classification and walking speed estimation using handheld devices. Proceedings of the 2012 ACM Conference on Ubiquitous Computing - UbiComp '12 (2012), 10.
20. Quinlan, J. Induction of decision trees. Machine learning (1986), 81--106.
21. Stodden, V. Model selection when the number of variables exceeds the number of observations. PhD thesis, 2006.
22. Tibshirani, R. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B 58 (1994).
23. Vespier, U., Knobbe, A., Nijssen, S., and Vanschoren, J. MDL-Based Analysis of Time Series at Multiple Time-Scales. In Proceedings of ECML PKDD '12 (2012).

Index Terms

• Computing methodologies

  • Machine learning

    • Learning paradigms

      • Supervised learning

        • Supervised learning by classification

    • Machine learning approaches

      • Classification and regression trees

• Mathematics of computing

  • Probability and statistics

    • Statistical paradigms

      • Time series analysis