#' @title Pairwise Jaccard Coefficients
#'
#' @description
#' Calculates the similarity of all pairwise topic combinations using a modified
#' Jaccard Coefficient.
#'
#' @details
#' The modified Jaccard Coefficient for two topics \eqn{\bm z_{i}} and
#' \eqn{\bm z_{j}} is calculated by
#' \deqn{J_m(\bm z_{i}, \bm z_{j} \mid \bm c) = \frac{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\wedge~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}{\sum_{v = 1}^{V} 1_{\left\{n_{i}^{(v)} > c_i ~\vee~ n_{j}^{(v)} > c_j\right\}}\left(n_{i}^{(v)}, n_{j}^{(v)}\right)}}
#' with \eqn{V} is the vocabulary size and \eqn{n_k^{(v)}} is the count of
#' assignments of the \eqn{v}-th word to the \eqn{k}-th topic. The threshold vector \eqn{\bm c}
#' is determined by the maximum threshold of the user given lower bounds \code{limit.rel}
#' and \code{limit.abs}. In addition, at least \code{atLeast} words per topic are
#' considered for calculation. According to this, if there are less than
#' \code{atLeast} words considered as relevant after applying \code{limit.rel}
#' and \code{limit.abs} the \code{atLeast} most common words per topic are taken
#' to determine topic similarities.
#'
#' The procedure of determining relevant words is executed for each topic individually.
#' The values \code{wordslimit} and \code{wordsconsidered} describes the number
#' of relevant words per topic.
#'
#' @family TopicSimilarity functions
#' @family workflow functions
#'
#' @param topics [\code{named matrix}]\cr
#' The counts of vocabularies/words (row wise) in topics (column wise).
#' @param limit.rel [0,1]\cr
#' A relative lower bound limit for which words are taken into account. Those words
#' are taken as relevant for a topic that have a count higher than \code{limit.rel}
#' multiplied by the total count of the given topic. Default is \code{1/500}.
#' @param limit.abs [\code{integer(1)}]\cr
#' An absolute lower bound limit for which words are taken into account. All words
#' are taken as relevant for a topic that have a count higher than \code{limit.abs}.
#' Default is \code{10}.
#' @param atLeast [\code{integer(1)}]\cr
#' An absolute count of how many words are at least considered as relevant for a topic.
#' Default is \code{0}.
#' @param progress [\code{logical(1)}]\cr
#' Should a nice progress bar be shown? Turning it off, could lead to significantly
#' faster calculation. Default is \code{TRUE}.
#' If \code{pm.backend} is set, parallelization is done and no progress bar will be shown.
#' @param pm.backend [\code{character(1)}]\cr
#' One of "multicore", "socket" or "mpi".
#' If \code{pm.backend} is set, \code{\link[parallelMap]{parallelStart}} is
#' called before computation is started and \code{\link[parallelMap]{parallelStop}}
#' is called after.
#' @param ncpus [\code{integer(1)}]\cr
#' Number of (physical) CPUs to use. If \code{pm.backend} is passed,
#' default is determined by \code{\link[future]{availableCores}}.
#' @return [\code{named list}] with entries
#' \describe{
#' \item{\code{sims}}{[\code{lower triangular named matrix}] with all pairwise
#' jaccard similarities of the given topics.}
#' \item{\code{wordslimit}}{[\code{integer}] with counts of words determined as
#' relevant based on \code{limit.rel} and \code{limit.abs}.}
#' \item{\code{wordsconsidered}}{[\code{integer}] with counts of considered
#' words for similarity calculation. Could differ from \code{wordslimit}, if
#' \code{atLeast} is greater than zero.}
#' \item{\code{param}}{[\code{named list}] with parameter specifications for
#' \code{type} [\code{character(1)}] \code{= "Jaccard Coefficient"},
#' \code{limit.rel} [0,1], \code{limit.abs} [\code{integer(1)}] and
#' \code{atLeast} [\code{integer(1)}]. See above for explanation.}
#' }
#'
#' @examples
#' res = LDARep(docs = reuters_docs, vocab = reuters_vocab, n = 4, K = 10, num.iterations = 30)
#' topics = mergeTopics(res, vocab = reuters_vocab)
#' jacc = jaccardTopics(topics, atLeast = 2)
#' jacc
#'
#' n1 = getConsideredWords(jacc)
#' n2 = getRelevantWords(jacc)
#' (n1 - n2)[n1 - n2 != 0]
#'
#' sim = getSimilarity(jacc)
#' dim(sim)
#'
#' # Comparison to Cosine and Jensen-Shannon (more interesting on large datasets)
#' cosine = cosineTopics(topics)
#' js = jsTopics(topics)
#'
#' sims = list(jaccard = sim, cosine = getSimilarity(cosine), js = getSimilarity(js))
#' pairs(do.call(cbind, lapply(sims, as.vector)))
#'
#' @export jaccardTopics
jaccardTopics = function(topics, limit.rel, limit.abs, atLeast, progress = TRUE,
pm.backend, ncpus){
if (missing(limit.rel)) limit.rel = .defaultLimit.rel()
if (missing(limit.abs)) limit.abs = .defaultLimit.abs()
if (missing(atLeast)) atLeast = .defaultAtLeast()
assert_matrix(topics, mode = "integerish", any.missing = FALSE,
col.names = "strict", min.cols = 2, min.rows = 2)
assert_integerish(topics, lower = 0, any.missing = FALSE)
assert_flag(progress)
assert_number(limit.rel, lower = 0, upper = 1)
assert_int(limit.abs, lower = 0)
assert_int(atLeast, lower = 0, upper = nrow(topics))
if (missing(ncpus)) ncpus = NULL
if (!missing(pm.backend) && !is.null(pm.backend)){
jaccardTopics.parallel(topics = topics, limit.rel = limit.rel, limit.abs = limit.abs,
atLeast = atLeast, pm.backend = pm.backend, ncpus = ncpus)
}else{
jaccardTopics.serial(topics = topics, limit.rel = limit.rel, limit.abs = limit.abs,
atLeast = atLeast, progress = progress)
}
}
#' @export
print.TopicSimilarity = function(x, ...){
elements = paste0("\"", names(which(!sapply(x, is.null))), "\"")
cat(
"TopicSimilarity Object with element(s)\n",
paste0(elements, collapse = ", "), "\n ",
nrow(getSimilarity(x)), " Topics from ",
length(unique(sapply(strsplit(colnames(getSimilarity(x)), "\\."), function(x) x[1]))),
" independent runs\n ",
round(mean(getConsideredWords(x)), 2), " (SD: ",
round(sd(getConsideredWords(x)), 2),") mean considered Words per Topic\n ",
paste0(paste0(names(getParam(x)), ": ", unlist(getParam(x))), collapse = ", "),
"\n\n", sep = ""
)
}
jaccardTopics.parallel = function(topics, limit.rel, limit.abs, atLeast, pm.backend, ncpus){
assert_choice(pm.backend, choices = c("multicore", "socket", "mpi"))
if (missing(ncpus) || is.null(ncpus)) ncpus = future::availableCores()
assert_int(ncpus, lower = 1)
N = ncol(topics)
if(ncpus > N-2){
ncpus = N-2
message("The selected number of cores exceeds the parallelizable complexity of the task, set ncpus to ", ncpus, ".")
}
if(ncpus == 1){
message("There is only one core on the running system or one core selected, falling back to serial version.")
jaccardTopics.serial(topics = topics, limit.rel = limit.rel, limit.abs = limit.abs,
atLeast = atLeast)
}
index = topics > limit.abs &
topics > rep(colSums(topics)*limit.rel, each = nrow(topics))
wordsconsidered = colSums(index)
ind = wordsconsidered < atLeast
if (any(ind)){
index[,ind] = apply(as.matrix(topics[,ind]), 2,
function(x) x >= -sort.int(-x, partial = atLeast)[atLeast])
}
parallelMap::parallelStart(mode = pm.backend, cpus = ncpus)
fun = function(s){
lapply(s, function(i)
colSums(index[,i] * index[,(i+1):N]) / colSums((index[,i] + index[,(i+1):N]) > 0))
}
parallelMap::parallelExport("index", "N")
sequences = lapply(seq_len(max(ncpus, 2)), function(x) seq(x, N-2, max(ncpus, 2)))
val = parallelMap::parallelMap(fun = fun, sequences)
parallelMap::parallelStop()
rearrangedlist = list()
for (i in seq_along(sequences)){
rearrangedlist[sequences[[i]]] = val[[i]]
}
rm(val)
sims = matrix(nrow = N, ncol = N)
colnames(sims) = rownames(sims) = colnames(topics)
sims[lower.tri(sims)] = c(unlist(rearrangedlist),
sum(index[, N] & index[, N-1]) / sum(index[, N] | index[, N-1]))
sims[is.nan(sims)] = 0
res = list(sims = sims, wordslimit = wordsconsidered, wordsconsidered = colSums(index),
param = list(type = "Jaccard Coefficient",
limit.rel = limit.rel, limit.abs = limit.abs, atLeast = atLeast))
class(res) = "TopicSimilarity"
res
}
jaccardTopics.serial = function(topics, limit.rel, limit.abs, atLeast, progress = TRUE){
N = ncol(topics)
index = topics > limit.abs &
topics > rep(colSums(topics)*limit.rel, each = nrow(topics))
wordsconsidered = colSums(index)
ind = wordsconsidered < atLeast
if (any(ind)){
index[,ind] = apply(as.matrix(topics[,ind]), 2,
function(x) x >= -sort.int(-x, partial = atLeast)[atLeast])
}
sims = matrix(nrow = N, ncol = N)
colnames(sims) = rownames(sims) = colnames(topics)
pb = .makeProgressBar(progress = progress,
total = N-1, format = "Calculate Similarities [:bar] :percent eta: :eta")
for(i in seq_len(N - 2)){
sims[(i+1):N,i] = colSums(index[,i] * index[,(i+1):N]) / colSums((index[,i] + index[,(i+1):N]) > 0)
pb$tick()
}
sims[N, N-1] = sum(index[, N] & index[, N-1]) / sum(index[, N] | index[, N-1])
pb$tick()
sims[is.nan(sims)] = 0
res = list(sims = sims, wordslimit = wordsconsidered, wordsconsidered = colSums(index),
param = list(type = "Jaccard Coefficient",
limit.rel = limit.rel, limit.abs = limit.abs, atLeast = atLeast))
class(res) = "TopicSimilarity"
res
}
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