funByBlocks function

Computation of function values by blocks

Computes a value of a function over blocks of a matrix, defined by a partition.

## Default S3 method:
funByBlocks(
  x = M,
  clu,
  M = x,
  ignore.diag = "default",
  sortNames = TRUE,
  FUN = "mean",
  ...
)

## S3 method for class 'optMorePar'
funByBlocks(x, which = 1, orderClu = FALSE, sortNames = NULL, ...)

## S3 method for class 'opt.more.par'
funByBlocks(x, which = 1, orderClu = FALSE, sortNames = NULL, ...)

funByBlocks(x, ...)

fun.by.blocks(x, ...)

Arguments

• x: An object of suitable class or a matrix/array representing the (usually valued) network. For multi-relational networks, this should be an array with the third dimension representing the relation. The network can have one or more modes (different kinds of units with no ties among themselves. If the network is not two-mode, the matrix must be square.
• clu: A partition. Each unique value represents one cluster. If the network is one-mode, then this should be a vector, else a list of vectors, one for each mode.
• M: A matrix representing the (usually valued) network. For multi-relational networks, this should be an array with the third dimension representing the relation. The network can have one or more modes (different kinds of units with no ties among themselves. If the network is not two-mode, the matrix must be square.
• ignore.diag: Should the diagonal be ignored.
• sortNames: Should the rows and columns of the matrix be sorted based on their names.
• FUN: The function to be computed over the blocks.
• ...: Further arguments to funByBlocks.default.
• which: Which (if several) of the "best" solutions should be used.
• orderClu: Should the partition be ordered before computing. FALSE by default. If TRUE, orderClu is used (using default arguments) to order the clusters in a partition in "decearsing" (see orderClu for interpretation) order. If TRUE, sortNames is set to FALSE.

Returns

A numerical matrix of FUN values by blocks, induced by a partition clu.

Examples

n <- 8 # If larger, the number of partitions increases dramatically,
# as does if we increase the number of clusters
net <- matrix(NA, ncol = n, nrow = n)
clu <- rep(1:2, times = c(3, 5))
tclu <- table(clu)
net[clu == 1, clu == 1] <- rnorm(n = tclu[1] * tclu[1], mean = 0, sd = 1)
net[clu == 1, clu == 2] <- rnorm(n = tclu[1] * tclu[2], mean = 4, sd = 1)
net[clu == 2, clu == 1] <- rnorm(n = tclu[2] * tclu[1], mean = 0, sd = 1)
net[clu == 2, clu == 2] <- rnorm(n = tclu[2] * tclu[2], mean = 0, sd = 1)
# Optimizing 10 random partitions with optRandomParC
res <- optRandomParC(M = net, k = 2, rep = 10, approaches = "hom", homFun = "ss", blocks = "com")
plot(res) # Hopefully we get the original partition
funByBlocks(res)
# Computing mean by blocks, ignoring the diagonal (default)

References

(2007). Generalized Blockmodeling of Valued Networks. Social Networks, 29(1), 105-126. doi: 10.1016/j.socnet.2006.04.002

(2008). Direct and indirect approaches to blockmodeling of valued networks in terms of regular equivalence. Journal of Mathematical Sociology, 32(1), 57-84. doi: 10.1080/00222500701790207

See Also

optRandomParC, optParC

Author(s)