diffusionMap: Creates a heatmap based on a graph layout and a vertex...

In srdyal/diffusiontest: Analysis of Diffusion and Contagion Processes on Networks

Creates a heatmap based on a graph layout and a vertex attribute

Description

Using bi-dimensional kernel smoothers, creates a heatmap based on a graph layout and colored accordingly to x. This visualization technique is intended to be used with large graphs.

Usage

diffusionMap(graph, ...)

diffmap(graph, ...)

## Default S3 method:
diffusionMap(
  graph,
  x,
  x.adj = round_to_seq,
  layout = NULL,
  jitter.args = list(),
  kde2d.args = list(n = 100),
  sharp.criter = function(x, w) {
     wvar(x, w) > (max(x, na.rm = TRUE) - min(x, na.rm
    = TRUE))^2/12
 },
  ...
)

## S3 method for class 'diffnet'
diffusionMap(graph, slice = nslices(graph), ...)

## S3 method for class 'diffnet_diffmap'
image(x, ...)

## S3 method for class 'diffnet_diffmap'
print(x, ...)

## S3 method for class 'diffnet_diffmap'
plot(x, y = NULL, ...)

Arguments

graph	A square matrix of size n\times n.
...	Arguments passed to method.
x	An vector of length n. Usually a toa vector.
x.adj	Function to adjust x. If not NULL then it is applied to x at the beginning (see details).
layout	Either a n\times 2 matrix of coordinates or a layout function applied to graph (must return coordinates).
jitter.args	A list including arguments to be passed to jitter.
kde2d.args	A list including arguments to be passed to kde2d.
sharp.criter	A function choose whether to apply a weighted mean for each cell, or randomize over the values present in that cell (see details).
slice	Integer scalar. Slice of the network to be used as baseline for drawing the graph.
y	Ignored.

Details

The image is created using the function kde2d from the MASS package. The complete algorithm follows:

1. x is coerced into integer and the range is adjusted to start from 1. NA are replaced by zero.

2. If no layout is passed, layout is computed using layout_nicely from igraph

3. Then, a kde2d map is computed for each level of x. The resulting matrices are added up as a weighted sum. This only holds if at the cell level the function sharp.criter returns FALSE.

4. The jitter function is applied to the repeated coordinates.

5. 2D kernel is computed using kde2d over the coordinates.

The function sharp.criter must take two values, a vector of levels and a vector of weights. It must return a logical scalar with value equal to TRUE when a randomization at the cell level must be done, in which case the final value of the cell is chosen using sample(x, 1, prob=w).

The resulting matrix can be passed to image or similar.

The argument x.adj uses by default the function round_to_seq which basically maps x to a fix length sequence of numbers such that x.adj(x) resembles an integer sequence.

Value

A list of class diffnet_diffmap

coords	A matrix of size n\times 2 of vertices coordinates.
map	Output from kde2d. This is a list with 3 elements, vectors x, y and matrix z of size n\times n (passed via kde2d.args).
h	Bandwidth passed to kde2d.

Author(s)

George G. Vega Yon

References

Vega Yon, George G., and Valente, Thomas W., Visualizing Large Annotated Networks as Heatmaps using Weighted Averages based on Kernel Smoothers (Working paper).

See Also

Other visualizations: dgr(), drawColorKey(), grid_distribution(), hazard_rate(), plot_adopters(), plot_diffnet(), plot_diffnet2(), plot_infectsuscep(), plot_threshold(), rescale_vertex_igraph()

Examples

# Example with a random graph --------------------------------------------------

set.seed(1231)

# Random scale-free diffusion network
x <- rdiffnet(500, 4, seed.graph="scale-free", seed.p.adopt = .025,
                           rewire = FALSE, seed.nodes = "central",
                           rgraph.arg=list(self=FALSE, m=4),
                           threshold.dist = function(id) runif(1,.2,.4))

# Diffusion map (no random toa)
dm0 <- diffusionMap(x, kde2d.args=list(n=150, h=.5), layout=igraph::layout_with_fr)

# Random
diffnet.toa(x) <- sample(x$toa, size = nnodes(x))

# Diffusion map (random toa)
dm1 <- diffusionMap(x, layout = dm0$coords, kde2d.args=list(n=150, h=.5))

oldpar <- par(no.readonly = TRUE)
col <- colorRampPalette(blues9)(100)
par(mfrow=c(1,2), oma=c(1,0,0,0))
image(dm0, col=col, main="Non-random Times of Adoption\nAdoption from the core.")
image(dm1, col=col, main="Random Times of Adoption")
par(mfrow=c(1,1))
mtext("Both networks have the same distribution on times of adoption", 1,
      outer = TRUE)
par(oldpar)

# Example with Brazilian Farmers --------------------------------------------
dn <- brfarmersDiffNet

# Setting last TOA as NA
diffnet.toa(dn)[dn$toa == max(dn$toa)] <-
  NA

# Coordinates
coords <- sna::gplot.layout.fruchtermanreingold(
  as.matrix(dn$graph[[1]]), layout.par=NULL
)

# Plotting diffusion
plot_diffnet2(dn, layout=coords, vertex.size = 300)

# Adding diffusion map
out <- diffusionMap(dn, layout=coords, kde2d.args=list(n=100, h=50))
col <- adjustcolor(colorRampPalette(c("white","lightblue", "yellow", "red"))(100),.5)
with(out$map, .filled.contour(x,y,z,pretty(range(z), 100),col))

srdyal/diffusiontest documentation built on Dec. 9, 2024, 1:14 a.m.