Kernel Local Fisher Discriminant Analysis

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.

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.

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.

Author

Kisung You

Examples

# \donttest{
## 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)
# }