scholarly journals A Hierarchical Procedure for the Synthesis of ANFIS Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Massimo Panella
Keyword(s):  
Computer Simulations ◽  
Function Approximation ◽  
Clustering Algorithms ◽  
Input Output ◽  
Computationally Efficient ◽  
Generalization Capability ◽  
Hyperplane Clustering ◽  
Approximation Problems ◽  
Inference Systems ◽  
Output Space

Adaptive neurofuzzy inference systems (ANFIS) represent an efficient technique for the solution of function approximation problems. When numerical samples are available in this regard, the synthesis of ANFIS networks can be carried out exploiting clustering algorithms. Starting from a hyperplane clustering synthesis in the joint input-output space, a computationally efficient optimization of ANFIS networks is proposed in this paper. It is based on a hierarchical constructive procedure, by which the number of rules is progressively increased and the optimal one is automatically determined on the basis of learning theory in order to maximize the generalization capability of the resulting ANFIS network. Extensive computer simulations prove the validity of the proposed algorithm and show a favorable comparison with other well-established techniques.

GENERATING BALANCED LEARNING AND TEST SETS FOR FUNCTION APPROXIMATION PROBLEMS

2011 ◽  
Vol 21 (03) ◽  
pp. 247-263 ◽  
Author(s):  
J. P. FLORIDO ◽  
H. POMARES ◽  
I. ROJAS
Keyword(s):  
Function Approximation ◽  
Nearest Neighbor ◽  
Learning Algorithm ◽  
Original Data ◽  
Input Output ◽  
Output Data ◽  
Data Set ◽  
Out Of Sample ◽  
Test Sets ◽  
Approximation Problems

In function approximation problems, one of the most common ways to evaluate a learning algorithm consists in partitioning the original data set (input/output data) into two sets: learning, used for building models, and test, applied for genuine out-of-sample evaluation. When the partition into learning and test sets does not take into account the variability and geometry of the original data, it might lead to non-balanced and unrepresentative learning and test sets and, thus, to wrong conclusions in the accuracy of the learning algorithm. How the partitioning is made is therefore a key issue and becomes more important when the data set is small due to the need of reducing the pessimistic effects caused by the removal of instances from the original data set. Thus, in this work, we propose a deterministic data mining approach for a distribution of a data set (input/output data) into two representative and balanced sets of roughly equal size taking the variability of the data set into consideration with the purpose of allowing both a fair evaluation of learning's accuracy and to make reproducible machine learning experiments usually based on random distributions. The sets are generated using a combination of a clustering procedure, especially suited for function approximation problems, and a distribution algorithm which distributes the data set into two sets within each cluster based on a nearest-neighbor approach. In the experiments section, the performance of the proposed methodology is reported in a variety of situations through an ANOVA-based statistical study of the results.

Flat Minima

1997 ◽  
Vol 9 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Sepp Hochreiter ◽  
Jürgen Schmidhuber
Keyword(s):  
Neural Networks ◽  
Error Function ◽  
Low Complexity ◽  
Generalization Error ◽  
Input Output ◽  
Generalization Capability ◽  
Training Set ◽  
Weight Decay ◽  
Optimal Brain Surgeon ◽  
And Training

We present a new algorithm for finding low-complexity neural networks with high generalization capability. The algorithm searches for a “flat” minimum of the error function. A flat minimum is a large connected region in weight space where the error remains approximately constant. An MDL-based, Bayesian argument suggests that flat minima correspond to “simple” networks and low expected overfitting. The argument is based on a Gibbs algorithm variant and a novel way of splitting generalization error into underfitting and overfitting error. Unlike many previous approaches, ours does not require gaussian assumptions and does not depend on a “good” weight prior. Instead we have a prior over input output functions, thus taking into account net architecture and training set. Although our algorithm requires the computation of second-order derivatives, it has backpropagation's order of complexity. Automatically, it effectively prunes units, weights, and input lines. Various experiments with feedforward and recurrent nets are described. In an application to stock market prediction, flat minimum search outperforms conventional backprop, weight decay, and “optimal brain surgeon/optimal brain damage.”

scholarly journals Fuzzified Pipes Dataset to Predict Failure Rates by Hybrid SVR-PSO Algorithm

2016 ◽  
Vol 10 (7) ◽  
pp. 29 ◽  
Author(s):  
Jaber Soltani ◽  
Moosa Kalanaki ◽  
Mohammad Soltani
Keyword(s):  
Support Vector Regression ◽  
Pso Algorithm ◽  
Experimental Results ◽  
Support Vector ◽  
Failure Rates ◽  
Input Output ◽  
Generalization Capability ◽  
Comparative Tests

This paper proposes a Support Vector Regression (SVR) based on Fuzzified Input-output Variables which has good comprehensibility as well as satisfactory generalization capability. SVM provides a mechanism to predict data from training ones. Then, results from proposed Fuzzified SVR-PSO (FSVR-PSO) model are compared with other methods; comparative tests are performed using pipe failures data. The analysis and the experimental results show this method has high comprehensibility as well as satisfactory generalization capability.

scholarly journals Artificial Hydrocarbon Networks Fuzzy Inference System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hiram Ponce ◽  
Pedro Ponce ◽  
Arturo Molina
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Inference Systems ◽  
Inference Model ◽  
Inference System ◽  
Position Controller ◽  
Inference Systems ◽  
Linguistic Units ◽  
Output Space

This paper presents a novel fuzzy inference model based on artificial hydrocarbon networks, a computational algorithm for modeling problems based on chemical hydrocarbon compounds. In particular, the proposed fuzzy-molecular inference model (FIM-model) uses molecular units of information to partition the output space in the defuzzification step. Moreover, these molecules are linguistic units that can be partially understandable due to the organized structure of the topology and metadata parameters involved in artificial hydrocarbon networks. In addition, a position controller for a direct current (DC) motor was implemented using the proposed FIM-model in type-1 and type-2 fuzzy inference systems. Experimental results demonstrate that the fuzzy-molecular inference model can be applied as an alternative of type-2 Mamdani’s fuzzy control systems because the set of molecular units can deal with dynamic uncertainties mostly present in real-world control applications.

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