ks (version 1.6.13)

kda, Hkda, Hkda.diag, hkda: Kernel discriminant analysis for multivariate data

Description

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

Usage

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)
kda(x, x.group, Hs, hs, y, prior.prob=NULL)

Arguments

x

matrix of training data values

x.group

vector of group labels for training data

y

matrix of test data

Hs

(stacked) matrix of bandwidth matrices

hs

vector of scalar bandwidths

prior.prob

vector of prior probabilities

bw

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

nstage

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

pilot

"amse" = AMSE pilot bandwidths, "samse" = single SAMSE pilot bandwidth

pre

"scale" = pre-scaling, "sphere" = pre-sphering

Hstart

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

binned

flag for binned kernel estimation

bgridsize

vector of binning grid sizes - required only if binned=TRUE

Value

• -- 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 result from kda is a vector of group labels estimated via the kernel discriminant rule. If the test data y are given then these are classified. Otherwise the training data x are classified.

Details

-- 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 analagous calls to diagonal selectors.

For d = 1, 2, 3, 4, and if eval.points is not specified, then the density estimate is computed over a grid defined by gridsize (if binned=FALSE) or by bgridsize (if binned=TRUE). For d = 1, 2, 3, 4, and if eval.points is specified, then the density estimate is computed exactly at eval.points. For d > 4, the kernel density estimate is computed exactly and eval.points must be specified. For details on the pre-transformations in pre, see pre.sphere and pre.scale.

-- 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.

References

Mardia, K.V., Kent, J.T. & Bibby J.M. (1979) Multivariate Analysis. Academic Press. London. Silverman, B. W. (1986) Data Analysis for Statistics and Data Analysis. Chapman & Hall. London. Simonoff, J. S. (1996) Smoothing Methods in Statistics. Springer-Verlag. New York

Venables, W.N. & Ripley, B.D. (1997) Modern Applied Statistics with S-PLUS. Springer-Verlag. New York.

See Also

compare, compare.kda.cv, kda.kde

Examples

### See examples in ? plot.kda.kde } 

<keyword>smooth</keyword>