spectralGraphTopology provides estimators to learn kcomponent, bipartite, and kcomponent bipartite graphs from data by imposing spectral constraints on the eigenvalues and eigenvectors of the Laplacian and adjacency matrices. Those estimators leverages spectral properties of the graphical models as a prior information, which turn out to play key roles in unsupervised machine learning tasks such as community detection.
Documentation: https://mirca.github.io/spectralGraphTopology.
From inside an R session, type:
Alternatively, you can install the development version from GitHub:
On MS Windows environments, make sure to install the most recent version of Rtools
.
spectralGraphTopology depends on RcppArmadillo
which requires gfortran
.
We illustrate the usage of the package with simulated data, as follows:
library(spectralGraphTopology)
library(clusterSim)
library(igraph)
set.seed(42)
# generate graph and data
n < 50 # number of nodes per cluster
twomoon < clusterSim::shapes.two.moon(n) # generate data points
k < 2 # number of components
# estimate underlying graph
S < crossprod(t(twomoon$data))
graph < learn_k_component_graph(S, k = k, beta = .5, verbose = FALSE, abstol = 1e3)
# plot
# build network
net < igraph::graph_from_adjacency_matrix(graph$Adjacency, mode = "undirected", weighted = TRUE)
# colorify nodes and edges
colors < c("#706FD3", "#FF5252")
V(net)$cluster < twomoon$clusters
E(net)$color < apply(as.data.frame(get.edgelist(net)), 1,
function(x) ifelse(V(net)$cluster[x[1]] == V(net)$cluster[x[2]],
colors[V(net)$cluster[x[1]]], '#000000'))
V(net)$color < colors[twomoon$clusters]
# plot nodes
plot(net, layout = twomoon$data, vertex.label = NA, vertex.size = 3)
We welcome all sorts of contributions. Please feel free to open an issue to report a bug or discuss a feature request.
If you made use of this software please consider citing:
J. V. de Miranda Cardoso, D. P. Palomar (2019). spectralGraphTopology: Learning Graphs from Data via Spectral Constraints. R package version 0.1.0. https://CRAN.Rproject.org/package=spectralGraphTopology
S. Kumar, J. Ying, J. V. de Miranda Cardoso, and D. P. Palomar (2019). A unified framework for structured graph learning via spectral constraints. https://arxiv.org/abs/1904.09792
In addition, consider citing the following bibliography according to their implementation:
function  reference 

cluster_k_component_graph

N., Feiping, W., Xiaoqian, J., Michael I., and H., Heng. (2016). The Constrained Laplacian Rank Algorithm for Graphbased Clustering, AAAI’16. 
learn_laplacian_gle_mm

Licheng Zhao, Yiwei Wang, Sandeep Kumar, and Daniel P. Palomar, Optimization Algorithms for Graph Laplacian Estimation via ADMM and MM, IEEE Trans. on Signal Processing, vol. 67, no. 16, pp. 42314244, Aug. 2019 
learn_laplacian_gle_admm

Licheng Zhao, Yiwei Wang, Sandeep Kumar, and Daniel P. Palomar, Optimization Algorithms for Graph Laplacian Estimation via ADMM and MM, IEEE Trans. on Signal Processing, vol. 67, no. 16, pp. 42314244, Aug. 2019 
README file: GitHubreadme
Vignette: GitHubhtmlvignette