kda: Kernel Classification Rules
In locClass: Collection of Local Classification Methods

Description Usage Arguments Details Value References See Also

Classification using the moving window and kernel classification rules.

  kda(x, ...)

  ## S3 method for class 'formula'
 kda(formula, data, ..., subset,
    na.action)

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

  ## S3 method for class 'matrix'
 kda(x, grouping, ..., subset,
    na.action = na.fail)

  ## Default S3 method:
 kda(x, grouping,
    wf = c("biweight", "cauchy", "cosine", "epanechnikov", "exponential", "gaussian", "optcosine", "rectangular", "triangular"),
    bw, k, nn.only = TRUE, ...)

`formula`	A formula of the form `groups ~ x1 + x2 + ...`, that is, the response is the grouping `factor` and the right hand side specifies the (usually non-`factor`) discriminators.
`data`	A `data.frame` from which variables specified in `formula` are to be taken.
`x`	(Required if no `formula` is given as principal argument.) A `matrix` or `data.frame` or `Matrix` containing the explanatory variables.
`grouping`	(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`.)
`...`	Further arguments. Currently unused.
`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.)

The kernel clasification rule is given as

hat g = arg max_g sum_{n:y_n=g} wf((x-x_n)/bw).

In the case that wf is the rectangular kernel it is also called moving window rule.

The name of the window function (wf) can be specified as a character string. In this case the window function is generated internally in predict.kda. 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 kda.

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.

An object of class "kda", a list containing the following components:

`x`	A `matrix` containing the explanatory variables.
`grouping`	A `factor` specifying the class membership for each observation.
`counts`	The number of observations per class.
`lev`	The class labels (levels of `grouping`).
`N`	The number of observations.
`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.
`variant`	(Only if `wf` is a string or if one of the weight functions documented in `wfs` is used, for internal use only). An integer indicating which weighting scheme is implied by `bw`, `k` and `nn.only`.
`call`	The (matched) function call.