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Position-Aware Random Transport (PARROT) Network Alignment

Source: R/all_generic.R, R/parrot.R
parrot.Rd

Performs PARROT alignment on hyperdesign data structures. Aligns networks using regularized optimal transport with position-aware features and consistency constraints.

Performs PARROT alignment on hyperdesign data structures. Aligns networks using regularized optimal transport with position-aware features and consistency constraints.

Performs PARROT alignment on hyperdesign data structures containing network domains.

Usage

parrot(data, anchors, ...)

parrot(data, anchors, ...)

# S3 method for class 'hyperdesign'
parrot(
  data,
  anchors,
  preproc = center(),
  ncomp = NULL,
  sigma = 0.15,
  lambda = 0.1,
  lambda_e = NULL,
  lambda_n = NULL,
  lambda_p = NULL,
  tau = 0.05,
  alpha = 0.2,
  gamma = 0.1,
  solver = c("sinkhorn", "exact"),
  max_iter = 100,
  tol = 1e-06,
  use_cpp = FALSE,
  verbose = FALSE,
  ...
)

# Default S3 method
parrot(data, anchors, ...)

Arguments

data

A hyperdesign object containing multiple network domains

anchors

Name of the anchor/correspondence variable for semi-supervised alignment

...

Additional arguments (currently unused)

preproc

Preprocessing function to apply to the data (default: center())

ncomp

Number of latent dimensions for barycenter (default: NULL, auto-determine)

sigma

RWR restart probability and diffusion parameter (default: 0.15)

lambda

Overall consistency regularization weight (default: 0.1). Can also specify lambda_e, lambda_n, lambda_p separately for fine control

lambda_e

Edge consistency weight (default: lambda * 0.5)

lambda_n

Neighborhood consistency weight (default: lambda * 0.5)

lambda_p

Anchor prior weight (default: lambda * 0.1)

tau

Entropy regularization parameter for Sinkhorn (default: 0.01)

alpha

Weight for feature vs RWR cost in Sylvester equation (default: 0.5)

gamma

Cross-graph mixing parameter for Sylvester iteration (default: 0.1)

solver

Transport solver: "sinkhorn" for entropic (default), "exact" for unregularized

max_iter

Maximum number of iterations (default: 100)

tol

Convergence tolerance (default: 1e-6)

use_cpp

Whether to use C++ optimizations (default: FALSE)

verbose

Logical flag to print progress information during fitting

Value

A multiblock_biprojector object containing:

  • s: Aligned network embeddings

  • v: Primal vectors for out-of-sample projection

  • alignment_matrix: Soft alignment/transport plan between networks

  • transport_plan: Dense transport matrix S

  • sdev: Standard deviations of aligned components

  • Additional metadata for reconstruction and validation

A multiblock_biprojector object containing:

  • s: Aligned network embeddings

  • v: Primal vectors for out-of-sample projection

  • alignment_matrix: Soft alignment/transport plan between networks

  • transport_plan: Dense transport matrix S

  • sdev: Standard deviations of aligned components

  • Additional metadata for reconstruction and validation

A multiblock_biprojector object containing the PARROT alignment results

Details

PARROT tackles network alignment by formulating it as a regularized optimal transport problem. The method incorporates position-aware features through Random Walk with Restart (RWR) descriptors and enforces structural consistency through neighborhood-preserving regularization terms.

PARROT operates through the following algorithmic components:

  • Position-Aware Features: Compute RWR descriptors capturing network position

  • Cross-Network Cost: Build transport cost matrix between networks

  • Consistency Regularization: Add structural similarity constraints

  • Optimal Transport: Solve regularized transport problem via Sinkhorn

The algorithm minimizes the objective: $$L(S) = \langle C, S \rangle + \lambda_1 \Omega_1(S) + \lambda_2 \Omega_2(S) + \tau H(S)$$

where \(C\) is the position-aware cost matrix, \(\Omega_1, \Omega_2\) are consistency regularizers, and \(H(S)\) is the entropy regularization term with parameter \(\tau\).

Key parameters:

  • sigma: RWR restart probability and diffusion parameter

  • lambda: Consistency regularization weights

  • tau: Entropy regularization parameter for Sinkhorn

  • solver: Transport solver ("sinkhorn" or "exact")

PARROT tackles network alignment by formulating it as a regularized optimal transport problem. The method incorporates position-aware features through Random Walk with Restart (RWR) descriptors and enforces structural consistency through neighborhood-preserving regularization terms.

PARROT operates through the following algorithmic components:

  • Position-Aware Features: Compute RWR descriptors capturing network position

  • Cross-Network Cost: Build transport cost matrix between networks

  • Consistency Regularization: Add structural similarity constraints

  • Optimal Transport: Solve regularized transport problem via Sinkhorn

The algorithm minimizes the objective: $$L(S) = \langle C, S \rangle + \lambda_1 \Omega_1(S) + \lambda_2 \Omega_2(S) + \tau H(S)$$

where \(C\) is the position-aware cost matrix, \(\Omega_1, \Omega_2\) are consistency regularizers, and \(H(S)\) is the entropy regularization term with parameter \(\tau\).

Key parameters:

  • sigma: RWR restart probability and diffusion parameter

  • lambda: Consistency regularization weights

  • tau: Entropy regularization parameter for Sinkhorn

  • solver: Transport solver ("sinkhorn" or "exact")

References

Wang, S., Chen, Z., Yu, X., Li, T., Yang, J., & Liu, X. (2022). PARROT: Position-aware regularized optimal transport for network alignment. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 1896-1905).

Wang, S., Chen, Z., Yu, X., Li, T., Yang, J., & Liu, X. (2022). PARROT: Position-aware regularized optimal transport for network alignment. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 1896-1905).

See also

parrot.hyperdesign

parrot.hyperdesign

Examples

# \donttest{
# Example with hyperdesign network data

# Create synthetic network domains
set.seed(123)
domain1 <- list(
  x = matrix(rnorm(200), 100, 2),  # Node features
  design = data.frame(
    node_id = 1:100,
    anchors = c(1:10, rep(NA, 90))  # First 10 nodes are anchors
  )
)
domain2 <- list(
  x = matrix(rnorm(200), 100, 2),
  design = data.frame(
    node_id = 1:100,
    anchors = c(1:10, rep(NA, 90))  # Corresponding anchors
  )
)

# Create hyperdesign
hd <- structure(list(domain1 = domain1, domain2 = domain2), class = "hyperdesign")

# Run PARROT alignment with default parameters
result <- parrot(hd, anchors = anchors)

# Access alignment results
transport_plan <- result$transport_plan
aligned_embeddings <- result$s

# Use different regularization settings
result_strong <- parrot(hd, anchors = anchors, lambda = 0.5, tau = 0.1)
# }

# \donttest{
# Example with hyperdesign network data
library(multidesign)
library(tibble)

# Create synthetic network domains (node features for PARROT)
set.seed(123)
X1 <- matrix(rnorm(200), 100, 2)  # Node features for domain 1
X2 <- matrix(rnorm(200), 100, 2)  # Node features for domain 2

# Create design data frames with anchor correspondences (PARROT uses anchors)
design1 <- tibble(
  node_id = 1:100,
  anchors = c(1:10, rep(NA, 90))  # First 10 nodes are anchors
)
design2 <- tibble(
  node_id = 1:100,
  anchors = c(1:10, rep(NA, 90))  # Corresponding anchors
)

# Create multidesign objects
md1 <- multidesign(X1, design1)
md2 <- multidesign(X2, design2)

# Create hyperdesign from multidesign objects
hd <- hyperdesign(list(domain1 = md1, domain2 = md2))

# Run PARROT alignment (uses anchors from design component)
result <- parrot(hd, anchors = anchors)

# Access alignment results
transport_plan <- result$transport_plan
aligned_embeddings <- result$s

# Use different regularization settings
result_strong <- parrot(hd, anchors = anchors, lambda = 0.5, tau = 0.1)
# }