This function computes the three 'DepthGram' representations from a p-variate functional data set.

```
depthgram(
Data,
marginal_outliers = FALSE,
boxplot_factor = 1.5,
outliergram_factor = 1.5,
ids = NULL
)
# S3 method for default
depthgram(
Data,
marginal_outliers = FALSE,
boxplot_factor = 1.5,
outliergram_factor = 1.5,
ids = NULL
)
# S3 method for fData
depthgram(
Data,
marginal_outliers = FALSE,
boxplot_factor = 1.5,
outliergram_factor = 1.5,
ids = NULL
)
# S3 method for mfData
depthgram(
Data,
marginal_outliers = FALSE,
boxplot_factor = 1.5,
outliergram_factor = 1.5,
ids = NULL
)
```

- Data
A

`list`

of length`L`

(number of components) in which each element is an`N x P`

matrix with`N`

individuals and`P`

time points. Alternatively, it can also be an object of class`fData`

or of class`mfData`

.- marginal_outliers
A boolean specifying whether the function should return shape and amplitude outliers over each dimension. Defaults to

`FALSE`

.- boxplot_factor
A numeric value specifying the inflation factor for marginal functional boxplots. This is ignored if

`marginal_outliers == FALSE`

. Defaults to`1.5`

.- outliergram_factor
A numeric value specifying the inflation factor for marginal outliergrams. This is ignored if

`marginal_outliers == FALSE`

. Defaults to`1.5`

.- ids
A character vector specifying labels for individual observations. Defaults to

`NULL`

, in which case observations will remain unlabelled.

An object of class `depthgram`

which is a list with the following
items:

`mbd.mei.d`

: vector MBD of the MEI dimension-wise.`mei.mbd.d`

: vector MEI of the MBD dimension-wise.`mbd.mei.t`

: vector MBD of the MEI time-wise.`mei.mbd.t`

: vector MEI of the MEI time-wise.`mbd.mei.t2`

: vector MBD of the MEI time/correlation-wise.`mei.mbd.t2`

: vector MEI of the MBD time/correlation-wise.`shp.out.det`

: detected shape outliers by dimension.`mag.out.det`

: detected magnitude outliers by dimension.`mbd.d`

: matrix`n x p`

of MBD dimension-wise.`mei.d`

: matrix`n x p`

of MEI dimension-wise.`mbd.t`

: matrix`n x p`

of MBD time-wise.`mei.t`

: matrix`n x p`

of MEI time-wise.`mbd.t2`

: matrix`n x p`

of MBD time/correlation-wise`mei.t2`

: matrix`n x p`

of MBD time/correlation-wise.

Aleman-Gomez, Y., Arribas-Gil, A., Desco, M. Elias-Fernandez, A., and Romo, J. (2021). "Depthgram: Visualizing Outliers in High Dimensional Functional Data with application to Task fMRI data exploration".

```
N <- 2e2
P <- 1e3
grid <- seq(0, 1, length.out = P)
Cov <- exp_cov_function(grid, alpha = 0.3, beta = 0.4)
Data <- list()
Data[[1]] <- generate_gauss_fdata(
N,
centerline = sin(2 * pi * grid),
Cov = Cov
)
Data[[2]] <- generate_gauss_fdata(
N,
centerline = sin(2 * pi * grid),
Cov = Cov
)
names <- paste0("id_", 1:nrow(Data[[1]]))
DG1 <- depthgram(Data, marginal_outliers = TRUE, ids = names)
fD <- fData(grid, Data[[1]])
DG2 <- depthgram(fD, marginal_outliers = TRUE, ids = names)
mfD <- mfData(grid, Data)
DG3 <- depthgram(mfD, marginal_outliers = TRUE, ids = names)
```