A Survey on Semi-parametric Machine Learning Technique for Time Series Forecasting

Artificial Intelligence (AI) has recently shown its capabilities for almost every field of life. Machine Learning, which is a subset of AI, is a ‘HOT’ topic for researchers. Machine Learning outperforms other classical forecasting techniques in almost all-natural applications. It is a crucial part of modern research. As per this statement, Modern Machine Learning algorithms are hungry for big data. Due to the small datasets, the researchers may not prefer to use Machine Learning algorithms. To tackle this issue, the main purpose of this survey is to illustrate, demonstrate related studies for significance of a semi-parametric Machine Learning framework called Grey Machine Learning (GML). This kind of framework is Khwaja Mutahir Ahmad School of Information and Software Engineering, University of Electronic Science and Technology of China, 611731 Chengdu, Sichuan, P.R.China. E-mail: khwajamutahir311@gmail.com Gang He( ) School of Computer Science and Technology, Southwest University of Science and Technology, 621010 Mianyang, Sichuan, P.R.China. E-mail: ganghe@swust.edu.cn Wenxin Yu School of Computer Science and Technology, Southwest University of Science and Technology, 621010 Mianyang, Sichuan, P.R.China. E-mail: yuwenxin@swust.edu.cn Xiaochuan Xu School of Mathematics and Statistics, Sichuan University of Science and Engineering, 643000 Zigong, Sichuan, P.R.China. E-mail: contactayesha@qq.com Jay Kumar School of Computer Science and Engineering, University of Electronic Science and Technology of China, 611731 Chengdu, Sichuan, P.R.China. E-mail: jay@std.uestc.edu.cn Muhammad Asim Saleem School of Information and Software Engineering, University of Electronic Science and Technology of China, 611731 Chengdu, Sichuan, P.R.China. E-mail: asim.saleem1@hotmail.com ar X iv :2 10 4. 00 87 1v 1 [ cs .L G ] 2 A pr 2 02 1 2 Khwaja Mutahir Ahmad et al. capable of handling large datasets as well as small datasets for time series forecasting likely outcomes. This survey presents a comprehensive overview of the existing semi-parametric machine learning techniques for time series forecasting. In this paper, a primer survey on the GML framework is provided for researchers. To allow an in-depth understanding for the readers, a brief description of Machine Learning, as well as various forms of conventional grey forecasting models are discussed. Moreover, a brief description on the importance of GML framework is presented.

[1]  Zheng-xin Wang,et al.  Grey forecasting method of quarterly hydropower production in China based on a data grouping approach , 2017 .

[2]  Carlos E. Pedreira,et al.  Neural networks for short-term load forecasting: a review and evaluation , 2001 .

[3]  José Cristóbal Riquelme Santos,et al.  An Experimental Review on Deep Learning Architectures for Time Series Forecasting , 2020, Int. J. Neural Syst..

[4]  Fan Zhang,et al.  A review on time series forecasting techniques for building energy consumption , 2017 .

[5]  Yu-Shan Chen,et al.  Applying DEA, MPI, and grey model to explore the operation performance of the Taiwanese wafer fabrication industry , 2011 .

[6]  Zheng-Xin Wang,et al.  Forecasting Chinese carbon emissions from fossil energy consumption using non-linear grey multivariable models , 2017 .

[7]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[8]  Stevan Harnad,et al.  The Annotation Game: On Turing (1950) on Computing, Machinery, and Intelligence (PUBLISHED VERSION BOWDLERIZED) , 2006 .

[9]  Hao Wang,et al.  The Optimization of Grey Model GM (1,1) Based on Posterior Error , 2020, 2020 5th International Conference on Control, Robotics and Cybernetics (CRC).

[10]  Amaury Lendasse,et al.  High-Performance Extreme Learning Machines: A Complete Toolbox for Big Data Applications , 2015, IEEE Access.

[11]  Big Data Processing Using Spark in Cloud , 2019, Studies in Big Data.

[12]  Tzu-Li Tien,et al.  The indirect measurement of tensile strength of material by the grey prediction model GMC(1, n) , 2005 .

[13]  Chun-I Chen,et al.  Forecasting Taiwan's major stock indices by the Nash nonlinear grey Bernoulli model , 2010, Expert Syst. Appl..

[14]  Xiaojin Zhu,et al.  --1 CONTENTS , 2006 .

[15]  Chun-I Chen,et al.  Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate , 2008 .

[16]  Konstantinos Kamnitsas,et al.  Anatomically Constrained Neural Networks (ACNNs): Application to Cardiac Image Enhancement and Segmentation , 2017, IEEE Transactions on Medical Imaging.

[17]  Kyung-Sup Kwak,et al.  The Internet of Things for Health Care: A Comprehensive Survey , 2015, IEEE Access.

[18]  Mani B. Srivastava,et al.  Did you hear that? Adversarial Examples Against Automatic Speech Recognition , 2018, ArXiv.

[19]  Dimitris Bertsimas,et al.  Interpretable clustering: an optimization approach , 2020, Machine Learning.

[20]  XinMa.  Research on a Novel Kernel Based Grey Prediction Model and Its Applications , 2022 .

[21]  Diogo M. Camacho,et al.  Next-Generation Machine Learning for Biological Networks , 2018, Cell.

[22]  Ammar Belatreche,et al.  Evaluating machine learning classification for financial trading: An empirical approach , 2016, Expert Syst. Appl..

[23]  Ahmed M. Alaa,et al.  How artificial intelligence and machine learning can help healthcare systems respond to COVID-19 , 2020, Machine Learning.

[24]  Yang Du,et al.  A Hybrid LSTM Neural Network for Energy Consumption Forecasting of Individual Households , 2019, IEEE Access.

[25]  Bernhard Pfahringer,et al.  Regularisation of neural networks by enforcing Lipschitz continuity , 2018, Machine Learning.

[26]  Yatsuka Nakamura,et al.  The Theorem of Weierstrass , 2007 .

[27]  Yanli Xiao,et al.  Using a novel multivariable grey model to forecast the electricity consumption of Shandong Province in China , 2018 .

[28]  Shoujun Li,et al.  A novel varistructure grey forecasting model with speed adaptation and its application , 2020, Math. Comput. Simul..

[29]  Demis Hassabis,et al.  Mastering the game of Go without human knowledge , 2017, Nature.

[30]  Kwang-Cheng Chen,et al.  Machine Learning for Wireless Communication Channel Modeling: An Overview , 2019, Wireless Personal Communications.

[31]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[32]  Peter Henderson,et al.  An Introduction to Deep Reinforcement Learning , 2018, Found. Trends Mach. Learn..

[33]  Gang He,et al.  N-Step Sliding Recursion Formula of Variance and Its Implementation , 2020 .

[34]  Ke Yan,et al.  Tunnel Surface Settlement Forecasting with Ensemble Learning , 2019, Sustainability.

[35]  Emanuele Giovannetti,et al.  The diffusion of mobile social networking: Exploring adoption externalities in four G7 countries , 2015 .

[36]  Yang Du,et al.  Short-Term Photovoltaic Power Forecasting Based on Long Short Term Memory Neural Network and Attention Mechanism , 2019, IEEE Access.

[37]  R. C. Macridis.  A review , 1963 .

[38]  Qiang Ji,et al.  Forecasting China's natural gas demand based on optimised nonlinear grey models , 2017 .

[39]  Liu Si-feng.  Improvement of a Forecasting Discrete GM(1,1) , 2007 .

[40]  R. Carmona-Benítez,et al.  SARIMA damp trend grey forecasting model for airline industry , 2020 .

[41]  Bo Zeng,et al.  Forecasting the output of shale gas in China using an unbiased grey model and weakening buffer operator , 2018 .

[42]  Ke Yan,et al.  Short-Term Solar Irradiance Forecasting Based on a Hybrid Deep Learning Methodology , 2020, Inf..

[43]  Wenrui Yang.  Analysis of sports image detection technology based on machine learning , 2019, EURASIP J. Image Video Process..

[44]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[45]  Pablo Marshall,et al.  A forecasting system for movie attendance , 2013 .

[46]  Hans P. Moravec.  Obstacle avoidance and navigation in the real world by a seeing robot rover , 1980 .

[47]  Tahira Mahboob,et al.  A Survey on Unsupervised Machine Learning Algorithms for Automation, Classification and Maintenance , 2015 .

[48]  Muhammad Umair Raza,et al.  A Comprehensive Overview of BIG DATA Technologies: A Survey , 2020, Proceedings of the 2020 5th International Conference on Big Data and Computing.

[49]  Igor Mozetic,et al.  Evaluating time series forecasting models: an empirical study on performance estimation methods , 2019, Machine Learning.

[50]  Tzu-Li Tien,et al.  A research on the grey prediction model GM(1, n) , 2012, Appl. Math. Comput..

[51]  Zahra Hajirahimi,et al.  Hybrid structures in time series modeling and forecasting: A review , 2019, Eng. Appl. Artif. Intell..

[52]  Yi Lin,et al.  Grey Systems: Theory and Applications , 2010 .

[53]  Chuan Li,et al.  Development of an optimization method for the GM(1, N) model , 2016, Eng. Appl. Artif. Intell..

[54]  Jane X. Wang,et al.  Reinforcement Learning, Fast and Slow , 2019, Trends in Cognitive Sciences.

[55]  N. Shah,et al.  Implementing Machine Learning in Health Care - Addressing Ethical Challenges. , 2018, The New England journal of medicine.

[56]  Wang Yi.  GM(1,1) Modeling Method of Optimum the Whiting Values of Grey Derivative , 2001 .

[57]  Christos Davatzikos,et al.  Two distinct neuroanatomical subtypes of schizophrenia revealed using machine learning. , 2020, Brain : a journal of neurology.

[58]  Zhengxin Wang,et al.  Unbiased Grey Verhulst Model and Its Application , 2009 .

[59]  J. Deng,et al.  Introduction to Grey system theory , 1989 .

[60]  Yong Wang,et al.  Analysis of novel FAGM(1, 1, tα) model to forecast health expenditure of China , 2019, Grey Syst. Theory Appl..

[61]  Santanu Kumar Rath,et al.  Software design pattern recognition using machine learning techniques , 2016, 2016 IEEE Region 10 Conference (TENCON).

[62]  Qin Li,et al.  The NLS-based nonlinear grey Bernoulli model with an application to employee demand prediction of high-tech enterprises in China , 2018, Grey Syst. Theory Appl..

[63]  Liu Si-feng,et al.  Discrete GM(1,1) and Mechanism of Grey Forecasting Model , 2005 .

[64]  Richard Fikes,et al.  Learning and Executing Generalized Robot Plans , 1993, Artif. Intell..

[65]  Peng-Yu Chen,et al.  Foundation Settlement Prediction Based on a Novel NGM Model , 2014 .

[66]  Bernhard Schölkopf,et al.  A Generalized Representer Theorem , 2001, COLT/EuroCOLT.

[67]  Naiming Xie,et al.  Optimal solution for novel grey polynomial prediction model , 2018, Applied Mathematical Modelling.

[68]  Geoffrey I. Webb,et al.  A Bayesian-inspired, deep learning, semi-supervised domain adaptation technique for land cover mapping , 2020, ArXiv.

[69]  Ji Zhu,et al.  Predicting the Path of Technological Innovation: SAW Versus Moore, Bass, Gompertz, and Kryder , 2012, Mark. Sci..

[70]  Yonghong Hao,et al.  A Piecewise Grey System Model for Study the Effects of Anthropogenic Activities on Karst Hydrological Processes , 2012, Water Resources Management.

[71]  So Young Sohn,et al.  Global stock market investment strategies based on financial network indicators using machine learning techniques , 2019, Expert Syst. Appl..

[72]  Rita P. Ribeiro,et al.  Imbalanced regression and extreme value prediction , 2020, Machine Learning.

[73]  Ahmed Tealab,et al.  Time series forecasting using artificial neural networks methodologies: A systematic review , 2018, Future Computing and Informatics Journal.

[74]  Redouane Boumghar,et al.  Machine Learning for Spacecraft Operations Support - The Mars Express Power Challenge , 2017, 2017 6th International Conference on Space Mission Challenges for Information Technology (SMC-IT).

[75]  Mu Yong.  An Unbiased GM(1,1) Model With Optimum Grey Derivative′s Whitening Values , 2003 .

[76]  Vivek Vaidya,et al.  Lung nodule detection in CT using 3D convolutional neural networks , 2017, 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017).

[77]  Jesse Davis,et al.  Learning from positive and unlabeled data: a survey , 2018, Machine Learning.

[78]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[79]  Sumit Das,et al.  Applications of Artificial Intelligence in Machine Learning: Review and Prospect , 2015 .

[80]  Xin Ma,et al.  A brief introduction to the Grey Machine Learning , 2018, ArXiv.

[81]  Okyay Kaynak,et al.  Grey system theory-based models in time series prediction , 2010, Expert Syst. Appl..

[82]  Hesham A. Rakha,et al.  Applying Machine Learning Techniques to Transportation Mode Recognition Using Mobile Phone Sensor Data , 2015, IEEE Transactions on Intelligent Transportation Systems.

[83]  Xie Wei.  A Study on Two-Stage Bass Model of E-Business Imitate Innovation and its Application , 2013 .

[84]  Jinchuan Li,et al.  An integrated auto-focusing system for biomedical digital microscope , 2010, 2010 3rd International Conference on Biomedical Engineering and Informatics.

[85]  Sofiène Tahar,et al.  A Machine Learning Approach for Big Data in Oil and Gas Pipelines , 2015, 2015 3rd International Conference on Future Internet of Things and Cloud.

[86]  L. Steffenel,et al.  Forecasting upper atmospheric scalars advection using deep learning: an $$O_3$$ O 3 experiment , 2021, Mach. Learn..

[87]  K. Ngiam,et al.  Big data and machine learning algorithms for health-care delivery. , 2019, The Lancet. Oncology.

[88]  Giulio Reina,et al.  A multi-sensor robotic platform for ground mapping and estimation beyond the visible spectrum , 2018, Precision Agriculture.

[89]  João Pedro de Magalhães,et al.  A review of supervised machine learning applied to ageing research , 2017, Biogerontology.

[90]  Chong Wang,et al.  Deep Speech 2 : End-to-End Speech Recognition in English and Mandarin , 2015, ICML.

[91]  Frédéric Magoulès,et al.  A review on the prediction of building energy consumption , 2012 .

[92]  I. Kohane,et al.  Big Data and Machine Learning in Health Care. , 2018, JAMA.

[93]  Thomas G. Dietterich.  What is machine learning? , 2020, Archives of Disease in Childhood.

[94]  R. Mooney,et al.  Explanation-Based Learning: An Alternative View , 1986, Machine Learning.

[95]  Alessandro Piscopo,et al.  Predicting sense of community and participation by applying machine learning to open government data , 2014 .

[96]  Liu Si-fen,et al.  The Range Suitable for GM (1,1) , 2000 .

[97]  Nelson Fumo,et al.  A review on the basics of building energy estimation , 2014 .

[98]  Willem Waegeman,et al.  Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods , 2019, Machine Learning.

[99]  Marcos M. López de Prado,et al.  Advances in Financial Machine Learning: Numerai's Tournament (seminar slides) , 2018, SSRN Electronic Journal.

[100]  Ling Guan,et al.  Machine Learning on Biomedical Images: Interactive Learning, Transfer Learning, Class Imbalance, and Beyond , 2019, 2019 IEEE Conference on Multimedia Information Processing and Retrieval (MIPR).

[101]  Suci Karunia Prilistya,et al.  Tourism Demand Time Series Forecasting: A Systematic Literature Review , 2020, 2020 12th International Conference on Information Technology and Electrical Engineering (ICITEE).

[102]  Johan A. K. Suykens,et al.  Kernel based partially linear models and nonlinear identification , 2005, IEEE Transactions on Automatic Control.

[103]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[104]  D. Tetlow.  A review in time. , 1989, The Health service journal.

[105]  Xianjun Sam Zheng,et al.  Beyond Winning and Losing: Modeling Human Motivations and Behaviors Using Inverse Reinforcement Learning , 2018, ArXiv.

[106]  Xin Ma,et al.  Application of a novel time-delayed polynomial grey model to predict the natural gas consumption in China , 2017, J. Comput. Appl. Math..

[107]  Shuo-Pei Chen,et al.  Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1) , 2008 .

[108]  Aixia Guo,et al.  Gene Selection for Cancer Classification using Support Vector Machines , 2014 .

[109]  Jangam J. S. Mani,et al.  Population Classification upon Dietary Data Using Machine Learning Techniques with IoT and Big Data , 2018, Social Network Forensics, Cyber Security, and Machine Learning.

[110]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[111]  Xin Ma,et al.  Predicting the oil production using the novel multivariate nonlinear model based on Arps decline model and kernel method , 2016, Neural Computing and Applications.

[112]  Peter Sincak,et al.  Psychophysiological Indicators for Modeling User Experience in Interactive Digital Entertainment † , 2019, Sensors.

[113]  Edward Tsang,et al.  Special Issue on Algorithms in Computational Finance , 2019, Algorithms.

[114]  Hakyeon Lee,et al.  Demand forecasting for new media services with consideration of competitive relationships using the competitive Bass model and the theory of the niche , 2012 .

[115]  Song Zhong.  Center Approach Grey GM(1,1) Model , 2001 .

[116]  F ROSENBLATT,et al.  The perceptron: a probabilistic model for information storage and organization in the brain. , 1958, Psychological review.

[117]  Neha Agarwal,et al.  Stock Market Analysis using Supervised Machine Learning , 2019, 2019 International Conference on Machine Learning, Big Data, Cloud and Parallel Computing (COMITCon).

[118]  Alvin C. Rencher,et al.  A Review Of “Methods of Multivariate Analysis, Second Edition” , 2005 .

[119]  Tom Drummond,et al.  Faster and Better: A Machine Learning Approach to Corner Detection , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[120]  Zheng-Xin Wang,et al.  Decomposition of the factors influencing export fluctuation in China's new energy industry based on a constant market share model , 2017 .

[121]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[122]  Xin Ma,et al.  A novel kernel regularized nonhomogeneous grey model and its applications , 2017, Commun. Nonlinear Sci. Numer. Simul..

[123]  Muhammad Mahtab Alam,et al.  A Survey on the Roles of Communication Technologies in IoT-Based Personalized Healthcare Applications , 2018, IEEE Access.

[124]  Zheng-Xin Wang,et al.  Nonlinear Grey Prediction Model with Convolution Integral NGMC (1, n) and Its Application to the Forecasting of China's Industrial SO2 Emissions , 2014, J. Appl. Math..

[125]  Francisco C. Pereira,et al.  Model-Based Machine Learning for Transportation , 2019, Mobility Patterns, Big Data and Transport Analytics.

[126]  Hoang Anh Ngo,et al.  A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM(1,1) and application in predicting total COVID-19 infected cases , 2020, 2008.07581.

[127]  Francisco Martínez-Álvarez,et al.  A Survey on Data Mining Techniques Applied to Electricity-Related Time Series Forecasting , 2015 .

[128]  Yi Lin,et al.  A historical introduction to grey systems theory , 2004, 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583).

[129]  J. Bouma,et al.  Future Directions of Precision Agriculture , 2005, Precision Agriculture.

[130]  C. Goose,et al.  Glossary of Terms , 2004, Machine Learning.

[131]  Claudia Gonzalez Viejo,et al.  Robotics and computer vision techniques combined with non-invasive consumer biometrics to assess quality traits from beer foamability using machine learning: A potential for artificial intelligence applications , 2018, Food Control.

[132]  Li-Chang Hsu,et al.  Applying the Grey prediction model to the global integrated circuit industry , 2003 .

[133]  Xiaomeng Ma,et al.  Financial credit risk prediction in internet finance driven by machine learning , 2019, Neural Computing and Applications.

[134]  Y. Hajizadeh.  Machine learning in oil and gas; a SWOT analysis approach , 2019, Journal of Petroleum Science and Engineering.

[135]  Zeyu Wang,et al.  A review of artificial intelligence based building energy prediction with a focus on ensemble prediction models , 2015, 2015 Winter Simulation Conference (WSC).

[136]  Wenqing Wu,et al.  Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption , 2018, Energy.

[137]  Charles Robert Koch,et al.  A grey-box machine learning based model of an electrochemical gas sensor , 2020 .

[138]  Pilsung Kang,et al.  Pre-launch new product demand forecasting using the Bass model: : A statistical and machine learning-based approach , 2014 .

[139]  Jill L. King,et al.  Computer-assisted diagnosis of breast cancer using a data-driven Bayesian belief network , 1999, Int. J. Medical Informatics.

[140]  Zheng-Xin Wang,et al.  The NLS-based Grey Bass Model for Simulating New Product Diffusion , 2017 .

[141]  Sung Hyun Park,et al.  Reinforcement Learning Based MAC Protocol (UW-ALOHA-Q) for Underwater Acoustic Sensor Networks , 2019, IEEE Access.

[142]  Robert E. Schapire,et al.  The Boosting Approach to Machine Learning An Overview , 2003 .

[143]  Ping Li,et al.  Liver Extraction Using Residual Convolution Neural Networks From Low-Dose CT Images , 2019, IEEE Transactions on Biomedical Engineering.

[144]  Vito Pirrelli,et al.  The hidden dimension: a paradigmatic view of data-driven NLP , 1999, J. Exp. Theor. Artif. Intell..

[145]  Joshua B. Tenenbaum,et al.  Human-level concept learning through probabilistic program induction , 2015, Science.

[146]  L. Suganthi,et al.  Energy models for demand forecasting—A review , 2012 .

[147]  S. Ridout,et al.  “Did you hear?” , 2015, Medical Humanities.

[148]  Liu Si-feng,et al.  Research on Extension of Discrete Grey Model and Its Optimize Formula , 2006 .

[149]  Yael Travis-Lumer,et al.  Kernel machines for current status data , 2015, Mach. Learn..

[150]  Zheng-Xin Wang.  A GM(1,N)-based economic cybernetics model for the high-tech industries in China , 2014, Kybernetes.

[151]  Brett Whelan,et al.  Definition and interpretation of potential management zones in Australia , 2003 .

[152]  Grey Nearing,et al.  Combining Parametric Land Surface Models with Machine Learning , 2020, ArXiv.

[153]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[154]  D Carvalho,et al.  Big data and machine learning in health , 2020 .

[155]  Wei Zhou,et al.  Generalized GM (1, 1) model and its application in forecasting of fuel production , 2013 .

[156]  Abbes Amira,et al.  A survey of recommender systems for energy efficiency in buildings: Principles, challenges and prospects , 2021, Inf. Fusion.

[157]  Christopher M. Bishop,et al.  Model-based machine learning , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[158]  Hongbin Zha,et al.  Non-rigid Craniofacial 2D-3D Registration Using CNN-Based Regression , 2017, DLMIA/ML-CDS@MICCAI.

[159]  Eduardo F. Morales,et al.  An Introduction to Reinforcement Learning , 2011 .

[160]  R. Bayindir,et al.  Forecasting of Daily Total Horizontal Solar Radiation Using Grey Wolf Optimizer and Multilayer Perceptron Algorithms , 2019, 2019 8th International Conference on Renewable Energy Research and Applications (ICRERA).

[161]  Yong He,et al.  Application of optimized grey discrete Verhulst–BP neural network model in settlement prediction of foundation pit , 2019, Environmental Earth Sciences.

[162]  Xin Ma,et al.  The kernel-based nonlinear multivariate grey model , 2018 .

[163]  He Zhongqiu,et al.  Dynamic prediction of forest fuel loads by Grey Verhulst model , 1996, Journal of Northeast Forestry University.