dannet: Discriminant Adaptive Neural Network
In schiffner/locClass: Collection of Local Classification Methods

Description Usage Arguments Details Value References See Also Examples

A local version of a single-hidden-layer neural network for classification that puts increased emphasis on a good model fit near the decision boundary.

dannet(x, ...)

## S3 method for class 'formula'
dannet(formula, data, weights, ..., subset, na.action,
  contrasts = NULL)

## S3 method for class 'data.frame'
dannet(x, ...)

## S3 method for class 'matrix'
dannet(x, y, weights = rep(1, nrow(x)), ..., subset,
  na.action = na.fail)

## Default S3 method:
dannet(x, y, wf = c("biweight", "cauchy", "cosine",
  "epanechnikov", "exponential", "gaussian", "optcosine", "rectangular",
  "triangular"), bw, k, nn.only, itr = 3, weights = rep(1, nrow(x)),
  reps = 1, ...)

`x`	(Required if no `formula` is given as principal argument.) A `matrix` or `data.frame` containing the explanatory variables.
`formula`	A formula of the form `groups ~ x1 + x2 + ...`, that is, the response is the grouping `factor` and the right hand side specifies the (normally non-`factor`) discriminators.
`data`	A `data.frame` from which variables specified in `formula` are to be taken.
`weights`	Initial observation weights (defaults to a vector of 1s).
`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 first the `na.action` setting of `options` and second `na.fail` if that is unset. 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.
`y`	(Required if no `formula` is given as principal argument.) A `factor` specifying the class membership for each observation.
`wf`	A window function which is used to calculate weights that are introduced into the fitting process. Either a character string or a function, e.g. `wf = function(x) exp(-x)`. For details see the documentation for `wfs`.
`bw`	(Required only if `wf` is a string.) The bandwidth parameter of the window function. (See `wfs`.)
`k`	(Required only if `wf` is a string.) The number of nearest neighbors of the decision boundary to be used in the fitting process. (See `wfs`.)
`nn.only`	(Required only if `wf` is a string indicating a window function with infinite support and if `k` is specified.) Should only the `k` nearest neighbors or all observations receive positive weights? (See `wfs`.)
`itr`	Number of iterations for model fitting, defaults to 3. See also the Details section.
`reps`	Neural networks are fitted repeatedly (`reps` times) for different initial values and the solution with largest likelihood value is kept. Defaults to 1. (`reps` larger one does not make sense if `Wts` is specified.)
`...`	Further arguments to `nnet`.

The idea of Hand and Vinciotti (2003) to put increased weight on observations near the decision boundary is generalized to the multiclass case and applied to neural networks. Since the decision boundary is not known in advance an iterative procedure is required. First, an unweighted neural network is fitted to the data. Based on the differences between the two largest estimated posterior probabilities observation weights are calculated. Then a weighted neural network (see nnet) from package nnet is fitted using these weights. Calculation of weights and model fitting is done several times in turn. The number of iterations is determined by the itr-argument that defaults to 3.

The name of the window function (wf) can be specified as a character string. In this case the window function is generated internally in dalda. Currently supported are "biweight", "cauchy", "cosine", "epanechnikov", "exponential", "gaussian", "optcosine", "rectangular" and "triangular".

Moreover, it is possible to generate the window functions mentioned above in advance (see wfs) and pass them to dalda.

Any other function implementing a window function can also be used as wf argument. This allows the user to try own window functions. See help on wfs for details.

If the predictor variables include factors, the formula interface must be used in order to get a correct model matrix.

In contrast to nnet this function is only appropriate for classification problems. As response in formula only factors are allowed. If the response is not a factor, it is coerced to a factor with a warning. 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 you use the default method, you get only meaningful results if y is a 0-1 class indicator matrix.

Optimization is done via the BFGS method of optim.

An object of class "dannet" or "dannet.formula" inheriting from "nnet". A list mostly containing internal structure, but with the following 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.
`weights`	A list of length `itr + 1`. The initial observation weights (a vector of 1s if none were given) and the observation weights calculated in the individual iterations.
`itr`	The number of iterations used.
`wf`	The window function used. Always a function, even if the input was a string.
`bw`	(Only if `wf` is a string or was generated by means of one of the functions documented in `wfs`.) The bandwidth used, `NULL` if `bw` was not specified.
`k`	(Only if `wf` is a string or was generated by means of one of the functions documented in `wfs`.) The number of nearest neighbors used, `NULL` if `k` was not specified.
`nn.only`	(Logical. Only if `wf` is a string or was generated by means of one of the functions documented in `wfs` and if `k` was specified.) `TRUE` if only the `k` nearest neighbors recieve a positive weight, `FALSE` otherwise.
`adaptive`	(Logical.) `TRUE` if the bandwidth of `wf` is adaptive to the local density of data points, `FALSE` if the bandwidth is fixed.
`call`	The (matched) function call.

Hand, D. J., Vinciotti, V. (2003), Local versus global models for classification problems: Fitting models where it matters, The American Statistician, 57(2) 124–130.

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.

predict.dannet, nnet and dalr for discriminant adaptive logistic regression.

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 fit <- dannet(Species ~ Sepal.Length + Sepal.Width, data = iris, size = 2, rang = 0.1, maxit = 200, bw = 2)
 pred <- predict(fit)
 mean(pred$class != iris$Species)