neuralnet (version 1.1)

neuralnet: Training of neural networks

Description

neuralnet is used to train neural networks using the Resilient Backpropagation with (Riedmiller, 1994) or without weightbacktracking (Riedmiller and Braun, 1993) or the modified globally convergent version by Anastasiadis et al. (2005). The function allows flexible settings through custom-choice of error- and activation-function. Furthermore the calculation of generalized weights (Intrator O. and Intrator N., 1993) is implemented.

Usage

neuralnet(formula, data, hidden = 1, threshold = c(0.001),
    stepmax = 1e+05, rep = 1, weights.mean = 0, weights.variance = 1,
    startweights = NULL, learningrate.limit = NULL, 
    learningrate.factor = list(minus = 0.5, plus = 1.2), lifesign = "none",
    lifesign.step = 1000, algorithm = "rprop+", err.fct = "sse", 
    act.fct = "logistic", linear.output=TRUE, family = NULL)

Arguments

formula

a symbolic description of the model to be fitted.

data

a data frame in which the variables specified in formula will be found.

hidden

a vector of integers specifying the number of hidden neurons (vertices) in each layer.

threshold

a vector of integers for the threshold of the minimal error. Threshold as a vector of size n, trains n different repetitions of the neural network with a component wise threshold.

stepmax

the maximum steps for the training of the neural network. Reaching this maximum leads to a stop of the neural network's training process.

rep

the number of repetitions for the neural network's training for every threshold.

weights.mean

the mean of the normal distribution, the initial weights are drawn from.

weights.variance

the variance of the normal distribution, the initial weights are drawn from.

startweights

a vector containing starting values for the weights. The weights will not be randomly initialized.

learningrate.limit

a vector or a list containing the lowest and highest limit for the learning rate.

learningrate.factor

a vector or a list containing the multiplication factors for the upper and lower learning rate.

lifesign

a string specifying how much the function will print during the calculation of the neural network. 'none', 'minimal' or 'full'.

lifesign.step

an integer specifying the stepsize to print the minimal threshold in full lifesign mode.

algorithm

a string containing the algorithm type to calculate the neural network. The following types are possible: 'rprop+', 'rprop-', 'sag', or 'slr'. 'rprop+' and 'rprop-' refer to the Resilient Backpropagation with and without weightbacktracking, while 'sag

err.fct

a differentiable function that is used for the calculation of the error. Alternatively, the strings 'sse' and 'ce' which stand for the sum of squared errors and the cross-entropy can be used.

act.fct

a differentiable function that is used for smoothing the result of the cross product of the covariate or neurons and the weights. Additionally the strings, 'logistic' and 'tanh' are possible for the logistic function and tangent hyperbolicus.

linear.output

logical. If act.fct should not be applied to the output neurons set linear output to TRUE, otherwise to FALSE.

family

a description of the error distribution and link function to be used only in the glm model. This can be a character string naming a family function, a family function or the result of a call to a family function.

Value

• neuralnet returns an object of class nn. An object of class nn is a list containing at most the following components:
• call
  the matched call.
• response
  extracted from the data argument.
• covariate
  the variables extracted from the data argument.
• model.list
  a list containing the covariates and the response variables extracted from the formula argument.
• err.fct
  the error function.
• act.fct
  the activation function.
• data
  the data argument.
• net.result
  a list containing the overall result of the neural network for every repetition.
• weights
  a list containing the fitted weights of the neural network for every repetition.
• gw
  a list containing the generalized weights of the neural network for every repetition.
• result.matrix
  a matrix containing the threshold, reached threshold, steps, error, aic (if computed) and weights for every repetition. Each column represents one repetition.
• list.glm
  a list of glm objects. It will be set to NULL if there is more than one response or family is not stated.
• predictions
  a list of the predictions of the repetitions, the data and the glm models. It will not be computed if at least one of the covariates has more than 50 factors.
• data.error
  the error of the data. This is 0, if no row in covariate has a duplicate. It will not be computed if at least one of the covariates has more than 50 factors.

Details

If family is stated, a glm model will additionally be calculated for comparison reasons, but only if the response consists of only one parameter. The globally convergent algorithm is based on the Resilient Backpropagation without weightbacktracking and additionally modifies one learning rate, either the learningrate associated with the smallest absolute gradient (sag) or the smallest learningrate (slr) itself. The learning rates in the grprop algorithm are limited to the boundaries defined in learningrate.limit.

References

Riedmiller M. (1994) Rprop - Description and Implementation Details. Technical Report. University of Karlsruhe. Riedmiller M. and Braun H. (1993) A direct adaptive method for faster backpropagation learning: The RPROP algorithm. Proceedings of the IEEE International Conference on Neural Networks (ICNN), pages 586-591. San Francisco. Anastasiadis A. et. al. (2005) New globally convergent training scheme based on the resilient propagation algorithm. Neurocomputing 64, pages 253-270. Intrator O. and Intrator N. (1993) Using Neural Nets for Interpretation of Nonlinear Models. Proceedings of the Statistical Computing Section, 244-249 San Francisco: American Statistical Society (eds).

See Also

plot.nn for plotting of the neural network. gwplot for plotting of the generalized weights. compute for computation of the calculated network.

Examples

AND <- c(rep(0,7),1)
OR <- c(0,rep(1,7))
SUM <- c(0,1,1,2,1,2,2,3)
binary.data <- data.frame(expand.grid(c(0,1), c(0,1), c(0,1)), AND, OR, SUM)
print(net <- neuralnet( AND+OR~Var1+Var2+Var3,  binary.data, hidden=0, rep=10,
	     err.fct="ce", linear.output=FALSE))
print(net.sum <- neuralnet( SUM~Var1+Var2+Var3,  binary.data, hidden=0, 
		 linear.output=TRUE))
net.sum$predictions

data(infert, package="datasets")
print(net.infert <- neuralnet( case~parity+induced+spontaneous,  infert, 
		    err.fct="ce", linear.output=FALSE, family=binomial()))