Test the convexity of set of data

Description

Provides the

Usage

1

Arguments

X

a matrix containing the data sets

Y

a vector containing -1 or +1 that reprensents the class of each elements of X.

Details

testConvexity test if one of the two data set is potentially convex.

Value

An object of class list containing the number of the class which is convex and the parameters of a set of hyperplanes separating the two classes

Author(s)

Vincent Moutoussamy

References

  • R.T. Rockafellar:
    Convex analysis
    Princeton university press, 2015.

See Also

LSVM modelLSVM

Examples

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# A limit state function
f <- function(x){  sqrt(sum(x^2)) - sqrt(2)/2 }

# Creation of the data sets
n <- 200
X <- matrix(runif(2*n), nrow = n)
Y <- apply(X, MARGIN = 1, function(w){sign(f(w))})

## Not run: 
  TEST.Convexity <- testConvexity(X, Y)
  if(length(TEST.Convexity) == 2){
    Convexity <- TEST.Convexity[[1]] 
    model.A   <- TEST.Convexity[[2]]
  }
  if(length(TEST.Convexity) == 1){
    # The problem is not convex
    Convexity <- 0 #the problem is not convex
  }

## End(Not run)