nnet: Fit Neural Networks

Description

Fit single-hidden-layer neural network, possibly with skip-layer connections.

Usage

nnet(x, ...)
# S3 method for formula
nnet(formula, data, weights, ...,
     subset, na.action, contrasts = NULL)
# S3 method for default
nnet(x, y, weights, size, Wts, mask,
     linout = FALSE, entropy = FALSE, softmax = FALSE,
     censored = FALSE, skip = FALSE, rang = 0.7, decay = 0,
     maxit = 100, Hess = FALSE, trace = TRUE, MaxNWts = 1000,
     abstol = 1.0e-4, reltol = 1.0e-8, ...)

Value

object of class "nnet" or "nnet.formula". Mostly internal structure, but has components

wts: the best set of weights found
value: value of fitting criterion plus weight decay term.
fitted.values: the fitted values for the training data.
residuals: the residuals for the training data.
convergence: 1 if the maximum number of iterations was reached, otherwise 0.

Arguments

formula: A formula of the form class ~ x1 + x2 + ...
x: matrix or data frame of x values for examples.
y: matrix or data frame of target values for examples.
weights: (case) weights for each example -- if missing defaults to 1.
size: number of units in the hidden layer. Can be zero if there are skip-layer units.
data: Data frame from which variables specified in formula are preferentially to be taken.
subset: An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
na.action: A function to specify the action to be taken if NAs are found. The default action is for the procedure to fail. An alternative is na.omit, which leads to rejection of cases with missing values on any required variable. (NOTE: If given, this argument must be named.)
contrasts: a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.
Wts: initial parameter vector. If missing chosen at random.
mask: logical vector indicating which parameters should be optimized (default all).
linout: switch for linear output units. Default logistic output units.
entropy: switch for entropy (= maximum conditional likelihood) fitting. Default by least-squares.
softmax: switch for softmax (log-linear model) and maximum conditional likelihood fitting. linout, entropy, softmax and censored are mutually exclusive.
censored: A variant on softmax, in which non-zero targets mean possible classes. Thus for softmax a row of (0, 1, 1) means one example each of classes 2 and 3, but for censored it means one example whose class is only known to be 2 or 3.
skip: switch to add skip-layer connections from input to output.
rang: Initial random weights on [-rang, rang]. Value about 0.5 unless the inputs are large, in which case it should be chosen so that rang * max(|x|) is about 1.
decay: parameter for weight decay. Default 0.
maxit: maximum number of iterations. Default 100.
Hess: If true, the Hessian of the measure of fit at the best set of weights found is returned as component Hessian.
trace: switch for tracing optimization. Default TRUE.
MaxNWts: The maximum allowable number of weights. There is no intrinsic limit in the code, but increasing MaxNWts will probably allow fits that are very slow and time-consuming.
abstol: Stop if the fit criterion falls below abstol, indicating an essentially perfect fit.
reltol: Stop if the optimizer is unable to reduce the fit criterion by a factor of at least 1 - reltol.
...: arguments passed to or from other methods.

Details

If the response in formula is a factor, an appropriate classification network is constructed; this has one output and entropy fit if the number of levels is two, and a number of outputs equal to the number of classes and a softmax output stage for more levels. If the response is not a factor, it is passed on unchanged to nnet.default.

Optimization is done via the BFGS method of optim.

References

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

Run this code

# use half the iris data
ir <- rbind(iris3[,,1],iris3[,,2],iris3[,,3])
targets <- class.ind( c(rep("s", 50), rep("c", 50), rep("v", 50)) )
samp <- c(sample(1:50,25), sample(51:100,25), sample(101:150,25))
ir1 <- nnet(ir[samp,], targets[samp,], size = 2, rang = 0.1,
            decay = 5e-4, maxit = 200)
test.cl <- function(true, pred) {
    true <- max.col(true)
    cres <- max.col(pred)
    table(true, cres)
}
test.cl(targets[-samp,], predict(ir1, ir[-samp,]))


# or
ird <- data.frame(rbind(iris3[,,1], iris3[,,2], iris3[,,3]),
        species = factor(c(rep("s",50), rep("c", 50), rep("v", 50))))
ir.nn2 <- nnet(species ~ ., data = ird, subset = samp, size = 2, rang = 0.1,
               decay = 5e-4, maxit = 200)
table(ird$species[-samp], predict(ir.nn2, ird[-samp,], type = "class"))

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