Description Usage Arguments Value

View source: R/gsbm_mcgd_parallel.R

Given an adjacency matrix with missing observations, the function `gsbm_mgcd`

robustly estimates the probabilities of connections between nodes.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
gsbm_mcgd_parallel(
A,
lambda1,
lambda2,
epsilon = 0.1,
maxit = 100,
step_L = 0.01,
step_S = 0.1,
trace.it = FALSE,
n_cores = detectCores(),
save = FALSE,
file = NULL
)
``` |

`A` |
nxn adjacency matrix |

`lambda1` |
regularization parameter for nuclear norm penalty (positive number) |

`lambda2` |
regularization parameter for 2,1-norm penalty (positive number) |

`epsilon` |
regularization parameter for the L2-norm penalty (positive number, if NULL, default method is applied) |

`maxit` |
maximum number of iterations (positive integer, if NULL, default method is applied) |

`step_L` |
step size for the gradient step of L parameter (positive number) |

`step_S` |
step size for the gradient step of S parameter (positive number) |

`trace.it` |
whether messages about convergence should be printed (boolean, if NULL, default is FALSE) |

`n_cores` |
number of cores to parallellize on (integer number, default is set with detectCores()) |

`save` |
whether or not value of current estimates should be saved at each iteration (boolean) |

`file` |
if save is set to TRUE, name of the folder where current estimates should be saved (character string, file saved in file/L_iter.txt at iteration iter) |

The estimate for the nxn matrix of probabilities of connections between nodes. It is given as the sum of a low-rank nxn matrix L, corresponding to connections between inlier nodes, and a column sparse nxn matrix S, corresponding to connections between outlier nodes and the rest of the network. The matrices L and S are such that

E(A) = L - diag(L) + S + S'

where E(A) is the expectation of the adjacency matrix, diag(L) is a nxn diagonal matrix with diagonal entries equal to those of L, and S' means S transposed.

The return value is a list of components

`A`

the adjacency matrix.`L`

estimate for the low-rank component.`S`

estimate for the column-sparse component.`objective`

the value of the objective function.`R`

a bound on the nuclear norm of the low-rank component.`iter`

number of iterations between convergence of the objective function.

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