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ANFIS: AdaptiveNetworkBased Fuzzy Inference System
, 1993
"... This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping bas ..."
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Cited by 432 (5 self)
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This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping based on both human knowledge (in the form of fuzzy ifthen rules) and stipulated inputoutput data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components onlinely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with illdefine...
Connectionist Learning Procedures
 ARTIFICIAL INTELLIGENCE
, 1989
"... A major goal of research on networks of neuronlike processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way ..."
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Cited by 338 (6 self)
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A major goal of research on networks of neuronlike processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way that internal units which are not part of the input or output come to represent important features of the task domain. Several interesting gradientdescent procedures have recently been discovered. Each connection computes the derivative, with respect to the connection strength, of a global measure of the error in the performance of the network. The strength is then adjusted in the direction that decreases the error. These relatively simple, gradientdescent learning procedures work well for small tasks and the new challenge is to find ways of improving their convergence rate and their generalization abilities so that they can be applied to larger, more realistic tasks.
Simple statistical gradientfollowing algorithms for connectionist reinforcement learning
 Machine Learning
, 1992
"... Abstract. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinfor ..."
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Cited by 318 (0 self)
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Abstract. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediatereinforcement tasks and certain limited forms of delayedreinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms.
An empirical study of learning speed in backpropagation networks
, 1988
"... Most connectionist or "neural network" learning systems use some form of the backpropagation algorithm. However, backpropagation learning is too slow for many applications, and it scales up poorly as tasks become larger and more complex. The factors governing learning speed are poorly understood. ..."
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Cited by 224 (0 self)
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Most connectionist or "neural network" learning systems use some form of the backpropagation algorithm. However, backpropagation learning is too slow for many applications, and it scales up poorly as tasks become larger and more complex. The factors governing learning speed are poorly understood. I have begun a systematic, empirical study of learning speed in backproplike algorithms, measured against a variety of benchmark problems. The goal is twofold: to develop faster learning algorithms and to contribute to the development of a methodology that will be of value in future studies of this kind. This paper is a progress report describing the results obtained during the first six months of this study. To date I have looked only at a limited set of benchmark problems, but the results on these are encouraging: I have developed a new learning algorithm that is faster than standard backprop by an order of magnitude or more and that appears to scale up very well as the problem size increases.
Task Decomposition Through Competition in a Modular Connectionist Architecture
 COGNITIVE SCIENCE
, 1990
"... A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture pe ..."
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Cited by 180 (5 self)
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A novel modular connectionist architecture is presented in which the networks composing the architecture compete to learn the training patterns. As a result of the competition, different networks learn different training patterns and, thus, learn to compute different functions. The architecture performs task decomposition in the sense that it learns to partition a task into two or more functionally independent vii tasks and allocates distinct networks to learn each task. In addition, the architecture tends to allocate to each task the network whose topology is most appropriate to that task, and tends to allocate the same network to similar tasks and distinct networks to dissimilar tasks. Furthermore, it can be easily modified so as to...
Nonlinear Neural Networks: Principles, Mechanisms, and Architectures
, 1988
"... An historical discussion is provided of the intellectual trends that caused nineteenth century interdisciplinary studies of physics and psychobiology by leading scientists such as Helmholtz, Maxwell, and Mach to splinter into separate twentiethcentury scientific movements. The nonlinear, nonstatio ..."
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Cited by 180 (20 self)
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An historical discussion is provided of the intellectual trends that caused nineteenth century interdisciplinary studies of physics and psychobiology by leading scientists such as Helmholtz, Maxwell, and Mach to splinter into separate twentiethcentury scientific movements. The nonlinear, nonstationary, and nonlocal nature of behavioral and brain data are emphasized. Three sources of contemporary neural network researchthe binary, linear, and continuousnonlinear modelsare noted. The remainder of the article describes results about continuousnonlinear models: Many models of contentaddressable memory are shown to be special cases of the CohenGrossberg model and global Liapunov function, including the additive, brainstateinabox, McCullochPitts, Boltzmann machine, HartlineRatliffMillet; shunting, maskingfield, bidirectional associative memory, VolterraLotka, GilpinAyala, and EigenSchuster models. A Liapunov functional method is described for proving global limit or oscillation theorems for nonlinear competitive systems when their decision schemes are globally consistent or inconsistent, respectively. The former case is illustrated by a model of a globally stable economic market, and the latter case is illustrated by a model of the voting paradox. Key properties of shunting competitive feedback networks are summarized, including the role of sigmoid signalling, automatic gain control, competitive choice and quantization, tunable filtering, total activity normalization, and noise suppression in pattern transformation and memory storage applications. Connections to models of competitive learning, vector quantization, and categorical perception are noted. Adaptive resonance
A Review of Evolutionary Artificial Neural Networks
, 1993
"... Research on potential interactions between connectionist learning systems, i.e., artificial neural networks (ANNs), and evolutionary search procedures, like genetic algorithms (GAs), has attracted a lot of attention recently. Evolutionary ANNs (EANNs) can be considered as the combination of ANNs and ..."
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Cited by 154 (23 self)
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Research on potential interactions between connectionist learning systems, i.e., artificial neural networks (ANNs), and evolutionary search procedures, like genetic algorithms (GAs), has attracted a lot of attention recently. Evolutionary ANNs (EANNs) can be considered as the combination of ANNs and evolutionary search procedures. This paper first distinguishes among three kinds of evolution in EANNs, i.e., the evolution of connection weights, of architectures and of learning rules. Then it reviews each kind of evolution in detail and analyses critical issues related to different evolutions. The review shows that although a lot of work has been done on the evolution of connection weights and of architectures, few attempts have been made to understand the evolution of learning rules. Interactions among different evolutions are seldom mentioned in current research. However, the evolution of learning rules and its interactions with other kinds of evolution play a vital role in EANNs. As t...
ADOLC: A Package for the Automatic Differentiation of Algorithms Written in C/C++
, 1995
"... The C++ package ADOLC described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked ..."
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Cited by 149 (24 self)
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The C++ package ADOLC described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked with C. The numerical values of derivative vectors are obtained free of truncation errors at a small multiple of the run time and randomly accessed memory of the given function evaluation program. Derivative matrices are obtained by columns or rows. For solution curves defined by ordinary differential equations, special routines are provided that evaluate the Taylor coefficient vectors and their Jacobians with respect to the current state vector. The derivative calculations involve a possibly substantial (but always predictable) amount of data that are accessed strictly sequentially and are therefore automatically paged out to external files.
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 147 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.