**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**.

From inside an R session, type:

`> install.packages("spectralGraphTopology")`

Alternatively, you can install the development version from GitHub:

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

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
<- 50 # number of nodes per cluster
n <- clusterSim::shapes.two.moon(n) # generate data points
twomoon <- 2 # number of components
k
# estimate underlying graph
<- crossprod(t(twomoon$data))
S <- learn_k_component_graph(S, k = k, beta = .25, verbose = FALSE, abstol = 1e-3)
graph
# plot
# build network
<- igraph::graph_from_adjacency_matrix(graph$adjacency, mode = "undirected", weighted = TRUE)
net # colorify nodes and edges
<- c("#706FD3", "#FF5252")
colors 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)$cluster[x[2]],
V(net)$cluster[x[1]]], '#000000'))
colors[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. 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:

function |
reference |
---|---|

`cluster_k_component_graph` |
N., Feiping, W., Xiaoqian, J., Michael I., and H., Heng. (2016). The Constrained Laplacian Rank Algorithm for Graph-based 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. 4231-4244, 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. 4231-4244, Aug. 2019 |

`learn_combinatorial_graph_laplacian` |
H. E. Egilmez, E. Pavez and A. Ortega, Graph learning from data under Laplacian and structural constraints, Journal of Selected Topics in Signal Processing, vol. 11, no. 6, pp. 825-841, Sept. 2017 |

README file: GitHub-readme

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