Benchmarking results and comparision with other packages • dcsbm

Microbenchmarks for Development

A. Scaling with network size

results <- bench::press(
  Nsize = c(10, 25, 50, 75, 100),
  {
    G <- sample_ppm(Nsize, c=0.9, k=10, B=3)
    G <- simplify(G)
    G <- delete.vertices(G, degree(G) == 0)
    p <- sample(1:3, Nsize, replace = TRUE)
    bench::mark(
      min_iterations = 5,
      entropy = get_entropy(G, p),
      mcmc_sweep = mcmc_single_sweep(G, p, 3),
      agglomerative_merge = invisible(capture.output(dcsbm(G, n.moves=1, n.sweeps=0))),
      check = FALSE
    )
  }
)
results

B. Entropy Convergence Tests

1. MCMC sweeps

# Initialize graph and a random starting partition
G <- sample_ppm(100, c = 0.9, k = 10, B = 3, directed = TRUE, loops = TRUE)

# Number of mcmcm sweeps
start_partition <- sample(1:3, size = 100, replace = TRUE)

# Perform Niter mcmc sweeps
result <- mcmc_sweep(G, start_partition, 3, n.sweeps = 100)

# Visualize start/end partition and entropy delta.
plot(G, vertex.color = start_partition, vertex.label = NA)
plot(result$entropy_delta/length(E(G)), type = "line")
plot(G, vertex.color = result$best_partition, vertex.label = NA)

2. Agglomerative Merge

G <- sample_ppm(100, 0.9, 10, 3, directed = TRUE, loops = TRUE)

model <- dcsbm(G, n.sweeps = 1, verbose = FALSE)
 
plot(G, vertex.color = model$best_partition, vertex.label = NA)

C. Degree correction tests

1. MCMC sweeps

# Initialize graph and a random starting partition
G <- sample_dcppm(100, 0.9, 10, 3, k_coef = 2, directed = TRUE, loops = TRUE)

start_partition <- sample(1:3, size = 100, replace = TRUE)

result <- mcmc_sweep(G, start_partition, 3, n.sweeps = 100, dc = TRUE)

# Visualize start/end partition and entropy delta.
plot(G, vertex.color = start_partition, vertex.label = NA)
plot(result$entropy_delta/length(E(G)), type = "line")
plot(G, vertex.color = result$best_partition, vertex.label = NA)

2. Agglomerative merge

G <- sample_dcppm(100, 0.9, 10, 3, k_coef = 2, directed = TRUE, loops = TRUE)

model <- dcsbm(G, degree_correction = TRUE, n.sweeps = 5, verbose = FALSE)
 
plot(G, vertex.color = model$best_partition, vertex.label = NA, sub = "Best partition")
plot(G, vertex.color = c(rep(1,34), rep(2,33), rep(3,33)), vertex.label = NA, sub = "True partition")