makeAdjGrid: Creating the adjacency structure for grid graphs

In bcp: Bayesian Analysis of Change Point Problems

Description

makeAdjGrid() produces a sparse representation of the adjacency structure for grid graphs, useful as the adj argument in bcp().

Usage

makeAdjGrid(n, m = NULL, k = 8)

Arguments

n	the number of rows of vertices in the graph data.
m	(optional) the number of column of vertices in the graph data. If not given, we assume m = n.
k	(optional) the number of neighbors assumed for a typical vertex (see details below), either 4 or 8. Default number of neighbors is assumed to be 8.

Details

makeAdjGrid() produces a list representation of the adjacency structure for grid graphs. The i-th entry in the list gives a vector of neighbor ids for the i-th node. Note that neighbor ids are offset by 1 because indexing starts at 0 in C++. If k = 8, then we assume each node is joined via edges to its 8 neighbors in the (top left, top middle, top right, left, right, bottom left, bottom middle, and bottom right) directions, where applicable. If k = 4, then we assume each node is joined via edges to its 4 neighbors in the (top, right, bottom, left) directions, where applicable.

Author(s)

Xiaofei Wang

See Also

bcp for performing Bayesian change point analysis.

Examples

# generates an adjacency list for a 10 node by 5 node grid, assuming a maximum of 8 neighbors
adj <- makeAdjGrid(10, 5) 

# generates an adjacency list for a 10 node by 5 node grid, assuming a maximum of 4 neighbors
adj4 <- makeAdjGrid(10, 5, 4)


### show a grid example
## Not run: 
set.seed(5)
adj <- makeAdjGrid(20)
z <- rep(c(0, 2), each=200)
y <- z + rnorm(400, sd=1)
out <- bcp(y, adj=adj, burnin=500, mcmc=500)

if (require("ggplot2")) {
  df <- data.frame(mean=z, data = y, post.means = out$posterior.mean[,1], 
                   post.probs = out$posterior.prob, 
                   i = rep(1:20, each=20), j = rep(1:20, times=20))

  # visualize the data
  g <- ggplot(df, aes(i,j)) + 
         geom_tile(aes(fill = data), color='white') +
         scale_fill_gradientn(limits=range(y), colours=c('white', 'steelblue'))+
         ggtitle("Observed Data")
  print(g)

  # visualize the means
  g <- ggplot(df, aes(i,j)) + 
         geom_tile(aes(fill = mean), color='white') +
         scale_fill_gradientn(limits=range(y), colours=c('white', 'steelblue'))+
         ggtitle("True Means")
  print(g)

  # visualize the posterior means/probs
  g <- ggplot(df, aes(i,j)) + 
         geom_tile(aes(fill = post.means), color='white') +
         scale_fill_gradientn(limits=range(y), colours=c('white', 'steelblue'))+
         ggtitle("Posterior Means")
  print(g)

  g <- ggplot(df, aes(i,j)) + 
         geom_tile(aes(fill = post.probs), color='white') +
         scale_fill_gradientn(limits=c(0, 1), colours=c('white', 'steelblue'))+
         ggtitle("Posterior Boundary Probabilities")
  print(g)
}

## End(Not run)

bcp documentation built on May 2, 2019, 9:16 a.m.