nnet {nnet} | R Documentation

## Fit Neural Networks

### Description

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

### Usage

    nnet.formula(formula, data=NULL, weights, ...,
                 subset, na.action=na.fail, contrasts=NULL)
    nnet.default(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)

### 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 `NA`s 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 (and perhaps uninterruptable under Windows).
`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`.

### 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`.

A quasi-Newton optimizer is used, written in `C`.

### 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.

### See Also

`predict.nnet`, `nnet.Hess`

### Examples

    data(iris3)
    # 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=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"))