frbs (version 1.0-0)

HGD: HGD model building

Description

This is the internal function that implements the fuzzy system using heuristics and gradient descent method (HGD). Users do not need to call it directly, but just use frbs.learn and predict.

Usage

HGD(range.data, data.train, num.labels, max.iter,
    step.size, alpha.heuristic = 1)

Arguments

data.train

a matrix(m x n) of data for the training process, where m is the number of instances and n is the number of variables; the last column is the output variable.

range.data

a matrix(2 x n) containing the range of the normalized data, where n is the number of variables, and first and second rows are the minimum and maximum value, respectively.

num.labels

a matrix(1 x n), whose elements represent the number of labels (fuzzy terms); n is the number of variables.

max.iter

maximal number of iterations.

step.size

step size of the descent method.

alpha.heuristic

a positive real number which is the heuristic parameter.

Details

This method was proposed by Ken Nozaki, H. Ishibuchi, and Hideo Tanaka. It uses fuzzy IF-THEN rules with nonfuzzy singletons (i.e. real numbers) in the consequent parts. The techniques of Wang and Mendel are implemented to generate the antecedent part, while the initial consequent part of each rule is determined by the weighted mean value of the given training data. Then, the gradient descent method updates the value of the consequent part. Futhermore, the heuristic value given by the user affects the value of weight of each data.

References

H. Ichihashi and T. Watanabe, "Learning control system by a simplified fuzzy reasoning model," Proc. IPMU'90 417 - 419 (1990).

H. Ishibuchi, K. Nozaki, H. Tanaka, Y. Hosaka and M. Matsuda, "Empirical study on learning in fuzzy systems by rice taste analysis," Fuzzy Set and Systems 64, 129 144 (1994).

See Also

frbs.learn, predict, and HGD.update