Type: Package
Title: Inductive Node-Splitting Cross-Validation for Community Detection
Version: 0.1.0
Description: Implements Inductive Node-Splitting Cross-Validation (INCV) for selecting the number of communities in stochastic block models. Provides f-fold and random-split node-level cross-validation, along with competing methods including CROISSANT, Edge Cross-Validation (ECV), and Node Cross-Validation (NCV). Supports both SBM and Degree-Corrected Block Models (DCBM), with multiple loss functions (L2, binomial deviance, AUC). Includes network simulation utilities for SBM, RDPG, and latent space models.
URL: https://github.com/ivylinzhang97/incv-community-detection
BugReports: https://github.com/ivylinzhang97/incv-community-detection/issues
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.3
Depends: R (≥ 3.5.0)
Imports: methods, Matrix, RSpectra, ClusterR, irlba, parallel, cluster, Rfast, data.table, IMIFA, stats
Suggests: latentnet, network, rdist, igraph, testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-03-07 18:02:22 UTC; linzhang
Author: Lin Zhang [aut, cre], Bokai Yang [aut]
Maintainer: Lin Zhang <linzhang1126@gmail.com>
Repository: CRAN
Date/Publication: 2026-03-12 08:10:15 UTC

INCVCommunityDetection: Inductive Node-Splitting Cross-Validation for Community Detection

Description

Implements Inductive Node-Splitting Cross-Validation (INCV) for selecting the number of communities in stochastic block models, along with competing methods (CROISSANT, ECV, NCV).

Main functions

nscv.f.fold

F-fold node-split cross-validation (INCV).

nscv.random.split

Random-split cross-validation (INCV).

croissant.blockmodel

CROISSANT for SBM/DCBM selection.

ECV.for.blockmodel

Edge cross-validation.

NCV.for.blockmodel

Node cross-validation.

Author(s)

Maintainer: Lin Zhang linzhang1126@gmail.com

Authors:

See Also

Useful links:

Negative AUC for matrix predictions

Description

Negative AUC for matrix predictions

Usage

AUC(A, P)

Arguments

A

Observed binary adjacency (matrix or vector).

P

Predicted probability (matrix or vector).

Value

Negative AUC value (for minimisation-based model selection).

Edge Cross-Validation for blockmodel selection

Description

Selects both the model type (SBM vs DCBM) and number of communities by holding out random edges and evaluating predictive performance.

Usage

ECV.for.blockmodel(
  A,
  max.K,
  cv = NULL,
  B = 3,
  holdout.p = 0.1,
  tau = 0,
  dc.est = 2,
  kappa = NULL
)

Arguments

A

Adjacency matrix (n x n).

max.K

Maximum number of communities to consider.

cv

Number of cross-validation folds (NULL for holdout; default NULL).

B

Number of holdout repetitions (default 3).

holdout.p

Fraction of edges held out (default 0.1).

tau

Regularisation parameter (default 0).

dc.est

DCBM estimation type (1 or 2; default 2).

kappa

Truncation parameter (default NULL).

Details

The algorithm is based on foundation code from Lin Zhang's PhD dissertation in 2019.

Value

A list with loss vectors and selected model strings:

l2

SBM L2 losses by K.

dev

SBM deviance losses by K.

auc

SBM AUC losses by K.

dc.l2, dc.dev, dc.auc

DCBM losses.

l2.model, dev.model, auc.model

Selected model strings.

Edge Cross-Validation for RDPG rank selection

Description

Selects the embedding rank for an RDPG by holding out random edges.

Usage

ECV.undirected.Rank(
  A,
  max.K,
  B = 3,
  holdout.p = 0.1,
  soft = FALSE,
  fast = FALSE
)

Arguments

A

Adjacency matrix.

max.K

Maximum rank to consider.

B

Number of holdout repetitions (default 3).

holdout.p

Fraction of edges held out (default 0.1).

soft

Logical (default FALSE).

fast

Logical (default FALSE).

Details

The algorithm is based on foundation code from Lin Zhang's PhD dissertation.

Value

A list with:

rank.sse, rank.dev, rank.auc

Selected ranks by each loss.

sse, dev, auc

Average loss vectors.

Node Cross-Validation for blockmodel selection

Description

Selects both the model type (SBM vs DCBM) and number of communities by holding out random nodes and evaluating predictive performance on the held-out subgraph.

Usage

NCV.for.blockmodel(A, max.K, cv = 3, dc.est = 1)

Arguments

A

Adjacency matrix (n x n).

max.K

Maximum number of communities to consider.

cv

Number of node folds (default 3).

dc.est

DCBM estimation type (1 or 2; default 1).

Value

A list with:

dev, l2, auc

SBM loss vectors by K.

dc.dev, dc.l2, dc.auc

DCBM loss vectors by K.

l2.model, dev.model, auc.model

Selected model strings.

Estimate SBM connection probabilities and negative log-likelihood

Description

Given a clustering and adjacency matrix, estimates the block probability matrix and computes the negative log-likelihood.

Usage

SBM.prob(cluster, k, A, restricted = TRUE)

Arguments

cluster

Integer vector of cluster labels.

k

Number of clusters.

A

Adjacency matrix corresponding to the nodes in cluster.

restricted

Logical. If TRUE, uses a restricted SBM with a single within-community probability p and a single between-community probability q. If FALSE, estimates a separate probability for each pair of communities.

Value

A list with:

p.matrix

k x k estimated block probability matrix.

negloglike

Negative log-likelihood of the model.

Spectral clustering for a Stochastic Block Model

Description

Performs spectral clustering on an adjacency matrix by computing the top k singular vectors and applying k-means++ via ClusterR::KMeans_rcpp.

Usage

SBM.spectral.clustering(A, k = 2)

Arguments

A

Symmetric adjacency matrix (n x n, binary or weighted).

k

Number of clusters (default 2).

Value

A list with component cluster, an integer vector of length n.

Examples

net <- community.sim(k = 3, n = 90, n1 = 30, p = 0.5, q = 0.1)
cl <- SBM.spectral.clustering(net$adjacency, k = 3)
table(cl$cluster, net$membership)

AUC via Wilcoxon statistic

Description

AUC via Wilcoxon statistic

Usage

auroc(score, bool)

Arguments

score

Numeric prediction scores.

bool

Logical/binary label vector.

Value

AUC value.

Find the best permutation label matching

Description

Matches community labels in lab to reference labels in fixed via a greedy maximum-overlap permutation.

Usage

best.perm.label.match(lab, fixed, n = length(lab), K = max(lab, fixed))

Arguments

lab

Integer vector of labels to permute.

fixed

Integer vector of reference labels.

n

Number of nodes (default length(lab)).

K

Number of communities (default max(lab, fixed)).

Value

A K x K permutation matrix.

Binomial deviance loss

Description

Binomial deviance loss

Usage

bin.dev(x, y)

Arguments

x

Observed binary matrix/vector.

y

Predicted probability matrix/vector.

Value

Total binomial deviance (non-finite terms set to 0).

Generate a fast SBM or DCBM network (sparse)

Description

Uses parallel edge sampling for speed; returns a sparse adjacency matrix.

Usage

blockmodel.gen.fast(n, K, B, psi = rep(1, n), PI = rep(1/K, K), ncore = 1)

Arguments

n

Number of nodes.

K

Number of communities.

B

K x K block probability matrix.

psi

Degree heterogeneity vector (length n); set to all 1s for SBM.

PI

Community prior probabilities (length K).

ncore

Number of cores for parallel computation.

Value

A list with:

A

Sparse symmetric adjacency matrix.

member

Community membership vector.

psi

Scaled degree heterogeneity vector.

Simulate a Stochastic Block Model network

Description

Generates an adjacency matrix from a planted-partition SBM with k communities. The first community has size n1; the remaining communities share the leftover nodes roughly equally.

Usage

community.sim(k = 2, n = 1000, n1 = 100, p = 0.3, q = 0.1)

Arguments

k

Number of communities (default 2).

n

Total number of nodes (default 1000).

n1

Size of the smallest community (default 100).

p

Within-community connection probability (default 0.3).

q

Between-community connection probability (default 0.1).

Value

A list with:

membership

Integer vector of community labels (length n).

adjacency

n x n binary symmetric adjacency matrix.

Examples

net <- community.sim(k = 3, n = 120, n1 = 30, p = 0.5, q = 0.1)
table(net$membership)

Simulate an SBM with distance-decaying block probabilities

Description

Generates an SBM where block probabilities decay exponentially with the distance between community indices: B[k1,k2] = rho * eta^min(|k1-k2|,3).

Usage

community.sim.sbm(n, n1, eta = 0.3, rho = 0.1, K = 3)

Arguments

n

Total number of nodes.

n1

Size of the first (smallest) community.

eta

Decay parameter for inter-community probabilities (default 0.3).

rho

Scaling factor for the block probability matrix (default 0.1).

K

Number of communities (default 3).

Value

A list with:

adjacency

n x n binary symmetric adjacency matrix.

membership

Integer vector of community labels.

conn

K x K block probability matrix.

CROISSANT for blockmodel selection

Description

Cross-validated, Overlapping, In-Sample Selection of the Number of communities and model Type. Jointly selects between SBM and DCBM and the number of communities K using overlapping node subsamples.

Usage

croissant.blockmodel(
  A,
  K.CAND,
  s,
  o,
  R,
  tau = 0,
  laplace = FALSE,
  dc.est = 2,
  loss = c("l2", "bin.dev", "AUC"),
  ncore = 1
)

Arguments

A

Adjacency matrix (n x n, can be sparse).

K.CAND

Candidate community numbers (integer vector, or a single integer interpreted as 1:K.CAND).

s

Number of non-overlapping subsamples.

o

Size of the overlapping set.

R

Number of independent repetitions.

tau

Regularisation parameter for the adjacency (default 0).

laplace

Logical; use graph Laplacian normalisation (default FALSE).

dc.est

DCBM estimation method: 1 = eigenvector, 2 = fast (default 2).

loss

Character vector of loss functions to evaluate. Supported: "l2", "bin.dev", "AUC".

ncore

Number of cores for parallel computation.

Value

A list containing:

loss

data.table of loss values by candidate model and K.

Candidate Models

"SBM and DCBM".

Candidate Values

The candidate K vector.

*.model

Selected model string (e.g. "SBM-3") for each loss.

CROISSANT for latent space model dimension selection

Description

Selects the latent dimension for a latent space network model using the CROISSANT framework with MLE fitting.

Usage

croissant.latent(
  A,
  d.cand,
  s,
  o,
  R,
  loss = c("l2", "bin.dev", "AUC"),
  ncore = 1
)

Arguments

A

Adjacency matrix.

d.cand

Candidate embedding ranks.

s

Number of non-overlapping subsamples.

o

Overlap size.

R

Number of repetitions.

loss

Loss functions to evaluate.

ncore

Number of cores.

Value

A list with loss table and selected dimension per loss.

CROISSANT for RDPG rank selection

Description

Selects the embedding rank for a Random Dot Product Graph model using the CROISSANT overlapping node-subsample framework.

Usage

croissant.rdpg(
  A,
  d.cand,
  s,
  o,
  R,
  laplace = FALSE,
  loss = c("l2", "bin.dev", "AUC"),
  ncore = 1
)

Arguments

A

Adjacency matrix.

d.cand

Candidate embedding ranks.

s

Number of non-overlapping subsamples.

o

Overlap size.

R

Number of repetitions.

laplace

Use Laplacian normalisation (default FALSE).

loss

Loss functions to evaluate.

ncore

Number of cores.

Value

A list with loss table and selected rank per loss.

CROISSANT for regularisation parameter tuning in spectral methods

Description

Selects the regularisation parameter tau for spectral clustering using the CROISSANT framework.

Usage

croissant.tune.regsp(
  A,
  K,
  tau.cand,
  DCBM = FALSE,
  s,
  o,
  R,
  laplace = FALSE,
  dc.est = 2,
  loss = c("l2", "bin.dev", "AUC"),
  ncore = 1
)

Arguments

A

Adjacency matrix.

K

Fixed number of communities.

tau.cand

Candidate regularisation parameter values.

DCBM

Logical; if TRUE, use row-normalised eigenvectors (DCBM).

s, o, R

CROISSANT design parameters.

laplace

Use Laplacian normalisation.

dc.est

DCBM estimation type (1 or 2).

loss

Loss functions to evaluate.

ncore

Number of cores.

Value

A list with loss table and selected tau per loss.

Map a linear edge index to row-column indices in the upper triangle

Description

Given a linear index u over the upper triangle of a symmetric matrix (column-major order), returns the corresponding row (x) and column (y) indices. The mapping is independent of matrix size.

Usage

edge.index.map(u)

Arguments

u

Integer vector of linear edge indices (1-based).

Value

A list with components x (row indices) and y (column indices).

Examples

edge.index.map(1:6)

Eigenvector-based DCBM estimation

Description

Estimates DCBM parameters using the row-norms of the leading eigenvectors for degree heterogeneity.

Usage

eigen.DCBM.est(A, g, n = nrow(A), K = max(g), psi.omit = 0, p.sample = 1)

Arguments

A

Adjacency matrix.

g

Community label vector.

n

Number of nodes.

K

Number of communities.

psi.omit

Number of leading nodes to exclude from psi estimation (used in CROISSANT overlapping designs).

p.sample

Sampling proportion for correction (default 1).

Value

A list with Bsum and psi.

Fast DCBM parameter estimation

Description

Estimates the block sum matrix and degree heterogeneity parameters for a Degree-Corrected Block Model.

Usage

fast.DCBM.est(A, g, n = nrow(A), K = max(g), psi.omit = 0, p.sample = 1)

Arguments

A

Adjacency matrix.

g

Community label vector.

n

Number of nodes.

K

Number of communities.

psi.omit

Number of leading nodes to exclude from psi estimation (used in CROISSANT overlapping designs).

p.sample

Sampling proportion for correction (default 1).

Value

A list with:

Bsum

K x K block sum matrix (divided by p.sample).

psi

Degree heterogeneity vector.

Fast SBM block probability estimation

Description

Estimates the K x K block probability matrix from an adjacency matrix and community labels.

Usage

fast.SBM.est(A, g, n = nrow(A), K = max(g))

Arguments

A

Adjacency matrix (n x n).

g

Integer community label vector (length n).

n

Number of nodes.

K

Number of communities.

Value

K x K estimated block probability matrix.

L2 loss between two matrices

Description

L2 loss between two matrices

Usage

l2(x, y)

Arguments

x, y

Numeric matrices of the same dimension.

Value

The Frobenius norm sqrt(sum((x - y)^2)).

Generate a latent space network

Description

Generate a latent space network

Usage

latent.gen(n, d, alpha = 1, sparsity = 1, ncore = 1)

Arguments

n

Number of nodes.

d

Latent dimension.

alpha

Intercept parameter controlling overall density.

sparsity

Sparsity multiplier.

ncore

Number of cores for parallel computation.

Value

A list with:

A

Sparse symmetric adjacency matrix.

Z

n x d latent position matrix.

Apply label permutation to match reference

Description

Apply label permutation to match reference

Usage

matched.lab(lab, fixed, n = length(lab), K = max(lab, fixed))

Arguments

lab

Integer vector of labels to relabel.

fixed

Integer vector of reference labels.

n

Number of nodes.

K

Number of communities.

Value

Relabelled integer vector aligned to fixed.

Description

Find the mode of a vector

Usage

modal(x)

Arguments

x

A vector.

Value

The most frequent value.

Safe negative log-likelihood term

Description

Computes -n * log(p), returning 0 when p <= 0.

Usage

neglog(n = 1, p = 0.5)

Arguments

n

Numeric count.

p

Probability (between 0 and 1).

Value

Numeric value of -n * log(p) or 0 if p <= 0.

Inductive Node-Splitting Cross-Validation with f-fold splitting

Description

Performs f-fold node-split cross-validation to select the number of communities k in a Stochastic Block Model. Nodes are randomly partitioned into f folds; for each fold the held-out nodes are assigned to communities via the training-set spectral clustering, and the held-out negative log-likelihood and MSE are computed.

Usage

nscv.f.fold(
  A,
  k.vec = 2:6,
  restricted = TRUE,
  f = 10,
  method = "affinity",
  p.est.type = 3
)

Arguments

A

Symmetric adjacency matrix (n x n, binary).

k.vec

Integer vector of candidate community numbers (default 2:6).

restricted

Logical. If TRUE, use a restricted SBM (one within- and one between-community probability). Default TRUE.

f

Number of folds (default 10).

method

Inference method for assigning held-out nodes: "affinity" (default) assigns by maximum average connection, or "loss" assigns by minimum negative log-likelihood.

p.est.type

How to re-estimate the probability matrix for evaluation: 1 = training only, 2 = training + testing, 3 = testing only (default 3).

Value

A list with:

k.loss

Selected k that minimises CV negative log-likelihood.

k.mse

Selected k that minimises CV MSE.

cv.loss

Average CV negative log-likelihood for each k.

cv.mse

Average CV MSE for each k.

Examples

set.seed(42)
net <- community.sim(k = 3, n = 150, n1 = 50, p = 0.5, q = 0.1)
result <- nscv.f.fold(net$adjacency, k.vec = 2:5, f = 5)
result$k.loss

Inductive Node-Splitting Cross-Validation with random node splits

Description

Performs repeated random-split node-level cross-validation. At each iteration a random fraction split of nodes is used for training.

Usage

nscv.random.split(
  A,
  k.vec = 2:6,
  restricted = TRUE,
  split = 0.66,
  ite = 100,
  method = "affinity",
  p.est.type = 3
)

Arguments

A

Symmetric adjacency matrix (n x n, binary).

k.vec

Integer vector of candidate community numbers (default 2:6).

restricted

Logical. If TRUE, use a restricted SBM (one within- and one between-community probability). Default TRUE.

split

Fraction of nodes used for training (default 0.66).

ite

Number of random split iterations (default 100).

method

Inference method for assigning held-out nodes: "affinity" (default) assigns by maximum average connection, or "loss" assigns by minimum negative log-likelihood.

p.est.type

How to re-estimate the probability matrix for evaluation: 1 = training only, 2 = training + testing, 3 = testing only (default 3).

Value

A list with:

k.chosen

Selected k minimising average CV loss.

k.choice

The candidate k.vec.

cv.loss

Average CV negative log-likelihood for each k.

Generate a sparse RDPG network

Description

Generate a sparse RDPG network

Usage

sparse.RDPG.gen(n, d, sparsity.multiplier = 1, ncore = 1)

Arguments

n

Number of nodes.

d

Latent dimension.

sparsity.multiplier

Multiplier to control network density.

ncore

Number of cores for parallel computation.

Value

A list with:

A

Sparse symmetric adjacency matrix.

P

n x n probability matrix.

Fast sum of matrix or vector elements

Description

Fast sum of matrix or vector elements

Usage

sumFast(X)

Arguments

X

A matrix or vector.

Value

The total sum of all elements.