Kernel Locality Sensitive Discriminant Analysis

Kernel LSDA (KLSDA) 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.klsda(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "whiten", "decorrelate"),
  alpha = 0.5,
  k1 = max(ceiling(nrow(X)/10), 2),
  k2 = max(ceiling(nrow(X)/10), 2),
  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.

alpha

balancing parameter for between- and within-class scatter in \([0,1]\).

k1

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

k2

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

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

Cai D, He X, Zhou K, Han J, Bao H (2007). “Locality Sensitive Discriminant Analysis.” In Proceedings of the 20th International Joint Conference on Artifical Intelligence, IJCAI'07, 708--713.

Author

Kisung You

Examples

## generate 3 different groups of data X and label vector
x1 = matrix(rnorm(4*10), nrow=10)-50
x2 = matrix(rnorm(4*10), nrow=10)
x3 = matrix(rnorm(4*10), nrow=10)+50
X     = rbind(x1, x2, x3)
label = rep(1:3, each=10)

## try different kernel bandwidths
out1 = do.klsda(X, label, t=0.1)
out2 = do.klsda(X, label, t=1)
out3 = do.klsda(X, label, t=10)

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

par(opar)