cellMGGMM: Calculation of the cellwise robust multi-group Gaussian...
In ssMRCD: Robust Estimators for Multi-Group and Spatial Data

cellMGGMM

R Documentation

Calculation of the cellwise robust multi-group Gaussian mixture model

Description

Performs robust estimation of multivariate location and scatter within predefined groups using an iiterative EM-based algorithm.

Usage

cellMGGMM(
  X,
  groups,
  alpha = 0.5,
  hperc = 0.75,
  nsteps = 100,
  crit = 1e-04,
  silent = TRUE,
  maxcond = 100
)

Arguments

`X`	A numeric matrix or data frame with observations in rows and variables in columns.
`groups`	A vector indicating the group membership for each observation (length must match 'nrow(X)').
`alpha`	A non-negative numeric value between '0.5' and '1' controlling the flexibility degree. Default is '0.5'.
`hperc`	A numeric value in '[0,1]' controlling robustness of the estimation. Default is '0.75'.
`nsteps`	Number of main iteration steps in the algorithm. Default is '100'.
`crit`	Convergence criterion for iterative updates. Default is '1e-4'.
`silent`	Logical; if 'TRUE', suppresses progress output. Default is 'FALSE'.
`maxcond`	Maximum allowed condition number for covariance matrices. Default is '100'.

Value

A list containing:

X: The original data matrix.
Ximp: The imputed and/or scaled data matrix.
groups: Vector specifying group assignments from the input.
class: Vector indicating the most likely group membership for each observation, as inferred by the model.
mu: A list of estimated location (mean) vectors for each group.
Sigma: A list of estimated covariance matrices for each group.
Sigmai: A list of estimated inverse covariance matrices for each group.
probs: A matrix of class probabilities for each observation (rows = observations, columns = groups).
pi_groups: A matrix of estimated mixture probabilities, where rows correspond to groups and columns to distributions.
W: A binary matrix indicating outlying cells (0 = outlier, 1 = no outlier).
Q: A matrix of penalty weights.
Sigma_reg: A list of estimated target (regularization) matrices.
rho: A vector of regularization factors used in the estimation.
alpha: Flexibility parameter, as provided in the function input.
hperc: A matrix or vector indicating the percentage of outlying cells per variable and group, based on input.
nsteps: The number of iteration steps taken until convergence.
objvals: The values of the objective function across the iteration steps.

References

Puchhammer, P., Wilms, I., & Filzmoser, P. (2025). A smooth multi-group Gaussian Mixture Model for cellwise robust covariance estimation. ArXiv preprint \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2504.02547")}.

Examples

data("weatherAUT2021")
cut_lon = c(min(weatherAUT2021$lon)-0.2, 12, 16, max(weatherAUT2021$lon) + 0.2)
cut_lat = c(min(weatherAUT2021$lat)-0.2, 48, max(weatherAUT2021$lat) + 0.2)
groups = groups_gridbased(weatherAUT2021$lon, weatherAUT2021$lat, cut_lon, cut_lat)
N = length(unique(groups))
model = cellMGGMM(X = weatherAUT2021[, c("p", "s", "vv", "t", "rsum", "rel")],
                 groups = groups,
                 alpha = 0.5)

ssMRCD documentation built on Nov. 5, 2025, 7:44 p.m.