R/seriate_QAP.R

In seriation: Infrastructure for Ordering Objects Using Seriation

#######################################################################
# seriation - Infrastructure for seriation
# Copyright (C) 2011 Michael Hahsler, Christian Buchta and Kurt Hornik
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

## QAP 2SUM seriation
seriate_dist_2SUM <- function(x, control = NULL) {
  ## param are passed on to QAP

  do.call(qap::qap, c(list(
    A = .A_2SUM(attr(x, "Size")),
    B = 1 / (1 + as.matrix(x))
  ), control))
}

## QAP Linear seriation
seriate_dist_LS <- function(x, control = NULL) {
  ## param are passed on to QAP

  do.call(qap::qap, c(list(A = .A_LS(attr(
    x, "Size"
  )),
    B = as.matrix(x)), control))
}

## QAP Inertia
seriate_dist_Inertia <- function(x, control = NULL) {
  ## param are passed on to QAP
  n <- attr(x, "Size")

  ## inertia uses the same A matrix as 2SUM
  ## we use n^2 since A needs to be positive
  do.call(qap::qap, c(list(
    A = n ^ 2 - .A_2SUM(n),
    B = as.matrix(x)
  ), control))
}


## QAP BAR
.qap_bar_contr <- structure(list(
  b = function(n)
    max(1, floor(n * .2))
),
help = list(b = "bandwidth (default is 20%)"))



seriate_dist_BAR <- function(x, control = NULL) {
  ## param are passed on to QAP

  if (is.null(control))
    control <- .qap_bar_contr
  if (is.null(control$b))
    control$b <- .qap_bar_contr$b

  .A_BAR <- function(n, b) {
    b <- floor(b)
    if (b < 1 || b >= n)
      stop("b: needs to be 1<=b<n!")
    A <- b + 1 - outer(
      1:n,
      1:n,
      FUN = function(i, j)
        abs(i - j)
    )
    A[A < 0] <- 0
    A
  }

  n <- attr(x, "Size")
  if (is.function(control$b))
    b <- control$b(n)
  else
    b <- floor(control$b)

  if (b < 1 || b > n)
    stop("BAR bandwidth is not between 1 and n!")

  control$b <- NULL

  ## inertia uses the same A matrix as 2SUM
  do.call(qap::qap, c(list(A = .A_BAR(n, b = b),
    B = as.matrix(x)), control))
}


set_seriation_method(
  "dist",
  "QAP_2SUM",
  seriate_dist_2SUM,
  "Quadratic assignment problem formulation for seriation solved using a simulated annealing solver to minimize the 2-Sum Problem criterion (Barnard, Pothen, and Simon 1993).",
  randomized = TRUE,
  optimizes = .opt("2SUM", "2-sum criterion")
)

set_seriation_method(
  "dist",
  "QAP_LS",
  seriate_dist_LS,
  "Quadratic assignment problem formulation for seriation solved using a simulated annealing solver to minimize the Linear Seriation Problem (LS) criterion (Hubert and Schultz 1976).",
  randomized = TRUE,
  optimizes = .opt("LS", "Linear seriation criterion")
)

set_seriation_method(
  "dist",
  "QAP_BAR",
  seriate_dist_BAR,
  "Quadratic assignment problem formulation for seriation solved using a simulated annealing solver to minimize the banded anti-Robinson form (BAR).",
  .qap_bar_contr,
  randomized = TRUE,
  optimizes = .opt("BAR", "Banded anti-robinson form")
)

set_seriation_method(
  "dist",
  "QAP_Inertia",
  seriate_dist_Inertia,
  "Quadratic assignment problem formulation for seriation solved using a simulated annealing solver to minimize the Inertia criterion.",
  randomized = TRUE,
  optimizes = .opt("Inertia")
)