Ugraph {rags2ridges}

Visualize undirected graph

Description

Function that visualizes the sparsified precision matrix as an undirected graph.

Usage

Ugraph(
  M,
  type = c("plain", "fancy", "weighted"),
  lay = "layout_in_circle",
  coords = NULL,
  Vsize = 15,
  Vcex = 1,
  Vcolor = "orangered",
  VBcolor = "darkred",
  VLcolor = "black",
  prune = FALSE,
  legend = FALSE,
  label = "",
  Lcex = 1.3,
  PTcex = 4,
  cut = 0.5,
  scale = 10,
  pEcolor = "black",
  nEcolor = "grey",
  main = ""
)

Arguments

M

(Possibly sparsified) precision matrix

type

A character indicating the type of graph to be produced. Must be one of: "plain", "fancy", "weighted".

lay

A character mimicking a call to igraph layout functions. Determines the placement of vertices.

coords

A matrix containing coordinates. Alternative to the lay-argument for determining the placement of vertices.

Vsize

A numeric determining the vertex size.

Vcex

A numeric determining the size of the vertex labels.

Vcolor

A character (scalar or vector) determining the vertex color.

VBcolor

A character determining the color of the vertex border.

VLcolor

A character determining the color of the vertex labels.

prune

A logical determining if vertices of degree 0 should be removed.

legend

A logical indicating if the graph should come with a legend.

label

A character giving a name to the legend label.

Lcex

A numeric determining the size of the legend box.

PTcex

A numeric determining the size of the exemplary vertex in the legend box.

cut

A numeric indicating the cut-off for indicating strong edges when type = "fancy".

scale

A numeric representing a scale factor for visualizing strength of edges when type = "weighted".

pEcolor

A character determining the color of the edges tied to positive precision elements. Only when type = "weighted".

nEcolor

A character determining the color of the edges tied to negative precision elements. Only when type = "weighted".

main

A character giving the main figure title.

Details

The intended use of this function is to visualize a sparsified precision/partial correlation matrix as an undirected graph. When type = "plain" a plain undirected graph is given representing the conditional (in)dependencies exemplified by the sparsified precision.

When type = "fancy" a more elaborate graph is given in which dashed lines indicate negative partial correlations while solid lines indicate positive partial correlations, and in which grey lines indicate strong edges. Strong edges are deemed such by setting cut. If a the absolute value of a precision element \geq cut the corresponding edge is deemed strong and colored grey in the graph. The argument cut is thus only used when type = "fancy".

When type = "weighted" an undirected graph is given in which edge thickness represents the strength of the partial correlations. The nEcolor colored edges then represent negative partial correlations while pEcolor colored edges represent positive partial correlations. (Relative) edge thickness in this type of graph can be set by the argument scale. The arguments scale, nEcolor, and pEcolor are thus only used when type = "weighted".

The default layout gives a circular placement of the vertices. Most layout functions supported by igraph are supported (the function is partly a wrapper around certain igraph functions). The igraph layouts can be invoked by a character that mimicks a call to a igraph layout functions in the lay argument. When using lay = NULL one can specify the placement of vertices with the coords argument. The row dimension of this matrix should equal the number of (pruned) vertices. The column dimension then should equal 2 (for 2D layouts) or 3 (for 3D layouts). The coords argument can also be viewed as a convenience argument as it enables one, e.g., to layout a graph according to the coordinates of a previous call to Ugraph. If both the the lay and the coords arguments are not NULL, the lay argument takes precedence

The legend allows one to specify the kind of variable the vertices represent, such as, e.g., mRNA transcripts. The arguments label, Lcex, and PTcex are only used when legend = TRUE.

If prune = TRUE the vertices of degree 0 (vertices not implicated by any edge) are removed. For the colors supported by the arguments Vcolor, VBcolor, VLcolor, pEcolor, and nEcolor see https://www.nceas.ucsb.edu/sites/default/files/2020-04/colorPaletteCheatsheet.pdf.

Value

The function returns a graph. The function also returns a matrix object containing the coordinates of the vertices in the given graph.

Author(s)

Carel F.W. Peeters <[e-mail]>

References

Csardi, G. and Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems 1695. http://igraph.sf.net

van Wieringen, W.N. & Peeters, C.F.W. (2016). Ridge Estimation of Inverse Covariance Matrices from High-Dimensional Data, Computational Statistics & Data Analysis, vol. 103: 284-303. Also available as arXiv:1403.0904v3 [stat.ME].

van Wieringen, W.N. & Peeters, C.F.W. (2015). Application of a New Ridge Estimator of the Inverse Covariance Matrix to the Reconstruction of Gene-Gene Interaction Networks. In: di Serio, C., Lio, P., Nonis, A., and Tagliaferri, R. (Eds.) 'Computational Intelligence Methods for Bioinformatics and Biostatistics'. Lecture Notes in Computer Science, vol. 8623. Springer, pp. 170-179.

See Also

ridgeP, optPenalty.LOOCV, optPenalty.aLOOCV, sparsify

Examples

## Obtain some (high-dimensional) data
p = 25
n = 10
set.seed(333)
X = matrix(rnorm(n*p), nrow = n, ncol = p)
colnames(X)[1:25] = letters[1:25]

## Obtain regularized precision under optimal penalty
OPT <- optPenalty.LOOCV(X, lambdaMin = .5, lambdaMax = 30, step = 100)

## Determine support regularized standardized precision under optimal penalty
PC0 <- sparsify(symm(OPT$optPrec), threshold = "localFDR")$sparseParCor

## Obtain graphical representation
Ugraph(PC0, type = "fancy", cut = 0.07)

## Obtain graphical representation with Fruchterman-Reingold layout
Ugraph(PC0, type = "fancy", lay = "layout_with_fr", cut = 0.07)

## Add pruning
Ugraph(PC0, type = "fancy", lay = "layout_with_fr",
       cut = 0.07, prune = TRUE)

## Obtain graph and its coordinates
Coordinates <- Ugraph(PC0, type = "fancy", lay = "layout_with_fr",
                      cut = 0.07, prune = TRUE)
Coordinates