compute_frechet_mean: Compute the Frechet Mean

In riemtan: Riemannian Metrics for Symmetric Positive Definite Matrices

Compute the Frechet Mean

Description

This function computes the Frechet mean of a sample using an iterative algorithm with optional parallel processing.

Usage

compute_frechet_mean(
  sample,
  tol = 0.05,
  max_iter = 20,
  lr = 0.2,
  batch_size = 32,
  progress = FALSE
)

Arguments

sample	An object of class CSample containing the sample data.
tol	A numeric value specifying the tolerance for convergence. Default is 0.05.
max_iter	An integer specifying the maximum number of iterations. Default is 20.
lr	A numeric value specifying the learning rate. Default is 0.2.
batch_size	Integer. The number of samples to process in each batch during computation. Default is 32.
progress	Logical indicating whether to show progress during computation (default: FALSE). Requires progressr package.

Details

The function iteratively updates the reference point of the sample until the change in the reference point is less than the specified tolerance or the maximum number of iterations is reached. If the tangent images are not already computed, they will be computed before starting the iterations.

When parallel processing is enabled (via set_parallel_plan()), the relocate() function will use parallel processing for relocating tangent images in each iteration, which can significantly speed up computation for large samples.

Value

The computed Frechet mean as a dppMatrix object.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  # Load the AIRM metric object
  data(airm)
  # Create a CSample object with example data
  conns <- list(
    diag(2) |> Matrix::nearPD() |> _$mat |> Matrix::pack(),
    diag(c(2, 3)) |> Matrix::nearPD() |> _$mat |> Matrix::pack()
  )
  sample <- CSample$new(conns = conns, metric_obj = airm)
  # Compute the Frechet mean
  compute_frechet_mean(sample, tol = 0.01, max_iter = 50, lr = 0.1)
}

riemtan documentation built on Nov. 11, 2025, 1:06 a.m.