ks (version 1.8.13)

kda: Kernel discriminant analysis for multivariate data

Description

Kernel discriminant analysis for 1- to 6-dimensional data.

Usage

kda(x, x.group, Hs, hs, prior.prob=NULL, gridsize, xmin, xmax, supp=3.7,
   eval.points, binned=FALSE, bgridsize, w, compute.cont=FALSE,
   approx.cont=TRUE, kde.flag=TRUE)
Hkda(x, x.group, Hstart, bw="plugin", nstage=2, pilot="samse", pre="sphere", 
   binned=FALSE, bgridsize)
Hkda.diag(x, x.group, bw="plugin", nstage=2, pilot="samse", pre="sphere", 
   binned=FALSE, bgridsize)
hkda(x, x.group, bw="plugin", nstage=2, binned=TRUE, bgridsize)
compare(x.group, est.group, by.group=FALSE)
compare.kda.cv(x, x.group, bw="plugin", prior.prob=NULL, Hstart,
   by.group=FALSE, verbose=FALSE, binned=FALSE, bgridsize, recompute=FALSE,
   ...)
compare.kda.diag.cv(x, x.group, bw="plugin", prior.prob=NULL, by.group=FALSE, 
   verbose=FALSE, binned=FALSE, bgridsize, recompute=FALSE, ...)

Arguments

x

matrix of training data values

x.group

vector of group labels for training data

Hs,hs

(stacked) matrix of bandwidth matrices/vector of scalar bandwidths. If these are missing, Hkda or hkda is called by default.

prior.prob

vector of prior probabilities

gridsize

vector of grid sizes

xmin,xmax

vector of minimum/maximum values for grid

supp

effective support for standard normal

eval.points

points at which estimate is evaluated

binned

flag for binned estimation. Default is FALSE.

bgridsize

vector of binning grid sizes

w

vector of weights. Not yet implemented.

compute.cont

flag for computing 1% to 99% probability contour levels. Default is FALSE.

approx.cont

flag for computing approximate probability contour levels. Default is TRUE.

kde.flag

flag for computing KDE on grid. Default is TRUE.

bw

bandwidth: "plugin" = plug-in, "lscv" = LSCV, "scv" = SCV

nstage

number of stages in the plug-in bandwidth selector (1 or 2)

pilot

pilot selector: see Hpi, Hscv

pre

"scale" = pre.scale, "sphere" = pre.sphere

Hstart

(stacked) matrix of initial bandwidth matrices, used in numerical optimisation

est.group

vector of estimated group labels

by.group

flag to give results also within each group

verbose

flag for printing progress information. Default is FALSE.

recompute

flag for recomputing the bandwidth matrix after excluding the i-th data item

...

other optional parameters for bandwidth selection, see Hpi, Hlscv, Hscv

Value

• --A kernel discriminant analysis is an object of class kda which is a list with fields
• x
  list of data points, one for each group label
• estimate
  list of density estimates at eval.points, one for each group label
• eval.points
  points that the estimate is evaluated at, one for each group label
• h
  vector of bandwidths (1-d only)
• H
  stacked matrix of bandwidth matrices or vector of bandwidths
• gridded
  flag for estimation on a grid
• binned
  flag for binned estimation
• w
  weights
• prior.prob
  prior probabilities
• x.group
  group labels - same as input
• x.group.estimate
  estimated group labels. If the test data eval.points are given then these are classified. Otherwise the training data x are classified.
• --The result from Hkda and Hkda.diag is a stacked matrix of bandwidth matrices, one for each training data group. The result from hkda is a vector of bandwidths, one for each training data group.

  --The compare functions create a comparison between the true group labels x.group and the estimated ones. It returns a list with fields

• cross
  cross-classification table with the rows indicating the true group and the columns the estimated group
• error
  misclassification rate (MR)
• In the case where we have test data that is independent of the training data, compare computes MR = (number of points wrongly classified)/(total number of points). In the case where we don't have independent test data e.g. we are classifying the training data set itself, then the cross validated estimate of MR is more appropriate. These are implemented as compare.kda.cv (full bandwidth selectors) and compare.kda.diag.cv (for diagonal bandwidth selectors). These functions are only available for d > 1.

  If by.group=FALSE then only the total MR rate is given. If it is set to TRUE, then the MR rates for each class are also given (estimated number in group divided by true number).

Details

--If the bandwidths Hs are missing from kda, then the default bandwidths are the binned 2-stage plug-in selectors Hkda(, bw="plugin", nstage=2, binned=TRUE). Likewise for missing hs. --The values that valid for bw are "plugin", "lscv" and "scv" for Hkda. These in turn call Hpi, Hlscv and Hscv. For plugin selectors, all of nstage, pilot and pre need to be set. For SCV selectors, currently nstage=1 always but pilot and pre need to be set. For LSCV selectors, none of them are required. Hkda.diag makes analogous calls to diagonal selectors.

--If you have prior probabilities then set prior.prob to these. Otherwise prior.prob=NULL is the default i.e. use the sample proportions as estimates of the prior probabilities. As of ks 1.8.11, kda.kde has been subsumed into kda, so all prior calls to kda.kde can be replaced by kda. To reproduce the previous behaviour of kda, the command is kda(, kde.flag=FALSE).

References

Simonoff, J. S. (1996) Smoothing Methods in Statistics. Springer-Verlag. New York

See Also

plot.kda

Examples

x <- c(rnorm.mixt(n=100, mus=1), rnorm.mixt(n=100, mus=-1))
x.gr <- rep(c(1,2), times=c(100,100))
y <- c(rnorm.mixt(n=100, mus=1), rnorm.mixt(n=100, mus=-1))
kda.gr <- kda(x, x.gr, eval.points=y)
compare(kda.gr$x.group, kda.gr$x.group.est, by.group=TRUE)

## See other examples in ? plot.kda