ann: Fit Artificial Neural Networks.
In validann: Validation Tools for Artificial Neural Networks

Description Usage Arguments Details Value See Also Examples

Fits a single hidden layer ANN model to input data x and output data y.

ann(x, y, size, act_hid = c("tanh", "sigmoid", "linear", "exp"),
  act_out = c("linear", "sigmoid", "tanh", "exp"), Wts = NULL, rang = 0.5,
  objfn = NULL, method = "BFGS", maxit = 1000, abstol = 1e-04,
  reltol = 1e-08, trace = TRUE, ...)

`x`	matrix, data frame or vector of numeric input values, with `ncol(x)` equal to the number of inputs/predictors and `nrow(x)` equal to the number of examples. A vector is considered to comprise examples of a single input or predictor variable.
`y`	matrix, data frame or vector of target values for examples.
`size`	number of hidden layer nodes. Can be zero.
`act_hid`	activation function to be used at the hidden layer. See ‘Details’.
`act_out`	activation function to be used at the output layer. See ‘Details’.
`Wts`	initial weight vector. If `NULL` chosen at random.
`rang`	initial random weights on [-rang,rang]. Default value is 0.5.
`objfn`	objective function to be minimised when fitting weights. This function may be user-defined with the first two arguments corresponding to `y` (the observed target data) and `y_hat` (the ANN output). If this function has additional parameters which require optimizing, these must be defined in argument `par_of` (see AR(1) case in ‘Examples’). Default is `sse` (internal function to compute sum squared error, with error given by `y - y_hat`) when `objfn = NULL`.
`method`	the method to be used by `optim` for minimising the objective function. May be “Nelder-Mead”, “BFGS”, “CG”, “L-BFGS-B”, “SANN” or “Brent”. Can be abbreviated. Default is “BFGS”.
`maxit`	maximum number of iterations used by `optim`. Default value is 1000.
`abstol`	absolute convergence tolerance (stopping criterion) used by `optim`. Default is `1e-4`.
`reltol`	relative convergence tolerance (stopping criterion) used by `optim`. Optimization stops if the value returned by `objfn` cannot be reduced by a factor of `reltol * (abs(val) + reltol)` at a step. Default is `1e-8`.
`trace`	logical. Should optimization be traced? Default = TRUE.
`...`	arguments to be passed to user-defined `objfn`. Initial values of any parameters (in addition to the ANN weights) requiring optimization must be supplied in argument `par_of` (see AR(1) case in ‘Examples’).

The “linear” activation, or transfer, function is the identity function where the output of a node is equal to its input f(x) = x.

The “sigmoid” function is the standard logistic sigmoid function given by f(x) = 1 / (1 + exp(-x)).

The “tanh” function is the hyperbolic tangent function given by f(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))

The “exp” function is the exponential function given by f(x) = exp(x)

The default configuration of activation functions is act_hid = "tanh" and act_out = "linear".

Optimization (minimization) of the objective function (objfn) is performed by optim using the method specified.

Derivatives returned are first-order partial derivatives of the hidden and output nodes with respect to their inputs. These may be useful for sensitivity analyses.

object of class ‘ann’ with components describing the ANN structure and the following output components:

`wts`	best set of weights found.
`par_of`	best values of additional `objfn` parameters. This component will only be returned if a user-defined `objfn` is supplied and argument `par_of` is included in the function call (see AR(1) case in ‘Examples’).
`value`	value of objective function.
`fitted.values`	fitted values for the training data.
`residuals`	residuals for the training data.
`convergence`	integer code returned by `optim`. 0 indicates successful completion, see `optim` for possible error codes.
`derivs`	matrix of derivatives of hidden (columns `1:size`) and output (final column) nodes.

predict.ann, validann

## fit 1-hidden node ann model with tanh activation at the hidden layer and
## linear activation at the output layer.
## Use 200 random samples from ar9 dataset.
## ---
data("ar9")
samp <- sample(1:1000, 200)
y <- ar9[samp, ncol(ar9)]
x <- ar9[samp, -ncol(ar9)]
x <- x[, c(1,4,9)]
fit <- ann(x, y, size = 1, act_hid = "tanh", act_out = "linear", rang = 0.1)

## fit 3-hidden node ann model to ar9 data with user-defined AR(1) objective
## function
## ---
ar1_sse <- function(y, y_hat, par_of) {
  err <- y - y_hat
  err[-1] <- err[-1] - par_of * err[-length(y)]
  sum(err ^ 2)
}
fit <- ann(x, y, size = 3, act_hid = "tanh", act_out = "linear", rang = 0.1,
           objfn = ar1_sse, par_of = 0.7)