Calculate Potential Space
Calculates the representation of the training classes in potential space.
depth.space.potential(data, cardinalities, pretransform = "NMom",
kernel = "GKernel", kernel.bandwidth = NULL, mah.parMcd = 0.75)data |
Matrix containing training sample where each row is a d-dimensional object, and objects of each class are kept together so that the matrix can be thought of as containing blocks of objects representing classes. |
cardinalities |
Numerical vector of cardinalities of each class in |
pretransform |
The method of data scaling.
The data may be scaled jointly or separately:
You may use traditional moments or Minimum Covariance Determinant (MCD) estimates for mean and covariance:
|
kernel |
|
kernel.bandwidth |
the bandwidth parameter of the kernel. If |
mah.parMcd |
is the value of the argument |
The potential representation is calculated in the same way as in depth.potential, see References below for more information and details.
Matrix of objects, each object (row) is represented via its potentials (columns) w.r.t. each of the classes of the training sample; order of the classes in columns corresponds to the one in the argument cardinalities.
Aizerman, M.A., Braverman, E.M., and Rozonoer, L.I. (1970). The Method of Potential Functions in the Theory of Machine Learning. Nauka (Moscow).
Pokotylo, O. and Mosler, K. (2015). Classification with the pot-pot plot. Mimeo.
ddalpha.train and ddalpha.classify for application, depth.potential for calculation of the potential.
# Generate a bivariate normal location-shift classification task
# containing 20 training objects
class1 <- mvrnorm(50, c(0,0),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
class2 <- mvrnorm(50, c(1,1),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
data <- rbind(class1, class2)
plot(data, col = c(rep(1,50), rep(2,50)))
# potential with rule of thumb bandwidth
ds = depth.space.potential(data, c(50, 50))
# draw.ddplot(depth.space = ds, cardinalities = c(50, 50))
# potential with bandwidth = 0.5 and joint scaling
ds = depth.space.potential(data, c(50, 50), kernel.bandwidth = 0.5,
pretransform = "1Mom")
# draw.ddplot(depth.space = ds, cardinalities = c(50, 50))
# potential with bandwidth = 0.5 and separate scaling
ds = depth.space.potential(data, c(50, 50), kernel.bandwidth = 0.5,
pretransform = "NahMom") # or without pretransform
# draw.ddplot(depth.space = ds, cardinalities = c(50, 50))
data <- getdata("hemophilia")
cardinalities = c(sum(data$gr == "normal"), sum(data$gr == "carrier"))
ds = depth.space.potential(data[,1:2], cardinalities)
# draw.ddplot(depth.space = ds, cardinalities = cardinalities)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.