find.cut: Computing the threshold

Description

The functions compute the maximum value of m/cut where a certain block is still classified as alt.blocks and not "null". The difference between find.m and find.m2 it that find.m uses an optimization approach and is faster and more precise than find.m2. However, find.m only supports regular ("reg") and complete ("com") as alt.blocks, while find.m2 supports all block types. Also, find.m does not always work, especially if cormet is not "none".

Usage

find.cut(M, clu, alt.blocks = "reg", cuts = "all", ...)
find.m(
  M,
  clu,
  alt.blocks = "reg",
  diag = !is.list(clu),
  cormet = "none",
  half = TRUE,
  FUN = "max"
)
find.m2(M, clu, alt.blocks = "reg", neval = 100, half = TRUE, ms = NULL, ...)

Value

A matrix of maximal m/cut values.

Arguments

M: A matrix representing the (usually valued) network. For now, only one-relational networks are supported. 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.
alt.blocks: Only one of allowed blocktypes, as alternative to the null block:
"com" - complete block
"rdo", "cdo" - row and column-dominant blocks (binary, valued, and implicit approach only)
"reg" - (f-)regular block
"rre", "cre" - row and column-(f-)regular blocks
"rfn", "cfn" - row and column-dominant blocks (binary, valued, and implicit approach only)
"den" - density block (binary approach only)
"avg" - average block (valued approach only).
cuts: The cuts, which should be evaluated. If cuts="all" (default), all unique values are evaluated.
...: Other parameters to critFunC.
diag: (default = TRUE) Should the special status of diagonal be acknowledged.
cormet: Which method should be used to correct for different maximum error contributions
"none" - no correction
"censor" - censor values larger than M
"correct" - so that the maximum possible error contribution of the cell is the same regardless of a condition (either that something must be 0 or at least M).
half: Should the returned value of m be one half of the value where the inconsistencies are the same.
FUN: (default = "max") Function f used in row-f-regular, column-f-regular, and f-regular blocks.
neval: A number of different m values to be evaluated.
ms: The values of m where the function should be evaluated.

Author

Aleš Žiberna

References

Doreian, P., Batagelj, V. & Ferligoj, A. Anuška (2005). Generalized blockmodeling, (Structural analysis in the social sciences, 25). Cambridge [etc.]: Cambridge University Press.

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

Žiberna, A. (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