Abstract
Environmental time series are often affected by missing data, namely data unavailability at certain time points. In this paper, it is presented an Iterated Prediction and Imputation algorithm, that makes possible time series prediction in presence of missing data. The algorithm uses Dynamics Reconstruction and Machine Learning methods for estimating the model order and the skeleton of time series, respectively. Experimental validation of the algorithm on an environmental time series with missing data, expressing the concentration of Ozone in a European site, shows an average percentage prediction error of \(0.45\%\) on the test set.
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Notes
- 1.
\(\mathcal {I}(u)\) is 1 if the condition u is fulfilled, 0 otherwise.
- 2.
\(|u|_{\epsilon }^2\) is u if \(u \ge \epsilon \), 0 otherwise.
References
Chianese, E., Camastra, F., Ciaramella, A., Landi, T., Staiano, A., Riccio, A.: Spatio-temporal learning in predicting ambient particulate matter concentration by multi-layer perceptron. Ecol. Inf. 49, 54–61 (2019)
Hirshberg, D., Merhav, N.: Robust methods for model order estimation. IEEE Trans. Signal Process. 44, 620–628 (1996)
Duda, R., Hart, P., Stork, D.: Pattern Classification. Wiley, New York (2001)
The Elements of Statistical Learning. SSS. Springer, New York (2009). https://doi.org/10.1007/978-0-387-84858-7_9
Camastra, F., Filippone, M.: A comparative evaluation of nonlinear dynamics methods for time series prediction. Neural Comput. Appl. 18, 1021–1029 (2009)
Mañé, R.: On the dimension of the compact invariant sets of certain non-linear maps. In: Rand, D., Young, L.-S. (eds.) Dynamical Systems and Turbulence, Warwick 1980. LNM, vol. 898, pp. 230–242. Springer, Heidelberg (1981). https://doi.org/10.1007/BFb0091916
Takens, F.: Detecting strange attractor in turbolence. In: Dynamical Systems and Turbolence, Warwick, pp. 366–381. MIT Press (1981)
Camastra, F., Staiano, A.: Intrinsic dimension estimation: advances and open problems. Inf. Sci. 328, 26–41 (2016)
Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Physica D 9, 189–208 (1983)
Camastra, F., Esposito, F., Staiano, A.: Linear SVM-based recognition of elementary juggling movements using correlation dimension of Euler angles of a single arm. Neural Comput. Appl. 26, 1005–1013 (2018)
Trucco, E., Verri, A.: Introductory Techniques for 3-D Computer Vision. Prentice Hall, Englewood Cliffs (1998)
Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)
Joachim, T.: Making large-scale SVM learning practical. In: Advances in Kernel Methods-Support Vector Learning, pp. 169–184. MIT Press (1999)
Allison, P.: Missing Data. Sage Publications, Thousand Oaks (2002)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. 39(1), 1–38 (1977)
Scheinkman, J., Le Baron, B.: Nonlinear dynamics and stock returns. J. Bus. 62, 311–337 (1989)
Williams, C., Rasmussen, C.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)
Camastra, F., Vinciarelli, A.: Markovian models for sequential data. In: Advanced Information and Knowledge Processing, pp. 294–340. MIT Press (2015)
Acknowledgements
Vincenzo Capone developed part of the work as final dissertation for B. Sc. in Computer Science, under supervision of F. Camastra, at University Parthenope of Naples.
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Camastra, F., Capone, V., Ciaramella, A., Landi, T.C., Riccio, A., Staiano, A. (2021). Environmental Time Series Prediction with Missing Data by Machine Learning and Dynamics Recostruction. In: Del Bimbo, A., et al. Pattern Recognition. ICPR International Workshops and Challenges. ICPR 2021. Lecture Notes in Computer Science(), vol 12666. Springer, Cham. https://doi.org/10.1007/978-3-030-68780-9_3
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