R/band_depths.R
BD_relative.RdThis function computes Band Depth (BD) of elements of a univariate functional dataset with respect to another univariate functional dataset.
BD_relative(Data_target, Data_reference)
# S3 method for fData
BD_relative(Data_target, Data_reference)
# S3 method for default
BD_relative(Data_target, Data_reference)is the univariate functional dataset, provided either as
a fData object or in matrix
form (N observations as rows and P measurements as columns), whose BD
have to be computed with respect to the reference dataset.
is the dataset, provided either as a fData
object or in matrix form (N observations
as rows and P measurements as columns), containing the reference
univariate functional data that must be used to compute the band depths of
elements in Data_target. If Data_target is fData, it
must be of class fData
The function returns a vector containing the BD of elements in
Data_target with respect to elements in Data_reference.
Given a univariate functional dataset of elements \(X_1(t), X_2(t), \ldots, X_N(t)\), and another univariate functional dataset of elements \(Y_1(t), Y_2(t) \ldots, Y_M(t)\), this function computes the BD of elements of the former with respect to elements of the latter, i.e.:
$$ BD( X_i( t ) ) = {M \choose 2 }^{-1} \sum_{1 \leq i_1 < i_2 \leq M} I( G(X_i) \subset B( Y_{i_1}, Y_{i_2} ) ), \quad \forall i = 1, \ldots, N,$$
where \(G(X_i)\) is the graphic of \(X_i(t)\) and \(B(Y_{i_1},Y_{i_2})\) is the envelope of \(Y_{i_1}(t)\) and \(Y_{i_2}(t)\).
BD, MBD, MBD_relative,
fData
grid = seq( 0, 1, length.out = 1e2 )
Data_ref = matrix( c( 0 + sin( 2 * pi * grid ),
1 + sin( 2 * pi * grid ),
-1 + sin( 2 * pi * grid ) ),
nrow = 3, ncol = length( grid ), byrow = TRUE )
Data_test_1 = matrix( c( 0.6 + sin( 2 * pi * grid ) ),
nrow = 1, ncol = length( grid ), byrow = TRUE )
Data_test_2 = matrix( c( 0.6 + sin( 2 * pi * grid ) ),
nrow = length( grid ), ncol = 1, byrow = TRUE )
Data_test_3 = 0.6 + sin( 2 * pi * grid )
Data_test_4 = array( 0.6 + sin( 2 * pi * grid ), dim = length( grid ) )
Data_test_5 = array( 0.6 + sin( 2 * pi * grid ), dim = c( 1, length( grid ) ) )
Data_test_6 = array( 0.6 + sin( 2 * pi * grid ), dim = c( length( grid ), 1 ) )
Data_test_7 = matrix( c( 0.5 + sin( 2 * pi * grid ),
-0.5 + sin( 2 * pi * grid ),
1.1 + sin( 2 * pi * grid ) ),
nrow = 3, ncol = length( grid ), byrow = TRUE )
fD_ref = fData( grid, Data_ref )
fD_test_1 = fData( grid, Data_test_1 )
fD_test_2 = fData( grid, Data_test_2 )
fD_test_3 = fData( grid, Data_test_3 )
fD_test_4 = fData( grid, Data_test_4 )
fD_test_5 = fData( grid, Data_test_5 )
fD_test_6 = fData( grid, Data_test_6 )
fD_test_7 = fData( grid, Data_test_7 )
BD_relative( fD_test_1, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_1, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_2, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_2, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_3, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_3, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_4, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_4, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_5, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_5, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_6, fD_ref )
#> [1] 0.6666667
BD_relative( Data_test_6, Data_ref )
#> [1] 0.6666667
BD_relative( fD_test_7, fD_ref )
#> [1] 0.6666667 0.6666667 0.0000000
BD_relative( Data_test_7, Data_ref )
#> [1] 0.6666667 0.6666667 0.0000000