Modified Orthogonal Discriminant Projection

Modified Orthogonal Discriminant Projection (MODP) is a variant of Orthogonal Discriminant Projection (ODP). Authors argue the assumption in modeling ODP's mechanism to reflect distance and class labeling seem unsound. They propose a modified method to explore the intrinsic structure of original data and enhance the classification ability.

do.modp(
  X,
  label,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten"),
  type = c("proportion", 0.1),
  symmetric = c("union", "intersect", "asymmetric"),
  alpha = 0.5,
  beta = 10
)

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.
alpha: balancing parameter of non-local and local scatter in \([0,1]\).
beta: scaling control parameter for distant pairs of data in \((0,\infty)\).

Value

a named list containing

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

References

Zhang S, Lei Y, Wu Y, Yang J (2011). “Modified Orthogonal Discriminant Projection for Classification.” Neurocomputing, 74(17), 3690--3694.

Examples

## 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 = rep(1:3, each=10)

## try different beta (scaling control) parameter
out1 = do.modp(X, label, beta=1)
out2 = do.modp(X, label, beta=10)
out3 = do.modp(X, label, beta=100)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, main="MODP::beta=1")
plot(out2$Y, main="MODP::beta=10")
plot(out3$Y, main="MODP::beta=100")

par(opar)