Check Outsiderness
Checks the belonging to at least one of class convex hulls of the training sample.
is.in.convex(x, data, cardinalities, seed = 0)
x |
Matrix of objects (numerical vector as one object) whose belonging to convex hulls is to be checked; each row contains a d-variate point. Should have the same dimension as |
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 |
seed |
the random seed. The default value |
Checks are conducted w.r.t. each separate class in data using the simplex algorithm, taken from the C++ implementation of the zonoid depth calculation by Rainer Dyckerhoff.
Matrix of number of objects rows and number of classes columns, containing 1 if an object belongs to the convex hull of the corresponding class, and 0 otherwise.
Implementation of the simplex algorithm is taken from the algorithm for computation of zonoid depth (Dyckerhoff, Koshevoy and Mosler, 1996) that has been implemented in C++ by Rainer Dyckerhoff.
Dyckerhoff, R., Koshevoy, G., and Mosler, K. (1996). Zonoid data depth: theory and computation. In: Prat A. (ed), COMPSTAT 1996. Proceedings in computational statistics, Physica-Verlag (Heidelberg), 235–240.
ddalpha.train and ddalpha.classify for application.
# Generate a bivariate normal location-shift classification task
# containing 400 training objects and 1000 to test with
class1 <- mvrnorm(700, c(0,0),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
class2 <- mvrnorm(700, c(2,2),
matrix(c(1,1,1,4), nrow = 2, ncol = 2, byrow = TRUE))
trainIndices <- c(1:200)
testIndices <- c(201:700)
propertyVars <- c(1:2)
classVar <- 3
trainData <- rbind(cbind(class1[trainIndices,], rep(1, 200)),
cbind(class2[trainIndices,], rep(2, 200)))
testData <- rbind(cbind(class1[testIndices,], rep(1, 500)),
cbind(class2[testIndices,], rep(2, 500)))
data <- list(train = trainData, test = testData)
# Count outsiders
numOutsiders = sum(rowSums(is.in.convex(data$test[,propertyVars],
data$train[,propertyVars], c(200, 200))) == 0)
cat(numOutsiders, "outsiders found in the testing sample.\n")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.