R: Functional boxplot of univariate and multivariate functional...

fbplot {roahd}

R Documentation

Functional boxplot of univariate and multivariate functional data

Description

This function can be used to perform the functional boxplot of univariate or multivariate functional data.

Usage

fbplot(
  Data,
  Depths = "MBD",
  Fvalue = 1.5,
  adjust = FALSE,
  display = TRUE,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  ...
)

## S3 method for class 'fData'
fbplot(
  Data,
  Depths = "MBD",
  Fvalue = 1.5,
  adjust = FALSE,
  display = TRUE,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  ...
)

## S3 method for class 'mfData'
fbplot(
  Data,
  Depths = list(def = "MBD", weights = "uniform"),
  Fvalue = 1.5,
  adjust = FALSE,
  display = TRUE,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  ...
)

Arguments

`Data`	the univariate or multivariate functional dataset whose functional boxplot must be determined, in form of `fData` or `mfData` object.
`Depths`	either a vector containing the depths for each element of the dataset, or: univariate case: a string containing the name of the method you want to use to compute it. The default is `'MBD'`. multivariate case: a list with elements `def`, containing the name of the depth notion to be used to compute depths (`BD` or `MBD`), and `weights`, containing the value of parameter `weights` to be passed to the depth function. Default is `list(def = 'MBD', weights = 'uniform')`. In both cases the name of the functions to compute depths must be available in the caller's environment.
`Fvalue`	the value of the inflation factor `F`, default is `F = 1.5`.
`adjust`	either `FALSE` if you would like the default value for the inflation factor, `F = 1.5`, to be used, or (for now only in the univariate functional case) a list specifying the parameters required by the adjustment: `N_trials`: the number of repetitions of the adjustment procedure based on the simulation of a gaussian population of functional data, each one producing an adjusted value of `F`, which will lead to the averaged adjusted value `\bar{F}`. Default is 20. `trial_size`: the number of elements in the gaussian population of functional data that will be simulated at each repetition of the adjustment procedure. Default is 8 * `Data$N`. `TPR`: the True Positive Rate of outliers, i.e. the proportion of observations in a dataset without amplitude outliers that have to be considered outliers. Default is `2 * pnorm(4 * qnorm(0.25))`. `F_min`: the minimum value of `F`, defining the left boundary for the optimization problem aimed at finding, for a given dataset of simulated gaussian data associated to `Data`, the optimal value of `F`. Default is 0.5. `F_max`: the maximum value of `F`, defining the right boundary for the optimization problem aimed at finding, for a given dataset of simulated gaussian data associated to `Data`, the optimal value of `F`. Default is 5. `tol`: the tolerance to be used in the optimization problem aimed at finding, for a given dataset of simulated gaussian data associated to `Data`, the optimal value of `F`. Default is `1e-3`. `maxiter`: the maximum number of iterations to solve the optimization problem aimed at finding, for a given dataset of simulated gaussian data associated to `Data`, the optimal value of `F`. Default is `100`. `VERBOSE`: a parameter controlling the verbosity of the adjustment process.
`display`	either a logical value indicating whether you want the functional boxplot to be displayed, or the number of the graphical device where you want the functional boxplot to be displayed.
`xlab`	the label to use on the x axis when displaying the functional boxplot.
`ylab`	the label (or list of labels for the multivariate functional case) to use on the y axis when displaying the functional boxplot.
`main`	the main title (or list of titles for the multivariate functional case) to be used when displaying the functional boxplot.
`...`	additional graphical parameters to be used in plotting functions.

Value

Even when used in graphical way to plot the functional boxplot, the function returns a list of three elements:

Depths: contains the depths of each element of the functional dataset.
Fvalue: is the value of F used to obtain the outliers.
ID_out: contains the vector of indices of dataset elements flagged as outliers (if any).

Adjustment

In the univariate functional case, when the adjustment option is selected, the value of F is optimized for the univariate functional dataset provided with Data.

In practice, a number adjust$N_trials of times a synthetic population (of size adjust$tiral_size with the same covariance (robustly estimated from data) and centerline as fData is simulated without outliers and each time an optimized value F_i is computed so that a given proportion (adjust$TPR) of observations is flagged as outliers. The final value of F for the functional boxplot is determined as an average of F_1, F_2, \dots, F_{N_{trials}}. At each time step the optimization problem is solved using stats::uniroot (Brent's method).

References

Sun, Y., & Genton, M. G. (2012). Functional boxplots. Journal of Computational and Graphical Statistics.
Sun, Y., & Genton, M. G. (2012). Adjusted functional boxplots for spatio-temporal data visualization and outlier detection. Environmetrics, 23(1), 54-64.

Examples


# UNIVARIATE FUNCTIONAL BOXPLOT - NO ADJUSTMENT

set.seed(1)

N = 2 * 100 + 1
P = 2e2

grid = seq( 0, 1, length.out = P )

D = 10 * matrix( sin( 2 * pi * grid ), nrow = N, ncol = P, byrow = TRUE )

D = D + rexp(N, rate = 0.05)


# c( 0, 1 : (( N - 1 )/2), -( ( ( N - 1 ) / 2 ) : 1 ) )^4


fD = fData( grid, D )

dev.new()
oldpar <- par(mfrow = c(1, 1))
par(mfrow = c(1, 3))

plot( fD, lwd = 2, main = 'Functional dataset',
      xlab = 'time', ylab = 'values' )

fbplot( fD, main = 'Functional boxplot', xlab = 'time', ylab = 'values', Fvalue = 1.5 )

boxplot(fD$values[,1], ylim = range(fD$values), main = 'Boxplot of functional dataset at t_0 ' )

par(oldpar)

# UNIVARIATE FUNCTIONAL BOXPLOT - WITH ADJUSTMENT


set.seed( 161803 )

P = 2e2
grid = seq( 0, 1, length.out = P )

N = 1e2

# Generating a univariate synthetic gaussian dataset
Data = generate_gauss_fdata( N, centerline = sin( 2 * pi * grid ),
                             Cov = exp_cov_function( grid,
                                                     alpha = 0.3,
                                                     beta  = 0.4 ) )
fD = fData( grid, Data )

dev.new()

fbplot( fD, adjust = list( N_trials = 10,
                           trial_size = 5 * N,
                           VERBOSE = TRUE ),
                     xlab = 'time', ylab = 'Values',
                     main = 'My adjusted functional boxplot' )


# MULTIVARIATE FUNCTIONAL BOXPLOT - NO ADJUSTMENT

set.seed( 1618033 )

P = 1e2
N = 1e2
L = 2

grid = seq( 0, 1, length.out = 1e2 )

C1 = exp_cov_function( grid, alpha = 0.3, beta = 0.4 )
C2 = exp_cov_function( grid, alpha = 0.3, beta = 0.4 )

# Generating a bivariate functional dataset of gaussian data with partially
# correlated components
Data = generate_gauss_mfdata( N, L,
                              centerline = matrix( sin( 2 * pi * grid ),
                                                   nrow = 2, ncol = P,
                                                   byrow = TRUE ),
                              correlations = rep( 0.5, 1 ),
                              listCov = list( C1, C2 ) )

mfD = mfData( grid, Data )

dev.new()
fbplot( mfD, Fvalue = 2.5, xlab = 'time', ylab = list( 'Values 1',
                                                       'Values 2' ),
        main = list( 'First component', 'Second component' ) )

[Package roahd version 1.4.3 Index]