do.klfda {Rdimtools}

Kernel Local Fisher Discriminant Analysis

Description

Kernel LFDA is a nonlinear extension of LFDA method using kernel trick. It applies conventional kernel method to extend excavation of hidden patterns in a more flexible manner in tradeoff of computational load. For simplicity, only the gaussian kernel parametrized by its bandwidth t is supported.

Usage

do.klfda(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect", "asymmetric"),
  localscaling = TRUE,
  t = 1
)

Arguments

X

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.

type

a vector of neighborhood graph construction. Following types are supported; c("knn",k), c("enn",radius), and c("proportion",ratio). Default is c("proportion",0.1), connecting about 1/10 of nearest data points among all data points. See also aux.graphnbd for more details.

symmetric

one of "intersect", "union" or "asymmetric" is supported. Default is "union". See also aux.graphnbd for more details.

localscaling

TRUE to use local scaling method for construction affinity matrix, FALSE for binary affinity.

t

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

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.

Author(s)

Kisung You

References

Sugiyama M (2006). “Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction.” In Proceedings of the 23rd International Conference on Machine Learning, 905–912.

Zelnik-manor L, Perona P (2005). “Self-Tuning Spectral Clustering.” In Saul LK, Weiss Y, Bottou L (eds.), Advances in Neural Information Processing Systems 17, 1601–1608. MIT Press.

See Also

do.lfda

Examples

## generate 3 different groups of data X and label vector
set.seed(100)
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 = rep(1:3, each=10)

## try different affinity matrices
out1 = do.klfda(X, label, t=0.1)
out2 = do.klfda(X, label, t=1)
out3 = do.klfda(X, label, t=10)

## visualize
opar = par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, pch=19, col=label, main="bandwidth=0.1")
plot(out2$Y, pch=19, col=label, main="bandwidth=1")
plot(out3$Y, pch=19, col=label, main="bandwidth=10")
par(opar)