Learning Graphs from Data via Spectral Constraints

In the era of big data and hyperconnectivity, learning high-dimensional structures such as graphs from data has become a prominent task in machine learning and has found applications in many fields such as finance, health care, and networks. 'spectralGraphTopology' is an open source, documented, and well-tested R package for learning graphs from data. It provides implementations of state of the art algorithms such as Combinatorial Graph Laplacian Learning (CGL), Spectral Graph Learning (SGL), Graph Estimation based on Majorization-Minimization (GLE-MM), and Graph Estimation based on Alternating Direction Method of Multipliers (GLE-ADMM). In addition, graph learning has been widely employed for clustering, where specific algorithms are available in the literature. To this end, we provide an implementation of the Constrained Laplacian Rank (CLR) algorithm.

spectralGraphTopology

spectralGraphTopology provides estimators to learn k-component, bipartite, and k-component bipartite graphs from data by imposing spectral constraints on the eigenvalues and eigenvectors of the Laplacian and adjacency matrices. Those estimators leverage spectral properties of the graphical models as a prior information which turn out to play key roles in unsupervised machine learning tasks such as clustering.

Documentation: https://mirca.github.io/spectralGraphTopology.

Installation

From inside an R session, type:

> install.packages("spectralGraphTopology")

Alternatively, you can install the development version from GitHub:

> devtools::install_github("dppalomar/spectralGraphTopology")

Microsoft Windows

On MS Windows environments, make sure to install the most recent version of Rtools.

macOS

spectralGraphTopology depends on RcppArmadillo which requires gfortran.

Usage: clustering

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 = .25, verbose = FALSE, abstol = 1e-3)

# 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)

Contributing

We welcome all sorts of contributions. Please feel free to open an issue to report a bug or discuss a feature request.

Citation

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. https://CRAN.R-project.org/package=spectralGraphTopology

• S. Kumar, J. Ying, J. V. de Miranda Cardoso, and D. P. Palomar (2020). A unified framework for structured graph learning via spectral constraints. Journal of Machine Learning Research (21), pages 1-60.

• S. Kumar, J. Ying, J. V. de Miranda Cardoso, D. P. Palomar (2019). Structured graph learning via Laplacian spectral constraints. Advances in Neural Information Processing Systems.

In addition, consider citing the following bibliography according to their implementation:

Links

Package: CRAN and GitHub

README file: GitHub-readme

Vignette: GitHub-html-vignette, CRAN-html-vignette, NeurIPS’19 Promotional slides, NeurIPS’19 Promotional video