| Title: | Multi-Layer Networks Analysis |
| Version: | 0.1 |
| Description: | Provides two general frameworks to generate a multi-layer network. This also provides several methods to reveal the embedding of both nodes and layers. The reference paper can be found from the URL mentioned below. Ting Li, Zhongyuan Lyu, Chenyu Ren, Dong Xia (2023) <doi:10.48550/arXiv.2302.04437>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| Imports: | dbscan, geigen, glmnet, graphics, Matrix, plotly, rTensor, stats |
| NeedsCompilation: | no |
| Packaged: | 2023-06-26 02:31:21 UTC; Ren Chenyu |
| Author: | Chenyu Ren  [aut,
cre] |
| Maintainer: | Chenyu Ren <chenyu.ren@connect.polyu.hk> |
| Repository: | CRAN |
| Date/Publication: | 2023-06-27 16:30:02 UTC |
Title
Description
Title
Usage
Community_cluster_dbscan(embedding, type, eps_value = 0.05, pts_value = 5)
Arguments
embedding |
the embedding results from different methods |
type |
node embedding ‘n’ or network embedding ‘N’ |
eps_value |
parameters for DBSCAN |
pts_value |
parameters for DBSCAN |
Value
the embedding results
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
U_list = InitializationMMSBM(tnsr, 3, 2, rank = NULL)
embed_list = PowerIteration(tnsr,3,2,rank=NULL,type="TUCKER",U_0_list=U_list)
em = embed_list[[2]]
Community_cluster_dbscan(em,"N")
Title
Description
Title
Usage
Community_cluster_km(embedding, type, cluster_number)
Arguments
embedding |
the embedding results from different methods |
type |
node embedding ‘n’ or network embedding ‘N’ |
cluster_number |
the number of clusters for Kmeans |
Value
the embedding results
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
U_list = InitializationMMSBM(tnsr, 3, 2, rank = NULL)
embed_list = PowerIteration(tnsr,3,2,rank=NULL,type="TUCKER",U_0_list=U_list)
em = embed_list[[2]]
Community_cluster_km(em,"N",5)
Title
Description
Title
Usage
Embedding_network(network_membership, L, paxis = 2)
Arguments
network_membership |
the number of types of the network or the number of groups of vertices |
L |
the number of layers |
paxis |
the number of eigenvectors to use in the plot |
Value
a plot table If the number of eigenvectors is more than two or plot the image
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
U_list = InitializationMMSBM(tnsr, 3, 2, rank = NULL)
embed_list = PowerIteration(tnsr,3,2,rank=NULL,type="TUCKER",U_0_list=U_list)
Embedding_network(embed_list[[2]],10,2)
Title
Description
Title
Usage
GenerateMMLSM(
n,
m,
L,
rank,
U_mean = 0.5,
cmax = 1,
d,
int_type = "Uniform",
kernel_fun = "logit",
scale_par = 1
)
Arguments
n |
the number of vertices |
m |
the number of types of the network |
L |
the number of layers |
rank |
the rank of latent position matrix U |
U_mean |
the mean of the normal distribution of each entry of U |
cmax |
the entrywise upper bound of core tensor C |
d |
the average degree of the network |
int_type |
represents the ways of generating tensor C (‘Uniform’ or ‘Norm’) |
kernel_fun |
the link function of generating the adjacency tensor (‘logit’ or ‘probit’ ) |
scale_par |
the scaling factor of the parameter tensor |
Value
a list including an adjacency tensor and the generating parameters
Examples
GenerateMMLSM(200,3,10,2,d=NULL)
Title
Description
Title
Usage
GenerateMMSBM(n, m, L, K, d = NULL, r = NULL)
Arguments
n |
the number of vertices |
m |
the number of types of the network |
L |
the number of layers |
K |
the number of groups of vertices |
d |
the average degree of the network |
r |
the out-in ratio in each layer |
Value
a list including an adjacency tensor and the generating parameters
Examples
GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
Title
Description
Title
Usage
InitializationLSM(
gen_list,
n,
m,
k,
rank = NULL,
perturb = 0.1,
int_type = "warm"
)
Arguments
gen_list |
a list including the adjacency tensor and the parameter of the mixture multilayer network |
n |
the number of nodes |
m |
the number of network types |
k |
the number of groups of vertices |
rank |
rank of U |
perturb |
the upper bound of Uniform distribution |
int_type |
the method to initialize U and W ( ‘spec’, ‘rand’ or ‘warm’) |
Value
a list including the adjacency tensor, U0, W0 and tuning parameters
Examples
gen_list = GenerateMMLSM(200,3,10,2,d=NULL)
InitializationLSM(gen_list,200,3,2)
Title A function for initialization
Description
Title A function for initialization
Usage
InitializationMMSBM(tnsr, m, k, rank = NULL)
Arguments
tnsr |
the tensor of network |
m |
the number of types of the network |
k |
the number of groups of vertices |
rank |
the rank of the core tensor calculated by the equation |
Value
U_list a list including the core tensor Z, network embedding and node embedding
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
U_list = InitializationMMSBM(tnsr, 3, 2, rank = NULL)
Title
Description
Title
Usage
PowerIteration(
tnsr,
m,
k,
rank = NULL,
type = "TWIST",
U_0_list,
delta1 = 1000,
delta2 = 1000,
max_iter = 5,
tol = 1e-05
)
Arguments
tnsr |
the adjacency tensor of the network |
m |
the number of types of the network |
k |
the number of groups of vertices |
rank |
the rank of the core tensor calculated by the equation |
type |
specifies the iterative algorithm to run ‘TWIST’ or ‘Tucker’ |
U_0_list |
InitializationMMSBM outputs |
delta1 |
tuning parameters for regularization in mode1 |
delta2 |
tuning parameters for regularization in mode2 |
max_iter |
the max times of iteration |
tol |
the convergence tolerance |
Value
a list including the core tensor Z, network embedding and node embedding
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
U_list = InitializationMMSBM(tnsr, 3, 2, rank = NULL)
embed_list = PowerIteration(tnsr,3,2,rank=NULL,type="TUCKER",U_0_list=U_list)
Title
Description
Title
Usage
ProjectedGD(
Ini_list,
cmax = 1,
eta_outer = 0.001,
tmax_outer = 10,
p_type = "logit",
rd = "Non",
show = TRUE,
sgma = 1,
sample_size = 500
)
Arguments
Ini_list |
the output of function InitializationLSM |
cmax |
the upper limits for adding the coefficient constraint |
eta_outer |
the learning rate in gradient descent |
tmax_outer |
the number of iterations in gradient descent |
p_type |
the type of link function (‘logit’, ‘probit’ or ‘poisson’ ) |
rd |
whether to use stochastic sampling (‘rand’ or ‘Non’ ) |
show |
if print the ietation process |
sgma |
the link function parameter |
sample_size |
the size of sampling |
Value
the embedding results of nodes and layers
Examples
gen_list = GenerateMMLSM(200,3,5,2,d=NULL)
Ini_list = InitializationLSM(gen_list,200,3,2)
Title
Description
Title
Usage
SpecClustering(tnsr, rank, embedding_type = "Layer")
Arguments
tnsr |
the adjacency tensor |
rank |
the number of columns of the output matrix U |
embedding_type |
SumAdj for ‘Node’ and M3SC for ‘Layer’ |
Value
The embeddding result can be applied in cluster methods like kmeans.
Examples
tnsr = GenerateMMSBM(200, 3, 10, 2, d = NULL, r = NULL)
emb_result = SpecClustering(tnsr,3)