The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial 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. >

ANFIS: adaptive-network-based fuzzy inference system

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Twitter mood predicts the stock market.

We propose a network architecture which uses a single internal layer of locally-tuned processing units to learn both classification tasks and real-valued function approximations (Moody and Darken 1988). We consider training such networks in a completely supervised manner, but abandon this approach in favor of a more computationally efficient hybrid learning method which combines self-organized and supervised learning. Our networks learn faster than backpropagation for two reasons: the local representations ensure that only a few units respond to any given input, thus reducing computational overhead, and the hybrid learning rules are linear rather than nonlinear, thus leading to faster convergence. Unlike many existing methods for data analysis, our network architecture and learning rules are truly adaptive and are thus appropriate for real-time use.

Fast learning in networks of locally-tuned processing units

The problem of the approximation of nonlinear mapping, (especially continuous mappings) is considered. Regularization theory and a theoretical framework for approximation (based on regularization techniques) that leads to a class of three-layer networks called regularization networks are discussed. Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks. Learning as approximation and learning as hypersurface reconstruction are discussed. Two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering. The theory of regularization networks is generalized to a formulation that includes task-dependent clustering and dimensionality reduction. Applications of regularization networks are discussed. >

Networks for approximation and learning

A general method is developed to generate fuzzy rules from numerical data. The method consists of five steps: divide the input and output spaces of the given numerical data into fuzzy regions; generate fuzzy rules from the given data; assign a degree of each of the generated rules for the purpose of resolving conflicts among the generated rules; create a combined fuzzy rule base based on both the generated rules and linguistic rules of human experts; and determine a mapping from input space to output space based on the combined fuzzy rule base using a defuzzifying procedure. The mapping is proved to be capable of approximating any real continuous function on a compact set to arbitrary accuracy. Applications to truck backer-upper control and time series prediction problems are presented. >

Generating fuzzy rules by learning from examples

The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing Simulations are presented that document the additional performance achieved by using nonlinear neural networks First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series Furthermore, the neural net more » seems to be extremely parsimonious in its requirements for data points from the time series We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps 24 refs, 13 figs « less

A. Lapedes

Papers

Nonlinear signal processing using neural networks: Prediction and system modelling