\r\n\tIn sum, the book presents a reflective analysis of the pedagogical hubs for a changing world, considering the most fundamental areas of the current contingencies in education.
",isbn:"978-1-83968-793-8",printIsbn:"978-1-83968-792-1",pdfIsbn:"978-1-83968-794-5",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"b01f9136149277b7e4cbc1e52bce78ec",bookSignature:"Dr. María Jose Hernandez-Serrano",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10229.jpg",keywords:"Teacher Digital Competences, Flipped Learning, Online Resources Design, Neuroscientific Literacy (Myths), Emotions and Learning, Multisensory Stimulation, Citizen Skills, Violence Prevention, Moral Development, Universal Design for Learning, Sensitizing on Diversity, Supportive Strategies",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 14th 2020",dateEndSecondStepPublish:"October 12th 2020",dateEndThirdStepPublish:"December 11th 2020",dateEndFourthStepPublish:"March 1st 2021",dateEndFifthStepPublish:"April 30th 2021",remainingDaysToSecondStep:"4 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Dr. Phil. Maria Jose Hernandez Serrano is a tenured lecturer in the Department of Theory and History of Education at the University of Salamanca, where she currently teaches on Teacher Education. She graduated in Social Education (2000) and Psycho-Pedagogy (2003) at the University of Salamanca. Then, she obtained her European Ph.D. in Education and Training in Virtual Environments by research with the University of Manchester, UK (2009).",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"187893",title:"Dr.",name:"María Jose",middleName:null,surname:"Hernandez-Serrano",slug:"maria-jose-hernandez-serrano",fullName:"María Jose Hernandez-Serrano",profilePictureURL:"https://mts.intechopen.com/storage/users/187893/images/system/187893.jpg",biography:"DPhil Maria Jose Hernandez Serrano is a tenured Lecturer in the Department of Theory and History of Education at the University of Salamanca (Spain), where she currently teaches on Teacher Education. She graduated in Social Education (2000) and Psycho-Pedagogy (2003) at the University of Salamanca. Then, she obtained her European Ph.D. on Education and Training in Virtual Environments by research with the University of Manchester, UK (2009). She obtained a Visiting Scholar Postdoctoral Grant (of the British Academy, UK) at the Oxford Internet Institute of the University of Oxford (2011) and was granted with a postdoctoral research (in 2021) at London Birbeck University.\n \nShe is author of more than 20 research papers, and more than 35 book chapters (H Index 10). She is interested in the study of the educational process and the analysis of cognitive and affective processes in the context of neuroeducation and neurotechnologies, along with the study of social contingencies affecting the educational institutions and requiring new skills for educators.\n\nHer publications are mainly of the educational process mediated by technologies and digital competences. Currently, her new research interests are: the transdisciplinary application of the brain-based research to the educational context and virtual environments, and the neuropedagogical implications of the technologies on the development of the brain in younger students. Also, she is interested in the promotion of creative and critical uses of digital technologies, the emerging uses of social media and transmedia, and the informal learning through technologies.\n\nShe is a member of several research Networks and Scientific Committees in international journals on Educational Technologies and Educommunication, and collaborates as a reviewer in several prestigious journals (see public profile in Publons).\n\nUntil March 2010 she was in charge of the Adult University of Salamanca, by coordinating teaching activities of more than a thousand adult students. She currently is, since 2014, the Secretary of the Department of Theory and History of Education. Since 2015 she collaborates with the Council Educational Program by training teachers and families in the translation of advances from educational neuroscience.",institutionString:"University of Salamanca",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"University of Salamanca",institutionURL:null,country:{name:"Spain"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"23",title:"Social Sciences",slug:"social-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"301331",firstName:"Mia",lastName:"Vulovic",middleName:null,title:"Mrs.",imageUrl:"https://mts.intechopen.com/storage/users/301331/images/8498_n.jpg",email:"mia.v@intechopen.com",biography:"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"6942",title:"Global Social Work",subtitle:"Cutting Edge Issues and Critical Reflections",isOpenForSubmission:!1,hash:"222c8a66edfc7a4a6537af7565bcb3de",slug:"global-social-work-cutting-edge-issues-and-critical-reflections",bookSignature:"Bala Raju Nikku",coverURL:"https://cdn.intechopen.com/books/images_new/6942.jpg",editedByType:"Edited by",editors:[{id:"263576",title:"Dr.",name:"Bala",surname:"Nikku",slug:"bala-nikku",fullName:"Bala Nikku"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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\n\t\t\t
1. Introduction
\n\t\t\t
Artificial neural network models (NN) have been widely adopted on the field of time series forecasting in the last two decades. As a kind of soft-computing method, neural forecasting systems can be built more easily because of their learning algorithms than traditional linear or nonlinear models which need to be constructed by advanced mathematic techniques and long process to find optimized parameters of models. The good ability of function approximation and strong performance of sample learning of NN have been known by using error back propagation learning algorithm (BP) with a feed forward multi-layer NN called multi-layer perceptron (MLP) (Rumelhart et. al, 1986), and after this mile stone of neural computing, there have been more than 5,000 publications on NN for forecasting (Crone & Nikolopoulos, 2007).
\n\t\t\t
To simulate complex phenomenon, chaos models have been researched since the middle of last century (Lorenz, 1963; May, 1976). For NN models, the radial basis function network (RBFN) was employed on chaotic time series prediction in the early time (Casdagli, 1989). To design the structure of hidden-layer of RBFN, a cross-validated subspace method is proposed, and the system was applied to predict noisy chaotic time series (Leung & Wang, 2001). A two-layered feed-forward NN, which has its all hidden units with hyperbolic tangent activation function and the final output unit with linear function, gave a high accuracy of prediction for the Lorenz system, Henon and Logistic map (Oliveira et. al, 2000).
\n\t\t\t
To real data of time series, NN and advanced NN models (Zhang, 2003) are reported to provide more accurate forecasting results comparing with traditional statistical model (i.e. the autoregressive integrated moving average (ARIMA)(Box & Jankins, 1976)), and the performances of different NNs for financial time series are confirmed by Kodogiannis & Lolis (Kodogiannis & Lolis, 2002). Furthermore, using benchmark data, several time series forecasting competitions have been held in the past decades, many kinds of NN methods showed their powerful ability of prediction versus other new techniques, e.g. vector quantization, fuzzy logic, Bayesian methods, Kalman filter or other filtering techniques, support vector machine, etc (Lendasse et. al, 2007; Crone & Nikolopoulos, 2007).
\n\t\t\t
Meanwhile, reinforcement learning (RL), a kind of goal-directed learning, has been generally applied in control theory, autonomous system, and other fields of intelligent computation (Sutton & Barto, 1998). When the environment of an agent belongs to Markov decision process (MDP) or the Partially Observable Markov Decision Processes (POMDP), behaviours of exploring let the agent obtain reward or punishment from the environment, and the policy of action then is modified to adapt to acquire more reward. When prediction error for a time series is considered as reward or punishment from the environment, one can use RL to train predictors constructed by neural networks.
\n\t\t\t
In this chapter, two kinds of neural forecasting systems using RL are introduced in detail: a self-organizing fuzzy neural network (SOFNN) (Kuremoto et al., 2003) and a multi-layer perceptron (MLP) predictor (Kuremoto et al., 2005). The results of experiments using Lorenz chaos showed the efficiency of the method comparing with the results by a conventional learning method (BP).
\n\t\t
\n\t\t
\n\t\t\t
2. Architecture of neural forecasting system
\n\t\t\t
The flow chart of neural forecasting processing is generally used by which in Fig. 1. The tth step time series data \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t can be embedded into a new n-dimensional space \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t according to Takens Theorem (Takens, 1981). Eq. (1) shows the detail of reconstructed vector space which serves input layer of NN, here \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tis an arbitrary delay. An example of 3-dimensional reconstruction is shown in Fig. 2. The output layer of neural forecasting systems is usually with one neuron whose output \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t equals prediction result.
There are various architectures of NN models, including MLP, RBFN, recurrent neural network (RNN), autoregressive recurrent neural network (ARNN), neuro-fuzzy hybrid network, ARIMA-NN hybrid model, SOFNN, and so on. The training rules of NNs are also very different not only well-known methods, i.e., BP, orthogonal least squares (OLS), fuzzy inference, but also evolutional computation, i.e., genetic algorithm (GA), particle swarm optimization (PSO), genetic programming (GP), RL, and so on.
\n\t\t\t
Figure 2.
Embedding a time series into a 3-dimensional space.
\n\t\t\t
\n\t\t\t\t
2.1. MLP with BP
\n\t\t\t\t
MLP, a feed-forward multi-layer network, is one of the most famous classical neural forecasting systems whose structure is shown in Fig. 3. BP is commonly used as its learning rule, and the system performs fine efficiency in the function approximation and nonlinear prediction.
\n\t\t\t\t
For the hidden layer, let the number of neurons is K, the output of neuron k is\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tH\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, then the output of MLP is obtained by Eq. (2) and Eq. (3).
A MLP with n input neurons, one hidden layer, and one neuron in output layer using BP training algorithm.
Here\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\trepresent the connection of kth hidden neuron with output neuron and input neurons, respectively. Activation function f (u) is a sigmoid function (or hyperblolic tangent function) given by Eq. (4).\n\t\t\t\t\t
Gradient parameter β is usually set to 1.0, and to correspond to f (u), the scale of time series data should be adjusted to (0.0, 1.0).
\n\t\t\t\t
BP is a supervised learning algorithm, using sample data trains NN providing more correct output data by modifying all of connections between layers. Conventionally, the error function is given by the mean square error as Eq. (5).
Here S is the size of train data set, y (t+1) is the actual data in time series. The error is minimized by adjusting the weights according to Eq. (6), Eq. (7) and Eq. (2), Eq. (3).
Here \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis a discount parameter (0.0<\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t1.0), \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis the learning rate (0.0 < \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t1.0). The training iteration keeps to be executed until the error function converges enough.
\n\t\t\t\t
Figure 4.
A MLP with n input neurons, two hidden layers, and one neuron in output layer using RL training algorithm.
\n\t\t\t
\n\t\t\t
\n\t\t\t\t
2.2. MLP with RL
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One important feature of RL is its statistical action policy, which brings out exploration of adaptive solutions. Fig. 4 shows a MLP which output layer is designed by a neuron with Gaussian function. A hidden layer consists of variables of the distribution function is added. The activation function of units in each hidden layer is still sigmoid function (or hyperbolic tangent function) (Eq. (8)-(10)).
Here \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are gradient constants, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t(\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t) represents the connection of kth hidden neuron with neuron μ,σ in statistical hidden layer and input neurons, respectively. The modification of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is calculated by RL algirthm which will be described in section 3.
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2.3. SOFNN with RL
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A neuro-fuzzy hybrid forecasting system, SOFNN, using RL training algorithm is shown in Fig. 5. A hidden layer consists of fuzzy membership functions \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is designed to categorize input data of each dimension in\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t,...,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\tn\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, t = 1, 2,..., S (Eq. (12)).
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Figure 5.
A SOFNN with n input neurons, three hidden layers, and one neuron in output layer using RL training algorithm.
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The fuzzy reference\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tλ\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, which calculates the fitness for an input set\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, is executed by fuzzy rules layer (Eq. 13).
Where i = 1, 2,..., n, j means the number of membership function which is 1 initially, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the mean and standard deviation of jth membership function for input\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, c means each of membership function which connects with kth rule, respectively. c\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t∈\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\tj, ( j = 1, 2,..., l ), and l is the maximum number of membership functions. If an adaptive threshold of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is considered, then the multiplication or combination of membership functions and rules can be realized automatically, the network owns self-organizing function to deal with different features of inputs.
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The output of neurons \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t in stochastic layer is given by Eq. (14), Eq. (15) respectively.
Where\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the connections between \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand rules, and\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare the mean and standard deviation of stochastic function \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tπ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t whose description is given by Eq. (11). The output of system can be obtained by generating a random data according this probability function.
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3. SGA of RL
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3.1. Algorithm of SGA
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A RL algorithm, Stochastic Gradient Ascent (SGA), is proposed by Kimura and Kobayashi (Kimura & Kobayashi, 1996, 1998) to deal with POMDP and continuous action space. Experimental results reported that SGA learning algorithm was successful for cart-pole control and maze problem. In the case of time series forecasting, the output of predictor can be considered as an action of agent, and the prediction error can be used as reward or punishment from the environment, so SGA can be used to train a neural forecasting system by renewing internal variable vector of NN (Kuremoto et. al, 2003, 2005).
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The SGA algorithm is given below.
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Step 1. Observe an input \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t from training data of time series.
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Step 2. Predict a future data \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t according to a probability\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tπ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\ty\n\t\t\t\t\t\t\t\t\t\t\t\t^\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t\t+\n\t\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tx\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t.
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Step 3. Receive the immediate reward \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tby calculating the prediction error.
\n\t\t\t\t\t\n\t\t\t\t Here\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tr\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t, \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tare evaluation constants greater than or equal to zero.
Here \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t0\n\t\t\t\t\t\t\t\t\t≤\n\t\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is a discount factor, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tdenotes ith internal variable vector.
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Step 5. Calculate \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t by Eq. (19).
Here \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t⋯\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\t\t⋯\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t denotes synaptic weights, and other internal variables of forecasting system, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\ts\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis a positive learning rate.
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Step 7. For next time step t+1, return to step 1.
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Characteristic eligibility\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, shown in Eq. (17), means that the change of the policy function is concerning with the change of system internal variable vector (Williams, 1992). In fact, the algorithm combines reward/punishment to modify the stochastic policy with its internal variable renewing by step 4 and step 5. The finish condition of training iteration is also decided by the enough convergence of prediction error of sample data.
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3.2. SGA for MLP
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For the MLP forecasting system described in section 2.2 (Fig. 4), the characteristic eligibility
\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\tof Eq. (21)-(23) can be derived from Eq. (8)-(11) with the internal viable \n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t
The initial values of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare random numbers in (0, 1) at the first iteration of training. Gradient constants \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t and reward parameters r, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tdenoted by Eq. (16) have empirical values.
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3.3. SGA for SOFNN
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For the SOFNN forecasting system described in section 2.3 (Fig. 5), the characteristic eligibility \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\te\n\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t(\n\t\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t\t)\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t of Eq. (24)-(27) can be derived from Eq. (11)-(15) with the internal viable \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\trespectively.
Here membership function \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tB\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t is described by Eq. (12), fuzzy inference \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tλ\n\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tis described by Eq. (13). The initial values of \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tare random numbers included in (0, 1) at the first iteration of training. Reward r, threshold of evaluation error\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tε\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tdenoted by Eq. (16) have empirical values.
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4. Experiments
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A chaotic time series generated by Lorenz equations was used as benchmark for forecasting experiments which were MLP using BP, MLP using SGA, SOFNN using SGA. Prediction precision was evaluated by the mean square error (MSE) between forecasted values and time series data.
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4.1. Lorenz chaos
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A butterfly-like attractor generated by the three ordinary differential equations (Eq. (28)) is very famous on the early stage of chaos phenomenon study (Lorenz, 1969).
Here \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tφ\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tϕ\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t are constants. The chaotic time series was obtained from dimension o(t) of Eq. (29) in forecasting experiments, where\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tΔ\n\t\t\t\t\t\t\t\t\tt\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0.005\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tδ\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t16.0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tφ\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t45.92\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t,\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tϕ\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t4.0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t.
The size of sample data for training is 1,000, and the continued 500 data were served as unknown data for evaluating the accuracy of short-term (i.e. one-step ahead) prediction.
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4.2. Experiment of MLP using BP
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It is very important and difficult to construct a good architecture of MLP for nonlinear prediction. An experimental study (Oliveira et. al, 2000) showed the different prediction results for Lorenz time series by the architecture of n : 2n : n : 1, where n denotes the embedding dimension and the cases of n = 2, 3, 4 were investigated for different term predictions (long-term prediction
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Figure 6.
Prediction results after 2,000 iterations of training by MLP using BP.
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Figure 7.
Prediction error (MSE) in training iteration of MLP using BP.
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For short-term prediction here, a three-layer MLP using BP and 3 : 6 : 1 structure shown in Fig. 3 was used in experiment, and time delay \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=1 was used in embedding input space. Gradient constant of sigmoid function \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t= 1.0, discount constant \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t= 1.0, learning rate \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tη\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t= 0.01,
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Figure 8.
One-step ahead forecasting results by MLP using BP.
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and the finish condition of training was set to E(W) <\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t5.0\n\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t4\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t. The prediction results after training 2,000 times are shown in Fig. 6, and the change of prediction error according to the iteration of training is shown in Fig. 7. The one-step ahead prediction results are shown in Fig. 8. The 500 steps MSE of one-step ahead forecasting by MLP using BP was 0.0129.
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4.3. Experiment of MLP using SGA
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A four-layer MLP forecasting system with SGA and 3 : 60 : 2 : 1 structure shown in Fig. 4 was used in experiment, and time delay \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=1 was used in embedding input space. Gradient
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Figure 9.
Prediction results before iteration by MLP using SGA.
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Figure 10.
Prediction results after 5,000 iterations of training by MLP using SGA.
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constants of sigmoid functions\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t1\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t8.0,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t2\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t18.0,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tβ\n\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t10.0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, discount constant \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t= 0.9, learning rate\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t2.0\n\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t2.0\n\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t5\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, the reward was set by Eq. (30), and the
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finish condition of training was set to 30,000 iterations where the convergence E(W) could be observed. The prediction results after 0, 5,000, 30,000 iterations of training are shown in Fig. 9, Fig. 10 and Fig. 11 respectively. The change of prediction error during training is shown in Fig. 12. The one-step ahead prediction results are shown in Fig. 13. The 500 steps MSE of one-step ahead forecasting by MLP using SGA was 0.0112, forecasting accuracy was 13.2% upped than MLP using BP.
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Figure 11.
Prediction results after 30,000 iterations of training by MLP using SGA.
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Figure 12.
Prediction error (MSE) in training iteration of MLP using SGA.
One-step ahead forecasting results by MLP using SGA.
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4.4. Experiment of SOFNN using SGA
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A five-layer SOFNN forecasting system with SGA and structure shown in Fig. 5 was used in experiment, time delay \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tτ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t=2 was used in 3, 4, or 5-dimensional embedding input spaces. Initial value of weight \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t had random values in (0.0, 1.0), \n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0.5,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t0.0,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t15.0\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\tand discount\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tγ\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t= 0.9, learning rate\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tm\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\ti\n\t\t\t\t\t\t\t\t\t\t\tj\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\tσ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t3.0\n\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t6\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t,\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\tα\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\tw\n\t\t\t\t\t\t\t\t\t\t\tμ\n\t\t\t\t\t\t\t\t\t\t\tk\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t=\n\t\t\t\t\t\t\t\t\t2.0\n\t\t\t\t\t\t\t\t\t×\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t10\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t−\n\t\t\t\t\t\t\t\t\t\t\t3\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t, the reward r was set by Eq. (31), and the finish condition of training was also set to 30,000 iterations where the convergence E(W) could be observed. The prediction results after training are shown in Fig. 14, where the number of input neurons was 4 and data scale of results was modified into (0.0, 1.0). The change of prediction error during the training is shown in Fig. 15. The one-step ahead prediction results are shown in Fig. 16. The 500 steps MSE of one-step ahead forecasting by SOFNN using SGA was 0.00048, forecasting accuracy was 95.7% and 96.3% upped than the case by MLP using BP and by MLP using SGA respectively.
Prediction results after 30,000 iterations of training by SOFNN using SGA.
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Figure 15.
Prediction error (MSE) in training iteration of SOFNN using SGA.
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Figure 16.
One-step ahead forecasting results by SOFNN using SGA.
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Figure 17.
The number of membership function neurons of SOFNN using SGA increased in training experiment.
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Figure 18.
The number of rules of SOFNN using SGA increased in training experiment.
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One advanced feature of SOFNN is its data-driven structure building. The number of membership function neurons and rules increased with samples (1,000 steps in training of experiment) and iterations (30,000 times in training of experiment), which can be confirmed by Fig. 17 and Fig. 18. The number of membership function neurons for the 4 input neurons was 44, 44, 44, 45 respectively, and the number of rules was 143 when the training finished.
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5. Conclusion
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Though RL has been developed as one of the most important methods of machine learning, it is still seldom adopted in forecasting theory and prediction systems. Two kinds of neural forecasting systems using SGA learning were described in this chapter, and the experiments of training and short-term forecasting showed their successful performances comparing with the conventional NN prediction method. Though the iterations of MLP with SGA and SOFNN with SGA in training experiments took more than that of MLP with BP, both of their computation time were not more than a few minutes by a computer with 3.0GHz CPU.
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A problem of these RL forecasting systems is that the value of reward in SGA algorithm influences learning convergence seriously, the optimum reward should be searched experimentally for different time series. Another problem of SOFNN with SGA is how to tune up initial value of deviation parameter in membership function and the threshold those
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were also modified by observing prediction error in training experiments. In fact, when SOFNN with SGA was applied on an neural forecasting competition “NN3” where 11 time series sets were used as benchmark, it did not work sufficiently in the long-term prediction comparing with the results of other methods (Kuremoto et. al, 2007; Crone & Nikolopoulos, 2007). All these problems remain to be resolved, and it is expected that RL forecasting systems will be developed remarkably in the future.
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Acknowledgments
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We would like to thank Mr. Yamamoto A. and Mr. Teramori N. for their early work in experiments, and a part of this study was supported by MEXT-KAKENHI (15700161) and JSPS-KAKENHI (18500230).
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\n',keywords:null,chapterPDFUrl:"https://cdn.intechopen.com/pdfs/670.pdf",chapterXML:"https://mts.intechopen.com/source/xml/670.xml",downloadPdfUrl:"/chapter/pdf-download/670",previewPdfUrl:"/chapter/pdf-preview/670",totalDownloads:5927,totalViews:916,totalCrossrefCites:2,totalDimensionsCites:7,hasAltmetrics:0,dateSubmitted:null,dateReviewed:null,datePrePublished:null,datePublished:"January 1st 2008",dateFinished:null,readingETA:"0",abstract:null,reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/670",risUrl:"/chapter/ris/670",book:{slug:"reinforcement_learning"},signatures:"Takashi Kuremoto, Masanao Obayashi and Kunikazu Kobayashi",authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Architecture of neural forecasting system",level:"1"},{id:"sec_2_2",title:"2.1. MLP with BP",level:"2"},{id:"sec_3_2",title:"2.2. MLP with RL",level:"2"},{id:"sec_4_2",title:"2.3. SOFNN with RL",level:"2"},{id:"sec_6",title:"3. SGA of RL",level:"1"},{id:"sec_6_2",title:"3.1. Algorithm of SGA",level:"2"},{id:"sec_7_2",title:"3.2. SGA for MLP",level:"2"},{id:"sec_8_2",title:"3.3. SGA for SOFNN",level:"2"},{id:"sec_10",title:"4. Experiments",level:"1"},{id:"sec_10_2",title:"4.1. Lorenz chaos",level:"2"},{id:"sec_11_2",title:"4.2. Experiment of MLP using BP",level:"2"},{id:"sec_12_2",title:"4.3. Experiment of MLP using SGA",level:"2"},{id:"sec_13_2",title:"4.4. Experiment of SOFNN using SGA",level:"2"},{id:"sec_15",title:"5. Conclusion",level:"1"},{id:"sec_16",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tBox\n\t\t\t\t\t\t\tG. E. P.\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\tJenkins\n\t\t\t\t\t\t\tG.\n\t\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t1970\n\t\t\t\t\tTime series analysis: Forecasting and control. 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'}],corrections:null},book:{id:"2220",title:"Reinforcement Learning",subtitle:null,fullTitle:"Reinforcement Learning",slug:"reinforcement_learning",publishedDate:"January 1st 2008",bookSignature:"Cornelius Weber, Mark Elshaw and Norbert Michael Mayer",coverURL:"https://cdn.intechopen.com/books/images_new/2220.jpg",licenceType:"CC BY-NC-SA 3.0",editedByType:"Edited by",editors:[{id:"130979",title:"Prof.",name:"Cornelius",middleName:null,surname:"Weber",slug:"cornelius-weber",fullName:"Cornelius Weber"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"670",title:"Neural Forecasting Systems",slug:"neural_forecasting_systems",totalDownloads:5927,totalCrossrefCites:2,signatures:"Takashi Kuremoto, Masanao Obayashi and Kunikazu Kobayashi",authors:[null]},{id:"671",title:"Reinforcement Learning in System Identification",slug:"reinforcement_learning_in_system_identification",totalDownloads:4160,totalCrossrefCites:2,signatures:"Mariela Cerrada and Jose Aguilar",authors:[null]},{id:"672",title:"Reinforcement Evolutionary Learning for Neuro-Fuzzy Controller Design",slug:"reinforcement_evolutionary_learning_for_neuro-fuzzy_controller_design",totalDownloads:3566,totalCrossrefCites:0,signatures:"Cheng-Jian Lin",authors:[null]},{id:"673",title:"Superposition-Inspired Reinforcement Learning and Quantum Reinforcement Learning",slug:"superposition-inspired_reinforcement_learning_and_quantum_reinforcement_learning",totalDownloads:4311,totalCrossrefCites:0,signatures:"Chun-Lin Chen and Dao-Yi Dong",authors:[null]},{id:"674",title:"An Extension of Finite-state Markov Decision Process and an Application of Grammatical Inference",slug:"an_extension_of_finite-state_markov_decision_process_and_an_application_of_grammatical_inference",totalDownloads:3340,totalCrossrefCites:0,signatures:"Takeshi Shibata and Ryo Yoshinaka",authors:[null]},{id:"675",title:"Interaction Between the Spatio-Temporal Learning Rule (Non Hebbian) and Hebbian in Single Cells: A Cellular Mechanism of Reinforcement Learning",slug:"interaction_between_the_spatio-temporal_learning_rule__non_hebbian__and_hebbian_in_single_cells__a_c",totalDownloads:3448,totalCrossrefCites:0,signatures:"Minoru Tsukada",authors:[null]},{id:"676",title:"Reinforcement Learning Embedded in Brains and Robots",slug:"reinforcement_learning_embedded_in_brains_and_robots",totalDownloads:3915,totalCrossrefCites:4,signatures:"Cornelius Weber, Mark Elshaw, Stefan Wermter, Jochen Triesch and Christopher Willmot",authors:[null]},{id:"677",title:"Decentralized Reinforcement Learning for the Online Optimization of Distributed Systems",slug:"decentralized_reinforcement_learning_for_the_online_optimization_of_distributed_systems",totalDownloads:4338,totalCrossrefCites:5,signatures:"Jim Dowling and Seif Haridi",authors:[null]},{id:"678",title:"Multi-Automata Learning",slug:"multi-automata_learning",totalDownloads:3832,totalCrossrefCites:0,signatures:"Verbeeck Katja, Nowe Ann, Vrancx Peter and Peeters Maarten",authors:[null]},{id:"679",title:"Abstraction for Genetics-Based Reinforcement Learning",slug:"abstraction_for_genetics-based_reinforcement_learning",totalDownloads:5189,totalCrossrefCites:1,signatures:"Will Browne, Dan Scott and Charalambos Ioannides",authors:[null]},{id:"680",title:"Dynamics of the Bush-Mosteller Learning Algorithm in 2x2 Games",slug:"dynamics_of_the_bush-mosteller_learning_algorithm_in_2x2_games",totalDownloads:3737,totalCrossrefCites:0,signatures:"Luis R. 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Alves, Li Weigang and Bueno B. Souza",authors:[null]}]},relatedBooks:[{type:"book",id:"2284",title:"Real-World Applications of Genetic Algorithms",subtitle:null,isOpenForSubmission:!1,hash:"6d5fc65bd034c0bc5384716fa643d336",slug:"real-world-applications-of-genetic-algorithms",bookSignature:"Olympia Roeva",coverURL:"https://cdn.intechopen.com/books/images_new/2284.jpg",editedByType:"Edited by",editors:[{id:"109273",title:"Dr.",name:"Olympia",surname:"Roeva",slug:"olympia-roeva",fullName:"Olympia Roeva"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"30289",title:"Different Tools on Multi-Objective Optimization of a Hybrid Artificial Neural Network – Genetic Algorithm for Plasma Chemical Reactor Modelling",slug:"different-tools-on-multi-objective-optimization-of-a-hybrid-artificial-neural-network-genetic-algori",signatures:"Nor Aishah Saidina Amin and I. 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1. Introduction
The evidences of impacts of climate change across the world are that there has been an increase in climate extremity phenomena such as cold wave, heat wave, extreme depressions, intense precipitation, rising number of warm days and nights, and decreasing number of cold days and nights. AR4 and AR5 IPCC have predicted an increase in frequency and intensity of warm spells or heat waves in the end of twenty-first century, affecting to increase vector-borne diseases, water-borne diseases, reduce cold-related mortality, and diminish food production and labor productivity at different levels over most land areas of the earth [1, 2]. As a matter of fact, there is large number of studies on health effects of heat waves [3, 4]. Some of the studies argue that the contribution of rising in minimum temperatures has decreased in number of deaths associated with cold spells [5, 6]. On the other hand, there are few studies dealing with cold spells and health impacts. For instance, some studies indicated that the effects of extreme cold temperatures are generally more prolonged than heat wave without mortality displacement [3, 7]. However, most of the existing studies on health effects of cold spells are found to be associated with the temperate climate regions in developed countries, while there are very few such studies carried out in tropical or subtropical regions of developing countries [3, 8, 9, 10, 11].
Nepal has experienced global warming and its impacts on forming climate extremities, ill-health of the people, change in agricultural production patterns, etc. over the past recent decades. Cold wave is one of the climate extremities due to global warming in Nepal. The studies of National Agriculture Research Council (NARC) have indicated negative impacts of cold wave on agricultural productivity in Nepal [12]. Other studies have shown the health of the inhabitants being affected due to cold wave in the Tarai region of Nepal in the last two decades [13, 14, 15, 16]. The present chapter intends to analyze the climate change patterns and the climate extremities such as cold wave and its impacts on the vulnerable populations in the Tarai region of Nepal.
2. Methodology
The vulnerable population is defined in terms of age group such as children below 5 years of age, pregnant women, and elderly population above 65 years of age [17]. The three subsets of under-five children, such as neonates <1 months, infant <1 year and <5 years, of which neonates is the most vulnerable and it is followed by other subsets [18].
The climate prevailing in Nepal can be divided into four seasons, based on rainfall and temperature conditions. They are rainy summer or Monsoon (June–September with rainy, hot, and humid weather), winter (December–February with coldest and driest weather), pre-monsoon (March–May with hot weather and thunderstorms) and post-monsoon (October–November with cool and pleasant weather). The climate data including monthly minimum and maximum temperatures for all individual years from 1974 to 2014 by the physiographic regions, such as mountain, hill, and Tarai have been acquired from all 67 weather stations from the Department of Hydrology and Meteorology, Kathmandu, and Nepal [19]. These data have been used for describing climate change patterns for all physiographic regions across the country in general and for analyzing seasonal trends of climate and climatic extremities for the Tarai region in particular. The prediction of trends of temperatures by year has been carried out for two distinct slots: 1974–2014 and 2000–2014.
Data on daily death of the vulnerable population groups due to cold wave during the winter season from 1974 to 2013 for all districts of the Tarai region were obtained from available sources [18, 19, 20, 21, 22]. The contribution of seasonal temperature change, mainly, cold wave to the deaths of the vulnerable groups, and the mortality rate have been analyzed by using multiple regression analysis.
The multiple linear regression analysis has been used to develop a model for predicting mortality from the climatic variables at different time lags. This relationship is given by the equation [23]:
Y=βo+β1X1+β2X2……..βkXk+εE1
where βk is coefficients, Xi is the predictor, Y is mortality (predicted), βo is a constant and 𝜀 is random error.
The perception about the death due to cold spell or wave and status of vulnerable population groups were carried out by informal talking among 25 respondents selected randomly: 5 each from different walks of life such as the local communities, government personnel, public health personnel, female community health volunteers and school teachers.
3. Findings
3.1. Brief introduction to physiography, climate, and population of Nepal
3.1.1. Physiography
Geographically, Nepal can be divided into three broad physiographic regions, namely mountain, hill, and Tarai from north to south (Figure 1). The altitudes of these three regions range from 8848 m above sea level (masl) in the north to 60 masl in the south over an average north-south span of 193 km [24]. Tarai refers to plain topography in Nepal.
Figure 1.
Physiographic regions of Nepal.
The Tarai is the smallest physiographic region, sharing 23% of the country’s total area, but it has the largest population with over 50% of the nation’s total population of 26.6 million (Table 1). Population has increased consistently in this region during the past decades. In 1971, the Tarai’s population had shared nearly 38% of the country’s total population that increased to over 50% in 2011 [17]. The rapid growth of the Tarai population is considered due to natural cause and other causes including internal migration of population from the hills and international migration from adjoining Indian states [17, 21].
Table 2 exhibits that the combined populations of the vulnerable groups (under-five children, pregnant women, and elderly) account for about 17% of the Tarai’s total population. For Nepal, the life expectancy at birth of Nepalese population is 66.51 years, whereas the death rate is 6.75 deaths/1000 population and infant mortality rate is 32 deaths/1000 live births [18].
Vulnerable groups
Total population
% of vulnerable population
Under-five population
1,380,169
10.3
Expected pregnancies
350,497
2.6
Elderly population
534,018
4.0
Total
2,264,684
16.9
Table 2.
Distribution of population of vulnerable groups in Tarai region, Nepal.
Nepal lies within the subtropical climatic zone over the globe [19]. The climate is largely influenced by the Monsoon system, but there is also an influence of the cyclonic system originating from the Mediterranean Sea during the winter season. Owing to rise of altitude of mountains considerably from the south to the north, Nepal possesses diverse climate types ranging from sub-tropical in the Tarai region to the arctic in the high Himalayas. Likewise, the annual precipitation also ranges from over 5000 mm in the Western and Eastern midland mountains to below 150 mm in the northern areas beyond high Himalayas, with an annual mean precipitation of 1858 mm [19, 25].
In Nepal, the annual trends of temperature patterns vary remarkably among four different seasons: summer monsoon, post-monsoon, winter and pre-monsoon, and those three physiographic regions (Table 3). The annual maximum and minimum temperature trends for the country as a whole are 0.056 and 0.002°C/year, respectively [19]. Table 3 shows a negative trend of maximum temperature in contrast to the positive trend of minimum temperature during the winter season in the Tarai region [19].
Physiographic regions
Temperature trends °C per year (1974–2014)
Winter
Pre-monsoon
Monsoon
Post-monsoon
Annual
Maximum temperature
Tarai
−0.004
0.018
0.036
0.028
0.021
Hill
0.046
0.049
0.055
0.052
0.052
Mountain
0.101
0.076
0.072
0.085
0.086
Minimum temperature
Tarai
0.025
0.015
0.015
0.013
0.018
Hill
0.004
0.004
0.014
0.006
0.010
Mountain
−0.056
−0.021
0.013
−0.025
−0.015
Table 3.
Seasonal temperature trends by physiographic regions, Nepal.
The mean annual maximum temperature for the Tarai region is 30.4 at 95% confidence interval (CI) of 36–30 and mean annual minimum temperature is 18.3 at 95% CI of 16–25. During the winter season, the mean minimum temperature in the Tarai region remains at 9.8°C with 95% CI of 9.5–10.1°C and mean maximum temperature is 23.2 with 95% CI of 22.7–23.7°C. While analysis of temperature trends by year is performed, a conspicuous distinction is found between two slots of years, such as 1974–2014 and 2000–2014 (Table 4). During the second slot of years: 2000–2014, negative trends are found in the annual mean minimum temperature, as well as in both mean maximum and minimum temperatures in the winter season in the Tarai region, but found a positive trend in the annual mean maximum temperature in this slot of years. Conversely, positive trends are found in all three temperature conditions during the first slot of years: 1974–2014 except in the winter maximum temperature, which shows negative trend. Thus, the analysis of two slots of periods of years shows a decreasing temperature scenario, particularly during the winter season in the Tarai region.
Temperature conditions (°C/year)
1974–2014
2000–2014
Annual maximum
0.021
0.031
Annual minimum
0.018
−0.040
Winter maximum
−0.016
−0.062
Winter minimum
0.024
−0,024
Table 4.
Trends of maximum and minimum temperature trends in the Tarai region.
Cold waves generally occur in the Tarai region from mid-November to mid-February. On average, the duration of cold waves is found to be 8 days. In 2003, the duration of cold waves remained to be up to 60 days. However, the duration of cold waves prevailing in the Tarai has risen since 2004, compared to that in 2000 (Figure 2).
Figure 2.
Trend of duration of cold waves in Tarai region, 2000–2013.
Record of hourly average temperature data shows that the peak cold temperature appears to remain from December to January, where minimum temperature goes below 5°C for few hours during night (Figure 3).
Figure 3.
Distribution of average hourly temperature by winter months, Tarai region.
There are altogether 30 different types of disaster events being recorded in Nepal [20]. Of these events so far recorded, cold wave is the most crucial one. It is as large and serious as damage of crops due to disaster (Table 5). The effect of the cold wave is found across the country (see also Figure 7), or primarily in the high mountain region, where there is cold in most of the year, which is, however, not so significant because there exists very thinly scattered population, which mostly have been adapted to the cold climate. But it is crucially very significant in the Tarai region of Nepal, as it possesses largest population size and its poverty level is comparably large [17].
Description
Cold wave
% of cold wave among the total impacts due to disaster
Figure 4 exhibits yearly trend of deaths of people due to cold wave, which is found to be increased exponentially at 13% per year. It is found that the number of deaths due to cold wave has speedily increased, particularly from the year 2000 onwards.
Figure 4.
Death trend due to cold wave during the years 1974–2013.
The magnitude of deaths of people due to cold wave in the Tarai is comparably large in the country, as shown in Figure 5. The total deaths from cold wave from 1974 to 2013 were recorded at 822. Of these total deaths, 89% took place in the Tarai region, followed by 9 and 2% in the Hill and the Mountain regions, respectively [20, 22].
Figure 5.
Spatial distribution of deaths due to cold wave by district in Nepal (1974–2013).
The distribution of average number of deaths due to cold wave by district across the country is found to be varied remarkably. Figure 5 shows that the number of deaths due to cold wave in the Tarai region were higher in its central and eastern districts than other parts [20].
Further, the deaths of people due to cold wave in the Tarai region are found to have taken place in 4 months (Figure 6). The distribution of the deaths is that: it has reached peak in January, with 71.5% and followed it by December (22.0%), February (3.8%), and November (2.4%).
Figure 6.
Total number of deaths in Tarai region from 1974 to 2013.
Figure 7 shows 2 years, 2004 and 2013, having the largest number of deaths due to cold wave in the Tarai. Though there is a fluctuation in the number of deaths due to cold wave, gradual rising of number of deaths is found since the year 2000 and more elevated trend of number of deaths since 2009.
Figure 7.
Mortality per month/year due to cold wave in Tarai region.
3.3. Age-specific vulnerable people
The number of deaths due to cold wave is found varied remarkably among the age groups of vulnerable people. Of the total deaths, about 60% were children below the age of 5 years, while the 35% elderly population occupied 35% and others the rest 5%.
3.4. Perception of the people
3.4.1. Cause of death
The perception survey indicated that the deaths of the people in the Tarai were mainly due to severe cold, as poor people (children and elderly) with inadequate living conditions (lack of warm cloths and poor house-huts) could not combat with the impacts of severe cold wave. The deaths are found due to diseases like pneumonia, ARI, influenza, COPD, asthma, fever, and hypothermia.
3.4.2. Adaptation
Undoubtedly, impact of cold wave is severe among the local communities, whose economic status is poor, and also daily wage laborers are affected the most, as their wage works are hindered due to cold wave. Normally, they use fuelwood to combat the cold wave but that is not adequate to manipulate the room temperature to bring to the normal standard. In response to this, the Government of Nepal is found distributing fire wood to the local inhabitants of certain pocket areas, and warm clothes to the new born baby and mother in the hospital during delivery.
3.5. Mortality prediction
The prediction of number of deaths of people due to cold wave has been carried out by using multiple linear regression, based on the data of three variables such as minimum temperature, maximum temperature and rainfall from 1974 to 2014. A significant regression equation was found at [F(3, 38) = 4.258, p < 0.05)], with an R2 of 0.252. The prediction of the number of deaths by employing the multiple linear regression is found equal to 814.84 + 20.07 (minimum temperature) − 40.70 (maximum temperature) − 0.561 (rainfall), where minimum temperature and maximum temperature are measured with degree centigrade (°C) and rainfall in millimeter (mm). Number of deaths of people is found to be decreased by 20 with an increase of 1° minimum temperature. On the other hand, the number of deaths is calculated at 54 people with a decrease of 1°C of temperature and 0.56 deaths with each millimeter decrease in rainfall.
The multiple regression tool has been used to predict the number of deaths from 2000 to 2013 considering the same three variables and the significant regression equation was found [F[3, 11] = 1.483, p < 0.05)], with an R2 of 0.29. Prediction of the number of deaths based on the multiple linear regression is equal to 980.45 − 32.442 (minimum temperature) − 25.695 (maximum temperature) − 0.066 (ml), where temperature conditions are measured with degree centigrade (°C) and rainfall is measured in millimeter (mm). The number of deaths is calculated to increase at 32, with a decrease of each degree in minimum temperature. Similarly, 26 people are expected to die with decrease of 1° temperature and 0.066 deaths will occur with a decrease of each millimeter of rainfall.
4. Discussions
As other countries across the world, Nepal has also experienced increasing trend in average annual temperature as well as in minimum and maximum temperature conditions [26]. But however, since the last two decades, Nepal’s Tarai region has got a decreasing trend of minimum temperature in winter season, unlike other regions [19]. While attempts have been made to analyze the temperature trend, two slots of year duration such as 1974–2014 and 2000–2014 were found as distinctive. In contrast to the trend of temperature conditions during 1974–2014, the analysis shows negative trends of minimum and maximum temperature conditions in the winter season during 2000–2014 years, indicating increase in the number of cold days in the Tarai. Globally, the annual numbers of warm nights and cold nights have increased and decreased by about 25 and 20 days, respectively, since 1951 [27]. In Nepal, the annual numbers of cool days and cool nights have decreased by about 5 and 9 days, respectively from 1971 to 2006, but however, during the same time period, the warm days have increased by about 16 days and warm nights have increased by only about 7 days [28]. It is interesting to note here that the decreasing trend of cool days and increasing trend of warm days are clearly seen at higher elevations in Nepal [28].
Death of people due to cold wave is increasing in the Tarai due to increasing duration of cold wave. Tarai region also suffers death of people from heat wave, as it is the hottest region of Nepal. However, the number of deaths due to cold wave is larger than that due to hot wave in the Tarai. The study of MoHA found that the number of deaths in the Tarai due to heat wave from May to August was 45 during the years 1974–2013, which was, however, quite low as compared to the 822 deaths due to cold wave from November to February during the same year duration [20]. The impact of heat wave was mostly on the elderly people, while that of cold wave was on children.
Death of people in the Tarai is found not only due to cold wave but also because of lack of facilities in living places or public hospitals [19, 26, 29]. For instance, during the severe cold months, the average indoor room temperature was found so low than the normal standard [13, 15]. Even in the hospitals, there was seldom provision of room heating system, resulted into death of neonatal and under-five children due to hypothermia and acute respiratory problem [15]. Further, there has been an increasing trend of mortality and morbidity due to respiratory diseases like ARI, COPD and cardiovascular diseases as a result of decreased temperature or cold wave in the Tarai region of Nepal [16]. The same study has predicted that there will be decrease in number of death of people by 2.68% due to ARI as per 1°C rise in minimum temperature. A study carried out in Sarlahi district of Tarai region found out that about 92% of new born babies born in winter suffered from the hypothermia [30]. Overall, only 10.7% of neonates have received optimum thermal care as per the WHO guidelines [15].
In addition to the deaths of people, there are other adverse impacts of cold wave in the Tarai region. Running schools and daily life and livelihoods of people usually are severely interrupted by the cold waves, especially, the vulnerable people like children, elderly and pregnant with low-income groups, and homeless people and daily waged people are affected the most. It is found that cold wave is a risk factor for diseases like respiratory, cardiovascular, viral influenza and Rotavirus infection [16]. Further, during the onset of cold wave, there would be poor visibility leading to increasing trend of road injuries and interruptions in aviation industry, which ultimately hinder livelihood. Outbreaks of avian influenza have a highly seasonal pattern, with nearly all outbreaks occurring in January and February [31]. In mid-winter, especially, the Tarai region can experience cold waves, which often cause crop damage that may lead to famine [20, 32].
Undoubtedly, impact of cold wave is severe on the community, whose economic status is poor, and daily wage laborers are also affected the most, as their activities are hindered due to cold wave. As they are poor, they burn locally available fuelwood or straw, which are also available in small quantity, to combat the cold wave, but this is found not adequate to manipulate the room temperature to bring to the normal standard. Government’s effort in this case is very crucial. The government agencies used to distribute fire wood in some pocket areas and warm clothes to the new born baby and delivered mother in the hospitals. Until now, these mere efforts so far undertaken by the government to address the adverse impacts of cold wave seem inadequate. As health is directly and indirectly affected by climate change via various pathways, there should be a priority focus on health in national adaptation sustainable plans for the medium- and long-term needs of all sectors, such as multisectoral preparedness plans [25, 26].
5. Conclusion and recommendation
It is evident that the average minimum temperature trend during the winter months is declining in the Tarai region of Nepal. The predictions of minimum and maximum temperature trend with regard to number of deaths have been made with different scenarios, that is, increasing or decreasing of 1°C affecting the change in number of death of people by using the modest model of multiple linear regression. Number of deaths due to cold wave in the Tarai has increased over the past two decades due to increasing duration of cold waves in the winter months. Adverse impacts are seen more on vulnerable groups of population such as under-five children and elderly. These are no doubt, the impacts due to global or regional warming, change in land uses, rapid urbanization, etc. It is urgently essential that the adaptation strategy and plans should be designed and implemented to address the increasing trend of cold wave in the Tarai region and other regions based on the findings and recommendations of the rigorous studies.
\n',keywords:"cold wave, temperature change, vulnerable people, number of death, Tarai region, Nepal",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/65192.pdf",chapterXML:"https://mts.intechopen.com/source/xml/65192.xml",downloadPdfUrl:"/chapter/pdf-download/65192",previewPdfUrl:"/chapter/pdf-preview/65192",totalDownloads:455,totalViews:171,totalCrossrefCites:0,dateSubmitted:"May 1st 2018",dateReviewed:"October 23rd 2018",datePrePublished:"January 17th 2019",datePublished:null,dateFinished:null,readingETA:"0",abstract:"Climate extremity phenomena are increasing with the global climate change. Cold wave is one of these climate extremities affecting the health of people, especially vulnerable groups. Nepal is also experiencing the impacts of global warming on its temperature patterns. The climate data of more than four decades have shown an increasing trend of annual temperatures across Nepal. However, the change in temperatures is found varying greatly among its three broad physiographic regions: Tarai, hill, and mountains, as well as among four distinct seasons: winter, pre-monsoon, monsoon, and post-monsoon during a year. Further, since the last two decades Nepal has experienced climatic extremities such as heat wave, cold wave, precipitation concentration, prolonged dryness affecting livelihood of the people and demographic features like mortality, morbidity, etc. This study intends to deal with the impact of cold extremity on the death of vulnerable people such as children and elderly in the Tarai region. It draws on meteorological data for four decades since 1974. The magnitude of mortality rate of those vulnerable people is analyzed from 1974 to 2013, and prediction of mortality rate is made with respect to decrease in temperature or intensity of cold wave.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/65192",risUrl:"/chapter/ris/65192",signatures:"Bandana Pradhan, Puspa Sharma and Pushkar K. Pradhan",book:{id:"7299",title:"Climate Change and Global Warming",subtitle:null,fullTitle:"Climate Change and Global Warming",slug:"climate-change-and-global-warming",publishedDate:"April 24th 2019",bookSignature:"Ata Amini",coverURL:"https://cdn.intechopen.com/books/images_new/7299.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"179844",title:"Associate Prof.",name:"Ata",middleName:null,surname:"Amini",slug:"ata-amini",fullName:"Ata Amini"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Methodology",level:"1"},{id:"sec_3",title:"3. Findings",level:"1"},{id:"sec_3_2",title:"3.1. Brief introduction to physiography, climate, and population of Nepal",level:"2"},{id:"sec_3_3",title:"Table 1.",level:"3"},{id:"sec_4_3",title:"Table 3.",level:"3"},{id:"sec_6_2",title:"3.2. Cold wave impacts on Tarai people",level:"2"},{id:"sec_7_2",title:"3.3. Age-specific vulnerable people",level:"2"},{id:"sec_8_2",title:"3.4. Perception of the people",level:"2"},{id:"sec_8_3",title:"3.4.1. Cause of death",level:"3"},{id:"sec_9_3",title:"3.4.2. Adaptation",level:"3"},{id:"sec_11_2",title:"3.5. Mortality prediction",level:"2"},{id:"sec_13",title:"4. Discussions",level:"1"},{id:"sec_14",title:"5. Conclusion and recommendation",level:"1"}],chapterReferences:[{id:"B1",body:'Pachauri RK, Allen MR, Barros VR, Broome J, Cramer W, Christ R, et al. Climate change 2014: Synthesis report. In: Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. IPCC; 2014'},{id:"B2",body:'Pachauri RK, Reisinger A. IPCC Fourth Assessment Report. Geneva: IPCC; 2007'},{id:"B3",body:'Analitis A, Katsouyanni K, Biggeri A, Baccini M, Forsberg B, Bisanti L, et al. Effects of cold weather on mortality: Results from 15 European cities within the PHEWE project. American Journal of Epidemiology. 2008;168(12):1397-1408'},{id:"B4",body:'Anderson GB, Dominici F, Wang Y, McCormack MC, Bell ML, Peng RD. Heat-related emergency hospitalizations for respiratory diseases in the medicare population. American Journal of Respiratory and Critical Care Medicine. 2013;187(10):1098-1103'},{id:"B5",body:'Arbuthnott K, Hajat S, Heaviside C, Vardoulakis S. Changes in population susceptibility to heat and cold over time: Assessing adaptation to climate change. Environmental Health: A Global Access Science Source. 2016;15(Suppl):1-33'},{id:"B6",body:'Ebi KL, Mills D. Winter mortality in a warming climate: A reassessment. Wiley Interdisciplinary Reviews: Climate Change. 2013;4(3):203-212'},{id:"B7",body:'Kysely J, Pokorna L, Kyncl J, Kriz B. Excess cardiovascular mortality associated with cold spells in the Czech Republic. BMC Public Health. 2009;9(1):19'},{id:"B8",body:'Cagle A, Hubbard R. Cold-related cardiac mortality in King County, Washington, USA 1980-2001. Annals of Human Biology. 2005;32(4):525-537'},{id:"B9",body:'Healy JD. Excess winter mortality in Europe: A cross country analysis identifying key risk factors. Journal of Epidemiology and Community Health. 2003;57(10):784-789'},{id:"B10",body:'Liu C, Yavar Z, Sun Q. Cardiovascular response to thermoregulatory challenges. The American Journal of Physiology—Heart and Circulatory Physiology. 2015;309(11):H1793-H1812'},{id:"B11",body:'Zhou MG, Wang LJ, Liu T, Zhang YH, Lin HL, Luo Y, et al. Health impact of the 2008 cold spell on mortality in subtropical China: The climate and health impact national assessment study (CHINAs). Environmental Health. 2014;13(1):60'},{id:"B12",body:'Malla G. Climate change and its impact on Nepalese agriculture. Journal of Agriculture and Environment. 2008;9:62-71'},{id:"B13",body:'Ellis M, Manandhar N, Shakya U, Manandhar D, Fawdry A, Costello A. Postnatal hypothermia and cold stress among newborn infants in Nepal monitored by continuous ambulatory recording. Archives of Disease in Childhood. Fetal and Neonatal Edition. 1996;75(1):F42-FF5'},{id:"B14",body:'Mullany LC, Katz J, Khatry SK, LeClerq SC, Darmstadt GL, Tielsch JM. Risk of mortality associated with neonatal hypothermia in southern Nepal. Archives of Pediatrics & Adolescent Medicine. 2010;164(7):650-656'},{id:"B15",body:'Khanal V, Gavidia T, Adhikari M, Mishra SR, Karkee R. Poor thermal care practices among home births in Nepal: Further analysis of Nepal demographic and health survey 2011. PLoS One. 2014;9(2):e89950'},{id:"B16",body:'WHO. Report on Assessment of Health Effects of Cold Waves in Terai Nepal. Kathmandu: The Green Move Consultancy; 2017'},{id:"B17",body:'CBS. Population Monograph of Nepal 2014. Government of Nepal; 2014'},{id:"B18",body:'MoH. Nepal Demographic and Health Survey 2016: Key Indicators. Kathmandu, Nepal: Ministry of Health, Nepal; New ERA; and ICF; 2016'},{id:"B19",body:'DHM. In: Meteriology DoHa, editor. Observed Climate Trend Analysis in the Districts and Physiographic Regions of Nepal (1971-2014). Kathmandu: MoPE; 2017'},{id:"B20",body:'MoHA. Nepal Disaster Report 2015. Government of Nepal, Ministry of Home Affairs (MoHA) & Disaster Preparedness Network-Nepal (DPNet-Nepal); 2015'},{id:"B21",body:'DoHS. In: Servises DoH, editor. Annual report 2013/14. Kathmandu: Ministry of Health and Population; 2015'},{id:"B22",body:'UNISDR. Disaster Database Sendai Framework Nepal [Internet]. Available from: http://www.desinventar.net/DesInventar/profiletab.jsp?countrycode=np'},{id:"B23",body:'Bolin JH, Hayes AF. Introduction to mediation, moderation, and conditional process analysis: A regression-based approach; 2013. New York, NY: The Guilford Press. Journal of Educational Measurement. 2014;51(3):335-337'},{id:"B24",body:'MoPE. Climate Change and Glacial Lake Outburst Floods in Nepal, Kathmandu. Kathmandu: ICEM—International Centre Environmental Management with the Nepal Ministry of Population and Environment (MoPE) as part of TA–7984 NEP; 2014'},{id:"B25",body:'MoPE. Synthesis of Stocktaking Report for National Adaptation Plan (NAP) Formulation Process in Nepal. Kathmandu: Ministry of Population and Environment; 2017'},{id:"B26",body:'MoPE. Vulnerability and Risk Assessment Framework and Indicators for National Adaptation Plan (NAP) Formulation Process in Nepal. Kathmandu: Ministry of Population and Environment (MoPE); 2017'},{id:"B27",body:'Alexander L, Zhang X, Peterson T, Caesar J, Gleason B, Tank AK, et al. Global observed changes in daily climate extremes of temperature and precipitation. Journal of Geophysical Research-Atmospheres. 2006;111(D5):1-22'},{id:"B28",body:'Baidya SK, Shrestha ML, Sheikh MM. Trends in daily climatic extremes of temperature and precipitation in Nepal. Journal of Hydrology and Meteorology. 2008;5(1):38-51'},{id:"B29",body:'Dhimal M, Dhimal ML, Pote-Shrestha RR, Groneberg DA, Kuch U. Health-sector responses to address the impacts of climate change in Nepal. WHO South-East Asia Journal of Public Health. 2017;6(2):9'},{id:"B30",body:'Mullany LC, Darmstadt GL, Khatry SK, Katz J, LeClerq SC, Shrestha S, et al. Topical applications of chlorhexidine to the umbilical cord for prevention of omphalitis and neonatal mortality in southern Nepal: A community-based, cluster-randomised trial. The Lancet. 2006;367(9514):910-918'},{id:"B31",body:'World-Bank. Project Performance Assessment Report Nepal: Avian Influenza Control Project (IDA-H2680); 2013'},{id:"B32",body:'Rohwerder B. Seasonal Vulnerability and Risk Calendar in Nepal. Applied Knowledge Services. Governance Social Development Humanitarian Conflict; 2016'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Bandana Pradhan",address:"bandana@reachpuba.org",affiliation:'
Institute of Medicine, Tribhuvan University, Nepal
Central Department of Geography, Tribhuvan University, Nepal
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Central Department of Geography, Tribhuvan University, Nepal
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