do.kmfa: Kernel Marginal Fisher Analysis

Description

Kernel Marginal Fisher Analysis (KMFA) is a nonlinear variant of MFA using kernel tricks. For simplicity, we only enabled a heat kernel of a form $k (x_{i}, x_{j}) = \exp (- d (x_{i}, x_{j})^{2} / 2 * t^{2})$ where $t$ is a bandwidth parameter. Note that the method is far sensitive to the choice of $t$ .

Usage

do.kmfa(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  k1 = max(ceiling(nrow(X)/10), 2),
  k2 = max(ceiling(nrow(X)/10), 2),
  t = 1
)

Arguments

an $(n \times p)$ matrix or data frame whose rows are observations.

label

a length- $n$ vector of data class labels.

ndim

an integer-valued target dimension.

preprocess

an additional option for preprocessing the data. Default is "center". See also aux.preprocess for more details.

the number of same-class neighboring points (homogeneous neighbors).

the number of different-class neighboring points (heterogeneous neighbors).

bandwidth parameter for heat kernel in $(0, \infty)$ .

Value

a named list containing

Y: an $(n \times n d i m)$ matrix whose rows are embedded observations.
trfinfo: a list containing information for out-of-sample prediction.

References

yan_graph_2007Rdimtools

Examples

Run this code

# NOT RUN {
## generate data of 3 types with clear difference
dt1  = aux.gensamples(n=33)-100
dt2  = aux.gensamples(n=33)
dt3  = aux.gensamples(n=33)+100

## merge the data and create a label correspondingly
X      = rbind(dt1,dt2,dt3)
label  = c(rep(1,33), rep(2,33), rep(3,33))

## try different numbers for neighborhood size
out1 = do.kmfa(X, label, k1=5, k2=5, t=1)
out2 = do.kmfa(X, label, k1=5, k2=5, t=2)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(out1$Y, main="bandwidth=1")
plot(out2$Y, main="bandwidth=2")
par(opar)
# }