vsp

The goal of vsp is to enable fast, spectral estimation of latent
factors in random dot product graphs. Under mild assumptions, the vsp
estimator is consistent for (degree-corrected) stochastic blockmodels,
(degree-corrected) mixed-membership stochastic blockmodels, and
degree-corrected overlapping stochastic blockmodels.

More generally, the vsp estimator is consistent for random dot product
graphs that can be written in the form

E(A) = Z B Y^T

where Z and Y satisfy the varimax assumptions of [1]. vsp works
on directed and undirected graphs, and on weighted and unweighted
graphs. Note that vsp is a semi-parametric estimator.

Installation

You can install the released version of vsp from CRAN with

install.packages("vsp")

You can install the development version of vsp with:

install.packages("devtools")
devtools::install_github("RoheLab/vsp")

Example

Obtaining estimates from vsp is straightforward. We recommend
representing networks as igraph objects or
sparse adjacency matrices using the
Matrix package. Once you
have your network in one of these formats, you can get estimates by
calling the vsp() function. The result is a vsp_fa S3 object.

Here we demonstrate vsp usage on an igraph object, using the enron
network from igraphdata package to demonstrate this functionality.
First we peak at the graph:

library(igraph)
data(enron, package = "igraphdata")

image(sign(get.adjacency(enron, sparse = FALSE)))

Now we estimate:

library(vsp)

fa <- vsp(enron, rank = 30)
fa
#> Vintage Sparse PCA Factor Analysis
#> 
#> Rows (n):   184
#> Cols (d):   184
#> Factors (rank): 30
#> Lambda[rank]:   0.2077
#> Components
#> 
#> Z: 184 x 30 [matrix] 
#> B: 30 x 30 [matrix] 
#> Y: 184 x 30 [matrix] 
#> u: 184 x 30 [matrix] 
#> d: 30      [numeric] 
#> v: 184 x 30 [matrix]

get_varimax_z(fa)
#> # A tibble: 184 × 31
#>    id         z01      z02      z03      z04      z05      z06      z07      z08
#>    <chr>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
#>  1 row0…  2.42e-4 -0.00245 -2.99e-2  3.37e-4  9.96e-5 -0.0114  -0.00849  0.502  
#>  2 row0… -2.52e-3  0.00135  6.70e-4 -1.63e-1 -1.47e-2  0.0471   0.190    0.00181
#>  3 row0…  2.98e-4 -0.100    1.17e-4 -3.62e-3 -2.06e-2  0.187   -0.158    0.00303
#>  4 row0… -7.75e-5 -0.0183   1.17e-4  5.42e-2 -5.58e-3  0.00165 -0.0367  -0.00106
#>  5 row0… -2.31e-3  0.00150  2.57e-1 -1.42e-2 -4.38e-2  0.00629  1.18    -0.0179 
#>  6 row0… -3.46e-2 -0.0527  -2.61e-2 -1.26e-2 -1.83e-2  0.0282   0.408   -0.0286 
#>  7 row0… -1.08e-3 -0.327   -6.01e-1 -6.98e-2 -9.85e-2 -0.0709   0.509    0.0511 
#>  8 row0…  1.58e-2 -0.0518  -1.34e-2 -1.03e-2 -4.12e-3 -0.0139   0.225   -0.0244 
#>  9 row0…  2.22e-3  0.0752   3.30e-2 -6.50e-4 -5.00e-1 -0.0278  -0.0740  -0.00556
#> 10 row0…  7.13e-4 -0.0119   1.95e-2 -5.06e-3 -7.08e-3  0.00341 -0.00369 13.4    
#> # ℹ 174 more rows
#> # ℹ 22 more variables: z09 <dbl>, z10 <dbl>, z11 <dbl>, z12 <dbl>, z13 <dbl>,
#> #   z14 <dbl>, z15 <dbl>, z16 <dbl>, z17 <dbl>, z18 <dbl>, z19 <dbl>,
#> #   z20 <dbl>, z21 <dbl>, z22 <dbl>, z23 <dbl>, z24 <dbl>, z25 <dbl>,
#> #   z26 <dbl>, z27 <dbl>, z28 <dbl>, z29 <dbl>, z30 <dbl>

To visualize a screeplot of the singular value, use:

screeplot(fa)

At the moment, we also enjoy using pairs plots of the factors as a
diagnostic measure:

plot_varimax_z_pairs(fa, 1:5)

plot_varimax_y_pairs(fa, 1:5)

Similarly, an IPR pairs plot can be a good way to check for singular
vector localization (and thus overfitting!).

plot_ipr_pairs(fa)

plot_mixing_matrix(fa)

References

[1] Rohe, Karl, and Muzhe Zeng. “Vintage Factor Analysis with Varimax
Performs Statistical Inference.” Journal of the Royal Statistical
Society Series B: Statistical Methodology 85, no. 4 (September 29,
2023): 1037–60. https://doi.org/10.1093/jrsssb/qkad029.

Code to reproduce the results from the paper is available
here.