| Title: | Variational Bayes Latent Position Cluster Model for Networks |
|---|---|
| Description: | Fit and simulate latent position and cluster models for network data, using a fast Variational Bayes approximation developed in Salter-Townshend and Murphy (2013) <doi:10.1016/j.csda.2012.08.004>. |
| Authors: | Michael Salter-Townshend |
| Maintainer: | Michael Salter-Townshend <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.4.9 |
| Built: | 2024-11-20 06:47:06 UTC |
| Source: | CRAN |
A faster approximate alternative to using latentnet. Interfaces C code to fit a Variational Bayes approximation to the posterior for the Latent Position Cluster Model for networks.
| Package: | VBLPCM |
| Type: | Package |
| Version: | 2.4.9 |
| Date: | 2023-03-22 |
| License: | GPL (>=2) |
| LazyLoad: | yes |
This package is designed to be used as an alternative to the latentnet package when network size computationally prohibits latentnet. It uses a Variational Bayesian Expectation Maximisation algorithm to compute a closed-form approximation to the posterior that the ergmm function in latentnet samples from. It may be thought of as an intermediary approximation that is more accurate than the two-stage MLE fit provided by latentnet but a faster approximation to the MCMC sampler provided by latentnet. In fact, the VB iterations also converge quicker than the two-stage MLE.
VBLPCM can also take advantage of the stratified sampler of Adrian Raftery, Xiaoyue Niu, Peter Hoff and Ka Yee Yeung. This approximation to the (log)likelihood allows for even larger networks to be analysed (see tech report below). Rather than using a fixed number of "controls" per geodesic distance we set a probability of sampling each non-link at each level.
We also provide four choices of model; these are "plain" and three with random node-specific social effects. "rsender" for sender random effects, "rreceiver" for receiver random effects and "rsocial" for both. For undirected networks only "plain" or "rsocial" may be chosen.
Michael Salter-Townshend and Thomas Brendan Murphy (2013). "Variational Bayesian Inference for the Latent Position Cluster Model." Computational Statistics and Data Analysis, volume 57, number 1, pages 661-671. DOI=10.1016/j.csda.2012.08.004
Pavel N. Krivitsky and Mark S. Handcock (2008). "Fitting Latent Cluster Models for Social Networks with latentnet." Journal of Statistical Software, number 5, volume 24, pages 1-23.
Mark S. Handcock, Adrian E. Raftery and Jeremy Tantrum (2007). "Model-Based Clustering for Social Networks." Journal of the Royal Statistical Society: Series A (Statistics in Society), 170(2), 301-354.
Adrian Raftery, Xiaoyue Niu, Peter Hoff and Ka Yee Yeung (2012). "Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood." Journal of Computational and Graphical Statistics. doi: 10.1080/10618600.2012.679240
Sucharita Gopal (2007). "The Evolving Social Geography of Blogs" Societies and Cities in the Age of Instant Access Berlin:Springer, 275–294
### Sampson's monks with sender random effects ### data(sampson,package="VBLPCM") v.start<-vblpcmstart(samplike,G=3,model="rreceiver",LSTEPS=1e3) v.fit<-vblpcmfit(v.start,STEPS=20) ### plot the mean posterior positions ### plot(v.fit, R2=0.05,main="Sampson's Monks: VB with Receiver Random Effects") ### Who's in each group? ### vblpcmgroups(v.fit) ### Look at a goodness-of-fit plot ### plot(gof(v.fit,GOF=~distance)) ### create a matrix of link posterior probabilities given the fitted model ### probs<-predict.vblpcm(v.fit) ### create a boxplot goodness-of-fit graphic ### boxplot(split(probs,as.sociomatrix(samplike))) ### run a bigger example, using the likelihood sampler set to 0.1 ### ## Not run: data(aids,package="VBLPCM") v.start<-vblpcmstart(aids.net,G=7,model="rsender",d=3) use the case-control sampler with 10 controls per case v.fit<-vblpcmfit(v.start,NC=10) plot the mean posterior positions ### plot(v.fit, R2=0.1,main="Aids Blogs with Sender Random Effects") ### Use ROC / AUC to get a measure of model fit to the data ### vblpcmroc(v.fit) ## End(Not run)### Sampson's monks with sender random effects ### data(sampson,package="VBLPCM") v.start<-vblpcmstart(samplike,G=3,model="rreceiver",LSTEPS=1e3) v.fit<-vblpcmfit(v.start,STEPS=20) ### plot the mean posterior positions ### plot(v.fit, R2=0.05,main="Sampson's Monks: VB with Receiver Random Effects") ### Who's in each group? ### vblpcmgroups(v.fit) ### Look at a goodness-of-fit plot ### plot(gof(v.fit,GOF=~distance)) ### create a matrix of link posterior probabilities given the fitted model ### probs<-predict.vblpcm(v.fit) ### create a boxplot goodness-of-fit graphic ### boxplot(split(probs,as.sociomatrix(samplike))) ### run a bigger example, using the likelihood sampler set to 0.1 ### ## Not run: data(aids,package="VBLPCM") v.start<-vblpcmstart(aids.net,G=7,model="rsender",d=3) use the case-control sampler with 10 controls per case v.fit<-vblpcmfit(v.start,NC=10) plot the mean posterior positions ### plot(v.fit, R2=0.1,main="Aids Blogs with Sender Random Effects") ### Use ROC / AUC to get a measure of model fit to the data ### vblpcmroc(v.fit) ## End(Not run)
Network of citations among blogs related to AIDS, patients, and their support networks, collected by Gopal, over a three-day period in August 2005. A directed graph representing the pattern of citation among 146 unique blogs related to AIDS, patients, and their support networks, collected by Gopal over a randomly selected three-day period in August 2005. Vertices correspond to blogs. A directed edge from one blog to another indicates that the former had a link to the latter in their web page (more specifically, the former refers to the latter in their so-called 'blogroll').
data(aids)data(aids)
http://math.bu.edu/people/kolaczyk/datasets/AIDSBlog.zip
S. Gopal, "The evolving social geography of blogs," in Societies and CIties in the Age of Instant Access, H. Miller, Ed. Berlin:Springer, 2007, pp. 275-294
network, plot.network, VBLPCM
uses a call to C to transform edgelist to adjacency matrix.
E_to_Y(N, NE, directed, E)E_to_Y(N, NE, directed, E)
N |
number of nodes |
NE |
number of edges |
directed |
logical indicator of directedness (TRUE=>directed, FALSE=>undirected |
E |
the input edgelist |
NxN sociomatrix / adjacency matrix
Michael Salter-Townshend
sociomatrix, Y_to_E
This was written and incorporated into the VBLPCM package because the Fruchterman-Reingold routine in the network package only works in two dimensions.
fruchterman_reingold(net, D=2, steps=1000, repulserad=N^D, m=N*(D-1), volume=N*(D-1))fruchterman_reingold(net, D=2, steps=1000, repulserad=N^D, m=N*(D-1), volume=N*(D-1))
net |
network object on which to perform Fruchterman-Reingold layout. |
D |
Desired dimension of the space in which to lay out the network. |
steps |
Number of desired iterations. |
repulserad |
The radius at which repulsion and attraction of linked nodes are equal. |
m |
The maximum change in position per iteration. |
volume |
The volume of space within which to position the nodes. |
An N*D matrix of coordinates.
Michael Salter-Townshend
log_like_forces
### 2D example ### load the aids blogs dataset data(aids) ### perform the Fruchterman-Reingold layout X<-fruchterman_reingold(aids.net, D=2, steps=1e3) ### plot the results plot(X) ### 3D example ### load the aids blogs dataset data(aids) ### perform the Fruchterman-Reingold layout X<-fruchterman_reingold(aids.net, D=3, steps=1e3) ### Not run ### plot the results in 3D # library(rgl) # plot3d(X)### 2D example ### load the aids blogs dataset data(aids) ### perform the Fruchterman-Reingold layout X<-fruchterman_reingold(aids.net, D=2, steps=1e3) ### plot the results plot(X) ### 3D example ### load the aids blogs dataset data(aids) ### perform the Fruchterman-Reingold layout X<-fruchterman_reingold(aids.net, D=3, steps=1e3) ### Not run ### plot the results in 3D # library(rgl) # plot3d(X)
Create a goodness of fit statistics and plots based on the degree distributions of networks simulated fitted from a fitted variational approximation.
## S3 method for class 'vblpcm' gof(object, ..., nsim=100, GOF=NULL, verbose=FALSE)## S3 method for class 'vblpcm' gof(object, ..., nsim=100, GOF=NULL, verbose=FALSE)
object |
fitted VBLPCM object; usually output from vblpcmfit() or vblpcmstart() |
... |
optional arguments for lower level functions |
nsim |
number of networks to simulate |
GOF |
formula; an R formula object, of the form
|
verbose |
Provide verbose information on the progress of the simulation. |
A sample of graphs is randomly drawn from the posterior of the vblpcmfit() result.
A plot of the summary measures may then be plotted using plot().
Michael Salter-Townshend
latentnet::gof.ergmm
data(sampson,package="VBLPCM") v.start<-vblpcmstart(samplike,G=3,model="rreceiver",LSTEPS=1e3) v.fit<-vblpcmfit(v.start,STEPS=20) ### plot the mean posterior positions plot(v.fit, R2=0.05,main="Sampson's Monks: VB with Receiver Effects") ### Look at gof plots plot(gof(v.fit,GOF=~distance,nsim=50))data(sampson,package="VBLPCM") v.start<-vblpcmstart(samplike,G=3,model="rreceiver",LSTEPS=1e3) v.fit<-vblpcmfit(v.start,STEPS=20) ### plot the mean posterior positions plot(v.fit, R2=0.05,main="Sampson's Monks: VB with Receiver Effects") ### Look at gof plots plot(gof(v.fit,GOF=~distance,nsim=50))
Designed for nternal use only; store the geodesic distances in a handy format Each node gets a vector in the hopslist matrix. Each row describes a node and for each row: The first diam entries state the number of nodes that are that distance away by shortest path where diam is the maximum shortest path between two nodes (the graph diameter). eg if entry 3 in row 4 is a 5 then there are exactly 5 nodes that are 4 hops away from node 3. This vector is followed by the indices of all the nodes, grouped by the length of the shortest paths.
hops_to_hopslist(hops, diam, N)hops_to_hopslist(hops, diam, N)
hops |
matrix of geodesic distances |
diam |
diameter of the network |
N |
total number of nodes in the network |
Michael Salter-Townshend
This performs an iterative relaxation type algorithm to approximately find the positions of the nodes in the latent space that maximises the log-likelihood.
log_like_forces(net, D, X, B, m ,steps)log_like_forces(net, D, X, B, m ,steps)
net |
network object on which to perform layout. |
D |
dimension of the latent space. |
X |
the initial guess for X |
B |
the intercept term. |
m |
usually N will suffice. |
steps |
maximum number of iteration steps. |
Usually only used internally in vblpcmstart()
Matrix of latent positions X
Michael Salter-Townshend
igraph::layout.fruchterman.reingold
data(sampson) N=network.size(samplike) X=matrix(runif(N*2,-2,2),ncol=2) XX=vblpcmcovs(N,"plain",as.sociomatrix(samplike)) out<-log_like_forces(samplike, 2, X, 0, m=N, 1e3) plot(samplike,coord=out$X)data(sampson) N=network.size(samplike) X=matrix(runif(N*2,-2,2),ncol=2) XX=vblpcmcovs(N,"plain",as.sociomatrix(samplike)) out<-log_like_forces(samplike, 2, X, 0, m=N, 1e3) plot(samplike,coord=out$X)
Plot the network using the estimated positions with clustering. The nodes are plotted as pie-charts to show group membership probabilities. The group means are coloured crosses and the group standard deviations are shown with coloured circles.
## S3 method for class 'vblpcm' plot(x, ..., R2 = 0.2, main = "Variational-Bayes Positions", alpha = 0.5, colours=1:x$G, RET=FALSE)## S3 method for class 'vblpcm' plot(x, ..., R2 = 0.2, main = "Variational-Bayes Positions", alpha = 0.5, colours=1:x$G, RET=FALSE)
x |
The fitted values; output from vblpcmfit() |
... |
optional arguments to be passed to lower level functions |
R2 |
scaling factor for the size of each node in the plot |
main |
main title for the plot |
alpha |
transparency of the links |
colours |
colours of the groups |
RET |
whether to return the 2D postions of nodes and clusters |
Plots the latent positions and clustering of a network fitted via vblpcmfit() or vblpcmstart()
Each node appears in the latent space as a pie chart with segments size proportional to group memberships. The clusters are represented as circles in the latent space centred on the expected position of the group mean and with size proportional to the cluster standard deviation.
If applicable, the size of the pie charts represents the expected sociality effect of the node.
Michael Salter-Townshend
latentnet::plot.ergmm
generate a matrix of link probabilities based on the fitted VB model.
## S3 method for class 'vblpcm' predict(object, ...)## S3 method for class 'vblpcm' predict(object, ...)
object |
The fitted values; output from vblpcmfit() |
... |
optional additional arguments. |
The posterior predictive link probabilities given the fitted object
Michael Salter-Townshend
data(sampson) v.fit<-vblpcmfit(vblpcmstart(samplike,G=3)) ### create a matrix of link posterior probabilities given the fitted model probs<-predict.vblpcm(v.fit) # show this graphically; separation of the boxes implies a good fit to the data boxplot(split(probs,v.fit$Y), ylab=expression(paste("P(",Y[i][j],"=1)")),xlab=expression(paste(Y[i][j])))data(sampson) v.fit<-vblpcmfit(vblpcmstart(samplike,G=3)) ### create a matrix of link posterior probabilities given the fitted model probs<-predict.vblpcm(v.fit) # show this graphically; separation of the boxes implies a good fit to the data boxplot(split(probs,v.fit$Y), ylab=expression(paste("P(",Y[i][j],"=1)")),xlab=expression(paste(Y[i][j])))
Print a vblpcm object.
## S3 method for class 'vblpcm' print(x, ...)## S3 method for class 'vblpcm' print(x, ...)
x |
The fitted values; output from vblpcmfit() |
... |
optional arguments to be passed to lower level functions |
Michael Salter-Townshend
latentnet::print.ergmm
Sampson (1969) recorded the social interactions among a group of monks while resident as an experimenter on vision, and collected numerous sociometric rankings. During his stay, a political “crisis in the cloister” resulted in the expulsion of four monks (Nos. 2, 3, 17, and 18) and the voluntary departure of several others - most immediately, Nos. 1, 7, 14, 15, and 16. (In the end, only 5, 6, 9, and 11 remained). Of particular interest is the data on positive affect relations (“liking”), in which each monk was asked if they had positive relations to each of the other monks.
The data were gathered at three times to capture changes in group sentiment over time. They were represent three time points in the period during which a new cohort entered the monastery near the end of the study but before the major conflict began.
Each member ranked only his top three choices on “liking”. (Some subjects offered tied ranks for their top four choices). A tie from monk A to monk B exists if A nominated B as one of his three best friends at that that time point.
samplike is the time-aggregated network.
It is the cumulative tie for “liking” over the three
periods. For this, a tie from monk A to monk B exists if A
nominated B as one of his three best friends at any of the
three time points.
This data is standard in the social network analysis literature, having been modeled by Holland and Leinhardt (1981), Reitz (1982), Holland, Laskey and Leinhardt (1983), and Fienberg, Meyer, and Wasserman (1981), Hoff, Raftery, and Handcock (2002), etc. This is only a small piece of the data collected by Sampson.
data(sampson)data(sampson)
Sampson, S.~F. (1968), A novitiate in a period of change: An experimental and case study of relationships, Unpublished ph.d. dissertation, Department of Sociology, Cornell University.
White, H.C., Boorman, S.A. and Breiger, R.L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81(4), 730-780.
network, plot.network, ergmm
data(sampson) plot(samplike)data(sampson) plot(samplike)
adjacency matrix simulated from the latent position cluster model with 3 well separated groups
data(simulated.network)data(simulated.network)
Michael Salter-Townshend
network, plot.network, VBLPCM
Summarise the output of a call to either vblpcmstart or vblpcmfit.
## S3 method for class 'vblpcm' summary(object, ...)## S3 method for class 'vblpcm' summary(object, ...)
object |
The fitted values; output from vblpcmstart() or vblpcmfit() |
... |
optional arguments to be passed to lower level functions |
Michael Salter-Townshend
latentnet::summary.ergmm
calculate the BIC for the fitted VBLPCM object
vblpcmbic(v.params)vblpcmbic(v.params)
v.params |
The fitted values; output from vblpcmfit() |
BIC = BIC(edges | positions) + BIC(positions | clusters) w/ BIC(edges | positions) = -2 loglikelihood + (P+1)log(number of edges) and BIC(positions | clusters) as per mclust
The scalar value of the BIC
Michael Salter-Townshend
Mark S. Handcock, Adrian E. Raftery and Jeremy Tantrum (2007). "Model-Based Clustering for Social Networks." Journal of the Royal Statistical Society: Series A (Statistics in Society), 170(2), 301-354.
latentnet::summary.ergmm
data(sampson) set.seed(1) ### plot the BIC for G=2,3,4 groups gbic<-list(groups=NULL,bic=NULL) for (g in 2:4) { v.fit<-vblpcmfit(vblpcmstart(samplike,G=g,LSTEPS=1e3),STEPS=20) gbic$groups[g]=v.fit$G gbic$bic[g]=v.fit$BIC$overall } plot(gbic$groups, gbic$bic, main="BIC results", xlab="# groups", ylab="BIC", t='b')data(sampson) set.seed(1) ### plot the BIC for G=2,3,4 groups gbic<-list(groups=NULL,bic=NULL) for (g in 2:4) { v.fit<-vblpcmfit(vblpcmstart(samplike,G=g,LSTEPS=1e3),STEPS=20) gbic$groups[g]=v.fit$G gbic$bic[g]=v.fit$BIC$overall } plot(gbic$groups, gbic$bic, main="BIC results", xlab="# groups", ylab="BIC", t='b')
Add intercept (column of ones) and degree-based covariates (if model is for sociality effects) to a user-supplied (default is NULL) edge covariates matrix of size N^2 rows and C columns where C is the number of covariates. Node covariates may be converted to difference-between-pairs for edges.
vblpcmcovs(N, model, Y, edgecovs=NULL, sendcovs=NULL, receivecovs=NULL, socialcovs=NULL)vblpcmcovs(N, model, Y, edgecovs=NULL, sendcovs=NULL, receivecovs=NULL, socialcovs=NULL)
N |
number of nodes |
model |
model; may be "plain", "rreceiver", "rsender" or "rsocial". See Details. |
Y |
adjacency matrix |
edgecovs |
optional additional covariate / attribute data on the edges |
sendcovs |
optional additional covariate / attribute data on the nodes for links out |
receivecovs |
optional additional covariate / attribute data on the nodes for links in |
socialcovs |
optional additional covariate / attribute data on the nodes for links in and out |
Can be used to construct design matrices with edge covariates or node covariates and / or sociality effects. "rreceiver", "rsender" and "rsocial" model random social effects. Node covariates are differenced and treated as edge covariates.
An edge design matrix that is Pe x N^2 and a node design matrix that is Pn x N where Pe is the number of edge covariates and Pn is the number of node covariates.
Michael Salter-Townshend
vblpcmstart
add a piechart of group memberships of a node to a network plot; taken mainly from latentnet equivalent
vblpcmdrawpie(center,radius,probs,n=50,colours=1:length(probs))vblpcmdrawpie(center,radius,probs,n=50,colours=1:length(probs))
center |
where to postion the piechart |
radius |
radius of the piechart / node |
probs |
probability vector of cluster memberships |
n |
order of polygon to approximate a circle |
colours |
the colours used; default is from palette() |
Thanks to Pavel N. Krivitsky of the latentnet package as I copied this from there.
Michael Salter-Townshend
plot.vblpcm
Perform optimisation of the variational parameters of the variational approximation to the posterior for the latent position cluster model for network data.
vblpcmfit(variational.start, STEPS = 50, maxiter = 100, tol=1e-6, NC=NULL, seed=NaN, d_vector=rep(TRUE,9))vblpcmfit(variational.start, STEPS = 50, maxiter = 100, tol=1e-6, NC=NULL, seed=NaN, d_vector=rep(TRUE,9))
variational.start |
The starting configuration; use vblpcmstart() to generate this. |
STEPS |
Maximum number of iterations in the main VBEM loop. |
maxiter |
Maximum number of iterations for the internal univariate optimisation loops. |
tol |
tolerance of change in variational parameter updates below which the algorithm is deemed to have converged for that parameter. |
NC |
Number of non-links sampled in the case-control type sampler. Results in a speedup but loss of accuracy. |
seed |
Optional seed for the random number generator. Supplying NaN is equivalent to not supplying it. Supply a value so that results may be replicated. |
d_vector |
Optional logical vector specifying which sets of variational parameters are to be updated. See Details for more information. |
d_vector is a logical vector of length 9 that can be used to select which variational parameters are held fixed and which are updated. The parameters are in the following order: z (latent positions), sigma2 (variance of latent positions), lambda (membership probability matrix), eta (cluster centres), omega2 (cluster variances), alpha (cluster specific variance of nodes), nu (Dirichlet parameter for marginal cluster probabilities), xi (likelihood intercept term mean), psi2 (likelihood intercept term variance).
A v.params list containing the fitted variational parameters for the latent positions, clustering membership probabilities, etc. conv indicated whether convergence was obtained within the specified number of iterations.
Michael Salter-Townshend
Michael Salter-Townshend and Thomas Brendan Murphy (2009). "Variational Bayesian Inference for the Latent Position Cluster Model." Workshop on Analyzing Networks and Learning with Graphs. Neural Information Processing Systems.
vblpcmstart, latentnet::ergmm
Prints to screen the most likely a-posteriori membership of each node.
vblpcmgroups(v.params, colours)vblpcmgroups(v.params, colours)
v.params |
The fitted values; output from vblpcmfit() |
colours |
The colours to be used. |
Prints to screen of the most probable group membership for each node.
Michael Salter-Townshend
print and returns the Kullback-Leibler divergence from the fitted vblpcm object to the true LPCM posterior
vblpcmKL(x)vblpcmKL(x)
x |
The fitted values; output from vblpcmfit() or vblpcmstart() |
The normalising constant of the posterior is unknown and therefore the Kullback-Leibler divergence is missing a constant.
Michael Salter-Townshend
Plot a Receiver Operating Curve to show model fit in terms of link prediction.
vblpcmroc(v.params, NUM=100)vblpcmroc(v.params, NUM=100)
v.params |
The fitted values; output from vblpcmfit() |
NUM |
The number of intervals on the roc curve |
A threshold is varied between zero and one. At each point the probability of a link between all pairs of nodes is calculated on the v.params argument containing a fitted vblpcm object. If greater than the threshold the link is "predicted" present, else it is "predicted" absent. A plot of the proportion of true and false positives for each threshold value is thus obtained.
The Area Under the Curve (AUC). The closer to 1 the better the fit.
Michael Salter-Townshend
Uses fast methods to generate sensible and coherent values for the parameters of the variational method. There are returned as a list and that list may be passed directly to vblpcmfit(). User specification of the configuration is recommended as tweaks to this list only.
vblpcmstart(g.network,G=1,d=2,LSTEPS=5e3,model="plain", CLUST=0, B=NULL, lcc=TRUE, edgecovs=NULL,sendcovs=NULL,receivecovs=NULL, socialcovs=NULL,START="FR", seed=NaN)vblpcmstart(g.network,G=1,d=2,LSTEPS=5e3,model="plain", CLUST=0, B=NULL, lcc=TRUE, edgecovs=NULL,sendcovs=NULL,receivecovs=NULL, socialcovs=NULL,START="FR", seed=NaN)
g.network |
a network object |
G |
Desired number of groups |
d |
Desired dimensionality of the latent space |
LSTEPS |
Number of steps in the log-likelihood forces algorithm |
model |
model specified as "plain", "rreceiver", "rsender" or "rsocial". See vblpcmcovs for details. |
CLUST |
degree of push to clustering at the start |
B |
default intercept value |
lcc |
logical indicator. TRUE => analyze largest connected component of g.network only FALSE => analyze the whole network. |
edgecovs |
optional edge covariates. |
sendcovs |
optional sender node covariates. |
receivecovs |
optional receiver node covariates. |
socialcovs |
optional sociality node covariates. |
START |
what to start the initial positions with. "FR" for Fruchterman-Reingold. "geodesic" for geodesic distances. "laplace" for using the Graph Laplacian. "random" for random. |
seed |
Optional seed for the random number generator in R. Equivalent to using set.seed(seed). The default NaN value does not call set.seed(). |
A v.params list containing the latent positions, clustering membership probabilities, etc.
Michael Salter-Townshend
vblpcmfit, vblpcmcovs
data(sampson) ### plot the mean posterior positions with initial estimations for variational parameters plot(vblpcmstart(samplike,G=3),main="Sampson's Monks: VB Initial Values") ### plot the mean posterior positions with final estimations for variational parameters plot(vblpcmfit(vblpcmstart(samplike,G=3)),main="Sampson's Monks: VB Solution")data(sampson) ### plot the mean posterior positions with initial estimations for variational parameters plot(vblpcmstart(samplike,G=3),main="Sampson's Monks: VB Initial Values") ### plot the mean posterior positions with final estimations for variational parameters plot(vblpcmfit(vblpcmstart(samplike,G=3)),main="Sampson's Monks: VB Solution")
calls C code to quickly transform from adjacency to edgelist
Y_to_E(N, NE, directed, Y)Y_to_E(N, NE, directed, Y)
N |
number of nodes |
NE |
number of edges |
directed |
logical indicator of directedness; TRUE=>directed FALSE=>undirected |
Y |
input adjacency matrix |
An edgelist matrix E of size NE x 2
Michael Salter-Townshend
edgelist, E_to_Y
uses C code to quickly find all pairs of nodes for which we do not know whether there is a link or not, given an adjacency matrix with NaNs indicating unknown / unobserved linkage
Y_to_M(N, NM, directed, Y)Y_to_M(N, NM, directed, Y)
N |
number of nodes |
NM |
number of missing edges |
directed |
logical indicator of directedness; TRUE=>directed FALSE=>undirected |
Y |
input adjacency matrix |
A matrix of missing edges M
Michael Salter-Townshend
Y_to_E, E_to_Y, Y_to_nonE
uses C code to quickly calculate all non-edges as a two column matrix given an adjacency matrix. i.e. all zeros in the adjacency matrix will correspond to a row in the non-edgelist nonE
Y_to_nonE(N, NnonE, directed, Y)Y_to_nonE(N, NnonE, directed, Y)
N |
number of nodes |
NnonE |
number of non-edges |
directed |
logical indicator of directedness; TRUE=>directed FALSE=>undirected |
Y |
input adjacency matrix |
A matrix of the non-edges with NnonE rows and 2 columns where NnonE is the number of non-edges.
Michael Salter-Townshend
Y_to_E, Y_to_M, E_to_Y