do.kmvp: Kernel-Weighted Maximum Variance Projection

Description

Kernel-Weighted Maximum Variance Projection (KMVP) is a generalization of Maximum Variance Projection (MVP). Even though its name contains kernel, it is not related to kernel trick well known in the machine learning community. Rather, it generalizes the binary penalization on class discrepancy, $$S_{ij} = \exp(-\|x_i-x_j\|^2/t) \quad\textrm{if}\quad C_i \ne C_j$$ where $x_i$ is an $i$-th data point and $t$ a kernel bandwidth (bandwidth). Note that when the bandwidth value is too small, it might suffer from numerical instability and rank deficiency due to its formulation.

Usage

do.kmvp(X, label, ndim = 2, preprocess = c("center", "scale", "cscale",
  "decorrelate", "whiten"), bandwidth = 1)

Arguments

an $(n\times p)$ matrix or data frame whose rows are observations and columns represent independent variables.

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.

bandwidth

bandwidth parameter for heat kernel as the equation above.

Value

a named list containing

Y: an $(n\times ndim)$ matrix whose rows are embedded observations.
trfinfo: a list containing information for out-of-sample prediction.
projection: a $(p\times ndim)$ whose columns are basis for projection.

References

zhang_maximum_2007Rdimtools

Examples

Run this code

# NOT RUN {
## generate 3 different groups of data X and label vector
x1 = matrix(rnorm(4*10), nrow=10)-20
x2 = matrix(rnorm(4*10), nrow=10)
x3 = matrix(rnorm(4*10), nrow=10)+20
X  = rbind(x1, x2, x3)
label = c(rep(1,10), rep(2,10), rep(3,10))

## perform KMVP with different bandwidths
out1 = do.kmvp(X, label, bandwidth=10)
out2 = do.kmvp(X, label, bandwidth=100)
out3 = do.kmvp(X, label, bandwidth=1000)

## visualize
par(mfrow=c(1,3))
plot(out1$Y[,1], out1$Y[,2], main="bandwidth=1e+1")
plot(out2$Y[,1], out2$Y[,2], main="bandwidth=1e+2")
plot(out3$Y[,1], out3$Y[,2], main="bandwidth=1e+3")

# }