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FANCFIS: fast adaptive neuro-complex fuzzy inference system. (English) Zbl 1452.68164
Summary: Large-scale multivariate time series forecasting is an increasingly important problem, with sensor networks pouring out sampled data at unprecedented rates, trillions of dollar’s worth of stock trades made every data, and zettabytes of traffic transmitted over the Internet every year. While they are only examples of the much larger domain of general data streams, the uniformly-sampled time series still remains a very large and important subdomain. Extensive research has shown that machine-learning algorithms can often be very effective forecasting models, but many of these algorithms do not scale well. The Adaptive Neuro-Complex-Fuzzy Inferential System is one such approach; built to leverage complex fuzzy sets, it is both an accurate and parsimonious forecasting algorithm. However, its scaling is poor due to a relatively slow training algorithm (gradient descent hybridized with chaotic simulated annealing). Before the algorithm can be used for large-scale forecasting, a fast training algorithm that preserves the system’s accuracy and compactness must be developed.
We propose the Fast Adaptive Neuro-Complex Fuzzy Inference System, which is designed for fast training of a compact, accurate forecasting model. We use the Fast Fourier Transform algorithm to identify the dominant frequencies in a time series, and then create complex fuzzy sets to match them as the antecedents of complex fuzzy rules. Consequent linear functions are then learned via recursive least-squares. We evaluate this algorithm on both univariate and multivariate time series, finding that this incremental-learning algorithm is as accurate and compact as its slower predecessor, and can be trained much more quickly.
MSC:
68T05 Learning and adaptive systems in artificial intelligence
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
68W27 Online algorithms; streaming algorithms
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[1] Aghakhani, S.; Dick, S., An on-line learning algorithm for complex fuzzy logic, (Fuzzy Systems (FUZZ), 2010 IEEE International Conference on, (2010)), 1-7
[2] Alkouri, A. U.M.; Salleh, A. R., Linguistic variables, hedges and several distances on complex fuzzy sets, J. Intell. Fuzzy Syst.: Appl. Eng. Technol., 26, 2527-2535, (2014) · Zbl 1305.03043
[3] Alkouri, A. U.M.; Salleh, A. R., Some operations on complex atanassov’s intuitionistic fuzzy sets, (The 2013 UKM FST Postgraduate Colloquium: Proceedings of the Universiti Kebangsaan Malaysia, Faculty of Science and Technology 2013 Postgraduate Colloquium, (2013)), 987-993
[4] Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, 87-96, (1986) · Zbl 0631.03040
[5] Brzeziński, D., Mining Data Streams with Concept Drift, (2010), Poznan University of Technology, Master’s thesis
[6] Cao, L.; Mees, A.; Judd, K., Dynamics from multivariate time series, Phys. D: Nonlinear Phenom., 121, 75-88, (1998) · Zbl 0933.62083
[7] Chen, Z.; Aghakhani, S.; Man, J.; Dick, S., ANCFIS: a neurofuzzy architecture employing complex fuzzy sets, IEEE Trans. Fuzzy Syst., 19, 305-322, (2011)
[8] Dick, S., Toward complex fuzzy logic, IEEE Trans. Fuzzy Syst., 13, 405-414, (2005)
[9] Dick, S.; Bethel, C.; Kandel, A., Software reliability modeling: the case for deterministic behavior, IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum., 37, 106-119, (2007)
[10] Dick, S.; Yager, R. R.; Yazdanbakhsh, O., On Pythagorean and complex fuzzy set operations, IEEE Trans. Fuzzy Syst., 24, 1009-1021, (2016)
[11] Dick, S.; Yazdanbaksh, O.; Tang, X.; Huynh, T.; Miller, J., An empirical investigation of Web session workloads: can self-similarity be explained by deterministic chaos?, Inf. Process. Manag., 50, 41-53, (2014)
[12] Frigo, M.; Johnson, S. G., FFTW: an adaptive software architecture for the FFT, (Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on, (1998)), 1381-1384
[13] Gaber, M. M.; Zaslavsky, A.; Krishnaswamy, S., Data stream mining, (Data Mining and Knowledge Discovery Handbook, (2009), Springer), 759-787
[14] Gama, J.; Žliobaitė, I.; Bifet, A.; Pechenizkiy, M.; Bouchachia, A., A survey on concept drift adaptation, ACM Comput. Surv., 46, 44, (2014) · Zbl 1305.68141
[15] Garcia, R. C.; Contreras, J.; Van Akkeren, M.; Garcia, J. B.C., A GARCH forecasting model to predict day-ahead electricity prices, IEEE Trans. Power Syst., 20, 867-874, (2005)
[16] Ghiassi, M.; Nangoy, S., A dynamic artificial neural network model for forecasting nonlinear processes, Comput. Ind. Eng., 57, 287-297, (2009)
[17] Graves, D.; Pedrycz, W., Fuzzy prediction architecture using recurrent neural networks, Neurocomputing, 72, 1668-1678, (2009)
[18] Haykin, S. S., Neural Networks and Learning Machines, vol. 3, (2009), Pearson Education: Pearson Education Upper Saddle River
[19] Hegger, R.; Kantz, H.; Schreiber, T., Practical implementation of nonlinear time series methods: the TISEAN package, Chaos: Interdiscip. J. Nonlinear Sci., 9, 413-435, (1999) · Zbl 0990.37522
[20] Hegger, R.; Kantz, H.; Schreiber, T., Practical implementation of nonlinear time series methods: the TISEAN package, (1998) · Zbl 0990.37522
[21] Hollander, M.; Wolfe, D. A.; Chicken, E., Nonparametric Statistical Methods, (2013), John Wiley & Sons
[22] Hong, X.; Harris, C. J., Experimental design and model construction algorithms for radial basis function networks, Int. J. Syst. Sci., 34, 733-745, (2003) · Zbl 1043.93004
[23] R.J. Hyndman, M. Akram, Time series data library, 2006.
[24] Jang, J.-S. R.; Sun, C.-T.; Mizutani, E., Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, (1997), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ, USA
[25] Jang, J. S.R., ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst. Man Cybern., 23, 665-685, (1993)
[26] Jha, A.; Dave, M.; Madan, S., A review on the study and analysis of big data using data mining techniques, Int. J. Latest Trends Eng. Technol., 6, (2016)
[27] Jo, T., VTG schemes for using back propagation for multivariate time series prediction, Appl. Soft Comput., 13, 2692-2702, (2013)
[28] Kantz, H.; Schreiber, T., Nonlinear Time Series Analysis, (1997), Cambridge University Press: Cambridge University Press Cambridge/New York · Zbl 0873.62085
[29] Kennel, M. B.; Brown, R.; Abarbanel, H. D., Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A, 45, 3403, (1992)
[30] Krempl, G.; Žliobaite, I.; Brzeziński, D.; Hüllermeier, E.; Last, M.; Lemaire, V.; Noack, T.; Shaker, A.; Sievi, S.; Spiliopoulou, M., Open challenges for data stream mining research, ACM SIGKDD Explor. Newsl., 16, 1-10, (2014)
[31] Li, C., Adaptive image restoration by a novel neuro-fuzzy approach using complex fuzzy sets, Int. J. Intell. Inf. Database Syst., 7, 479-495, (2013)
[32] Li, C.; Chiang, T.-W., Complex fuzzy computing to time series prediction a multi-swarm PSO learning approach, (Intelligent Information and Database Systems, (2011), Springer), 242-251
[33] Li, C.; Chiang, T.-W., Function approximation with complex neuro-fuzzy system using complex fuzzy sets - a new approach, New Gener. Comput., 29, 261-276, (2011) · Zbl 1251.68245
[34] Li, C.; Chiang, T.-W., Intelligent financial time series forecasting: a complex neuro-fuzzy approach with multi-swarm intelligence, Int. J. Appl. Math. Comput. Sci., 22, 787-800, (2012) · Zbl 1286.91149
[35] Li, C.; Chiang, T.-W.; Yeh, L.-C., A novel self-organizing complex neuro-fuzzy approach to the problem of time series forecasting, Neurocomputing, (2012)
[36] Li, C.; Chiang, T., Complex neuro-fuzzy ARIMA forecasting—a new approach using complex fuzzy sets, IEEE Trans. Fuzzy Syst., 21, 567-584, (2012)
[37] Lyu, M. R., Handbook of Software Reliability Engineering, (1996), McGraw-Hill: McGraw-Hill New York, NY
[38] Ma, J.; Zhang, G.; Lu, J., A method for multiple periodic factor prediction problems using complex fuzzy sets, IEEE Trans. Fuzzy Syst., 20, 32-45, (2012)
[39] Masters, T., Neural, Novel and Hybrid Algorithms for Time Series Prediction, (1995), John Wiley & Sons, Inc.
[40] Muja, M.; Lowe, D., Scalable nearest neighbor algorithms for high dimensional data, IEEE Trans. Pattern Anal. Mach. Intell., 36, 2227-2240, (2014)
[41] Muthukrishnan, S., Data Streams: Algorithms and Applications, (2005), Now Publishers Inc. · Zbl 1128.68025
[42] NASDAQ Composite Index, (2014), Yahoo Finance. Available
[43] Pozna, C.; Minculete, N.; Precup, R.-E.; Kóczy, L. T.; Ballagi, A., Signatures: definitions, operators and applications to fuzzy modelling, Fuzzy Sets Syst., 201, 86-104, (2012) · Zbl 1251.93022
[44] Ramot, D.; Friedman, M.; Langholz, G.; Kandel, A., Complex fuzzy logic, IEEE Trans. Fuzzy Syst., 11, 450-461, (2003)
[45] Ramot, D.; Milo, R.; Friedman, M.; Kandel, A., Complex fuzzy sets, IEEE Trans. Fuzzy Syst., 10, 171-186, (2002)
[46] Salleh, A. R., Complex intuitionistic fuzzy sets, (AIP Conference Proceedings, (2012)), 464
[47] Schneider, G.; Chicken, E.; Becvarik, R., NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition, (2015), 1.3 ed.
[48] Stull, R. B., An Introduction to Boundary Layer Meteorology, vol. 13, (2012), Springer Science & Business Media
[49] Takens, F., Detecting strange attractors in turbulence, (Dynamical Systems and Turbulence. Dynamical Systems and Turbulence, Warwick 1980, (1981)), 366-381
[50] Tamir, D. E.; Jin, L.; Kandel, A., A new interpretation of complex membership grade, Int. J. Intell. Syst., 26, 285-312, (2011) · Zbl 1219.03061
[51] Tamir, D. E.; Kandel, A., Axiomatic theory of complex fuzzy logic and complex fuzzy classes, Int. J. Comput. Commun. Control, 6, 3, 562-576, (2011)
[52] Tamir, D. E.; Last, M.; Kandel, A., The theory and applications of generalized complex fuzzy propositional logic, (Soft Computing: State of the Art Theory and Novel Applications, (2013), Springer), 177-192 · Zbl 1283.03053
[53] Tamir, D. E.; Rishe, N. D.; Kandel, A., Complex fuzzy sets and complex fuzzy logic an overview of theory and applications, (Fifty Years of Fuzzy Logic and Its Applications, (2015), Springer), 661-681 · Zbl 1359.03039
[54] Tamir, D. E.; Teodorescu, H. N.; Last, M.; Kandel, A., Discrete complex fuzzy logic, (Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American, (2012)), 1-6
[55] Tomé, J. A.B.; Carvalho, J. P., One step ahead prediction using fuzzy Boolean neural networks, (EUSFLAT Conf., (2005)), 500-505
[56] Wackerly, D.; Mendenhall, W.; Scheaffer, R., Mathematical Statistics with Applications, (2007), Cengage Learning
[57] Wan, L.; Ng, W. K.; Dang, X. H.; Yu, P. S.; Zhang, K., Density-based clustering of data streams at multiple resolutions, ACM Trans. Knowl. Discov. Data, 3, 14, (2009)
[58] Yager, R., Pythagorean membership grades in multi-criteria decision making, IEEE Trans. Fuzzy Syst., 22, 958-965, (2014)
[59] Yager, R. R.; Abbasov, A. M., Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., (2013)
[60] Yazdanbakhsh, O.; Dick, S., ANCFIS-ELM: a machine learning algorithm based on complex fuzzy sets, (World Congress on Computational Intelligence. World Congress on Computational Intelligence, Vancouver, Canada, (2016))
[61] Yazdanbakhsh, O.; Dick, S., Forecasting of multivariate time series via complex fuzzy logic, IEEE Trans. Syst. Man Cybern. Syst., 47, 2160-2171, (2017)
[62] Yazdanbakhsh, O.; Dick, S., Induction of complex fuzzy infernetial system via randomized learning, Int. J. Intell. Syst., (2018), submitted for publication
[63] Yazdanbakhsh, O.; Dick, S., Multi-variate timeseries forecasting using complex fuzzy logic, (Fuzzy Information Processing Society (NAFIPS) Held Jointly with 2015 5th World Conference on Soft Computing (WConSC), 2015 Annual Conference of the North American, (2015)), 1-6
[64] Yazdanbakhsh, O.; Dick, S., A systematic review of complex fuzzy sets and logic, Fuzzy Sets Syst., (2018), in press · Zbl 1397.03093
[65] Yazdanbakhsh, O.; Dick, S., Time-series forecasting via complex fuzzy logic, (Sadeghian, A.; Tahayori, H., Frontiers of Higher Order Fuzzy Sets, (2015), Springer: Springer Heidelberg, Germany)
[66] Yazdanbakhsh, O.; Dick, S.; Reay, I.; Mace, E., On deterministic chaos in software reliability growth models, Appl. Soft Comput., 49, 1256-1269, (2016)
[67] Yazdanbaksh, O.; Krahn, A.; Dick, S., Predicting solar power output using complex fuzzy logic, (IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013 Joint, (2013)), 1243-1248
[68] Yeganejou, M.; Dick, S., Inductive learning of classifiers via complex fuzzy sets and logic, (Fuzzy Systems (FUZZ-IEEE), 2017 IEEE International Conference on, (2017)), 1-6
[69] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning—I, Inf. Sci., 8, 199-249, (1975) · Zbl 0397.68071
[70] Zhang, G.; Dillon, T. S.; Cai, K.-Y.; Ma, J.; Lu, J., Operation properties and δ-equalities of complex fuzzy sets, Int. J. Approx. Reason., 50, 1227-1249, (2009) · Zbl 1196.03077
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