Information technology of classification of fractal time series
DOI:
https://doi.org/10.34185/1562-9945-3-128-2020-11Keywords:
інформаційна технологія, класіфікація часових рядів, машинне навчання, фрактальні часові рядиAbstract
We can formulate the task of time series classification in this way. There are many time series that are divided into classes in some way. A finite set of time series is defined for which it is known to which classes they belong. This set is a training set. Belonging to the class of other time series is not known. It is necessary to get an algorithm of classifying an arbitrary time series from the initial set.
In machine learning, there are a number of basic classification methods: decision trees, support vector machines, neural networks, and others. Most often, a set of some features of given object, in our case, time series, comes to the input of the classifier. At the output, we get the class value of the investigated time series.
One of the most important classification issues is the selection of features by which the division into classes is carried out. A change in the fractal properties of time series entails a change in statistical and correlation properties. Therefore, fractal, statistical and recurrent characteristics calculated from time series were chosen as features.
Studies have shown that the statistical characteristics that reflect changes in fractal properties are variance, coefficient of variation, median, asymmetry coefficient, etc. As fractal features, it is convenient to use the value of the Hurst exponent and the generalized Hurst exponent.
A fairly new approach to the use of time series features in machine learning is the calculation of recurrence characteristics. A recurrence plot is an array of points, where an element with coordinates (i, j) characterizes the proximity of points i and j of the time series in the phase space. The numerical analysis of recurrence plots allows one to calculate the quantitative degrees of complexity of the structures of recurrence plots, such as a measure of recurrence, a measure of determinism, a measure of entropy, etc. These characteristics are useful as features in machine learning
A comparative analysis of the classification methods for fractal time series allows us to offer an information classification technology based on machine learning methods. Let's consider its short description.
1. Pre-processing of data.
2. Evaluation of self-similar and multifractal properties of time series for different classes. The key point is the determination of the fact that different classes of time series have quite different fractal properties. If the fractal properties for different classes are almost the same, then this approach does not make sense to use.
3. Studies have shown that the classification of time series with strong multifractal properties is the best. In this case, the series are most accurately classified using a random forest based on regression trees. It is sufficient to use the statistical and fractal characteristics as features.
4. In the case when the time series has average multifractal properties, statistical and fractal characteristics can be used as features. In the persistent case, the bagging method with regression trees v, and in the antipersistent case the Random Forest with regression trees is used.
5. If the multifractal properties are weakly expressed, that is, the time series can be considered as conditionally monofractal, then recurrent characteristics should be used as additional features. Studies have shown that in the case of monofractality, the best classification results are obtained by the use of neural networks.
References
Esling P., Agon C.: Time series data mining, ACM Computing Surveys, v.46, №.1, (2012).
Krisztian Buza: Time Series Classification and its Applications WIMS '18: Proceedings of the 8th International Conference on Web Intelligence, Mining and Semantics 2018 https://doi.org/10.1145/3227609.3227690
André L., Coelho V., Clodoaldo A., Lima M.: Assessing fractal dimension methods as feature extractors for EMG signal classification. Engineering Applications of Artificial Intelligence 36 81–98 (2014).
Symeonidis S.: Sentiment analysis via fractal dimension. Proceedings of the 6th Symposium on Future Directions in Information Access, 48-50 (2015).
S. P. Arjunan, D. K. Kumar, G. R. Naik A machine learning based method for classification of fractal features of forearm sEMG using Twin Support Vector Machines. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society, 4821-4 (2010).
Ledesma-Orozco, S.E. Ruiz, García G., Aviña G., Hernández D. Analysis of self-similar data by artificial neural networks. In: Proceedings of the 2011 International Conference on Networking, Sensing and Control, Delft, pp. 480-485 (2011). doi: 10.1109/ICNSC.2011.5874873
Kirichenko L., RadivilovaT. Estimation of multifractal characteristics of stochastic processes. International Journal Information content and processing. 2018. Vol. 5 (2). P. 106–141.
Breiman L. Bagging predictors. Machine Learning. (1996), 24 (2), P.123–140.
Breiman L. Random Forests. Machine Learning. (2001), 45 (1), P.5–32.
Kirichenko L., Radivilova T., Bulakh V. Binary Classification of Fractal Time Series by Machine Learning Methods. Lecture Notes in Computational Intelligence and Decision Making. ISDMCI 2019. Advances in Intelligent Systems and Computing, vol 1020. Springer, Cham, 2018. P. 701–711. doi: https://doi.org/10.1007/978-3-030-26474-1_49.
Kirichenko L., Radivilova T., Bulakh V. Generalized approach to Hurst exponent estimating by time series. Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska. 2018. Volume 8, No. 1. P. 28–31. doi: 10.5604/01.3001.0010.8639.
Kirichenko L., Radivilova T., Bulakh V. Classification of Fractal Time Series Using Recurrence Plots. Problems of Infocommunications. Science and Technology (PIC S&T): Proceedings of International Science-Practical Conference, 2018, Kharkiv, Ukraine. IEEE, 2018. P. 719–724. doi: 10.1109/INFOCOMMST.2018.8632010.
Bulakh V., Kirichenko L., Radivilova T. Classification of Multifractal Time Series by Decision Tree Methods. ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer: Proceedings of the 14th International Conference, May 14–17 2018, Kyiv, Ukraine. 2018. 2105. P. 457-460.
Bulakh V., Kirichenko L., Radivilova T. Time Series Classification Based on Fractal Properties. Data Stream Mining & Processing (DSMP): 2018 IEEE Second International Conference, Lviv, Ukraine. IEEE, 2018. P. 198–201. doi: 10.1109/DSMP.2018.8478532.
Kirichenko L., Radivilova T., Bulakh V. Machine Learning in Classification Time Series with Fractal Properties. Data. 2019. Vol. 4, issue 1, 5. P. 1–13. doi:10.3390/data4010005 8632010.
