Key Features

• High-level interface for handling connectome data
• Support for multiple Riemannian metrics (AIRM, Log-Euclidean, Euclidean, Log-Cholesky, Bures-Wasserstein)
• Efficient parallel computation capabilities
• Memory-efficient operations through reference-based manipulation
• Comprehensive tools for geometric operations and statistical analysis

Loading the Package and Setting Up

library(riemtan)
library(Matrix)
library(future)

# Enable parallel processing
plan(multisession)

Working with Metrics

The package provides several pre-configured metrics:

# Load the AIRM metric
data(airm)

# Other available metrics
data(log_euclidean)
data(euclidean)
data(log_cholesky)
data(bures_wasserstein)

Creating and Manipulating Samples

# Create an identity matrix
id <- diag(10) |> 
  as("dpoMatrix") |>
  Matrix::pack()

# Generate two random samples
sample1 <- rspdnorm(30, id, id, airm)  # Centered at I
sample2 <- rspdnorm(30, 2*id, id, airm)  # Centered at 2I

# Compute tangent space representations
sample1$compute_unvecs()
sample1$compute_tangents()

# Compute manifold representations
sample1$compute_conns()

# Check if computations were successful
!is.null(sample1$connectomes)  # Should be TRUE

Statistical Analysis

# Create a sample from your connectome data
conn_sample <- CSample$new(conns = your_connectomes, metric_obj = airm)

# Compute the Fréchet mean
conn_sample$compute_fmean()

# Center the sample at the Fréchet mean
conn_sample$center()

# Compute variation
conn_sample$compute_variation()

# Compute sample covariance
conn_sample$compute_sample_cov()

Discriminating Between Two Samples

This example shows how to prepare data for clustering analysis:

# Combine two samples
joint_conns <- c(sample1$connectomes, sample2$connectomes)
combined_sample <- CSample$new(conns = joint_conns, metric_obj = airm)

# Prepare for clustering
combined_sample$compute_tangents()
combined_sample$center()  # Center at Fréchet mean
combined_sample$compute_vecs()  # Get vectorized representation

# The vectorized representations can now be used with standard clustering algorithms

Working with Real Data

When working with real connectome data, you’ll typically need to pre-process your matrices:

# Convert your matrices to the correct format
parsed_conns <- your_raw_conns |>
  purrr::map(\(x) as(x, "dpoMatrix")) |>
  purrr::map(Matrix::pack)

# Create a CSample object
conn_sample <- CSample$new(parsed_conns, airm)

# Compute geometric statistics
conn_sample$compute_fmean()
conn_sample$compute_tangents()
conn_sample$center()
conn_sample$compute_vecs()

CSample Class

The CSample class is the main workhorse of the package. It manages:

• Connectome data in different representations (manifold, tangent space, vectorized)
• Statistical computations
• Automatic parallel processing when possible
• Memory-efficient operations

Key methods include: - compute_tangents(): Computes tangent space representations - compute_conns(): Computes manifold representations - compute_vecs(): Computes vectorized representations - compute_fmean(): Computes Fréchet mean - center(): Centers the sample at its Fréchet mean - compute_variation(): Computes sample variation - compute_sample_cov(): Computes sample covariance

Metric Objects

Metric objects (class rmetric) contain four essential functions: - log: Computes Riemannian logarithm - exp: Computes Riemannian exponential - vec: Performs vectorization - unvec: Performs inverse vectorization