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```
#######################################################################
# dbscan - Density Based Clustering of Applications with Noise
# and Related Algorithms
# Copyright (C) 2017 Michael Hahsler
# 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.
# number of shared nearest neighbors including the point itself.
#' Find Shared Nearest Neighbors
#'
#' Calculates the number of shared nearest neighbors, the shared nearest
#' neighbor similarity and creates a shared nearest neighbors graph.
#'
#' The number of shared nearest neighbors is the intersection of the kNN
#' neighborhood of two points. Note: that each point is considered to be part
#' of its own kNN neighborhood. The range for the shared nearest neighbors is
#' \eqn{[0, k]}.
#'
#' Javis and Patrick (1973) use the shared nearest neighbor graph for
#' clustering. They only count shared neighbors between points that are in each
#' other's kNN neighborhood.
#'
#' @aliases sNN snn
#' @family NN functions
#'
#' @param x a data matrix, a [dist] object or a [kNN] object.
#' @param k number of neighbors to consider to calculate the shared nearest
#' neighbors.
#' @param kt minimum threshold on the number of shared nearest neighbors to
#' build the shared nearest neighbor graph. Edges are only preserved if
#' `kt` or more neighbors are shared.
#' @param jp use the definition by Javis and Patrick (1973), where shared
#' neighbors are only counted between points that are in each other's
#' neighborhood, otherwise 0 is returned. If `FALSE`, then the number of shared
#' neighbors is returned, even if the points are not neighbors.
#' @param search nearest neighbor search strategy (one of `"kdtree"`, `"linear"` or
#' `"dist"`).
#' @param sort sort by the number of shared nearest neighbors? Note that this
#' is expensive and `sort = FALSE` is much faster. sNN objects can be
#' sorted using `sort()`.
#' @param bucketSize max size of the kd-tree leafs.
#' @param splitRule rule to split the kd-tree. One of `"STD"`, `"MIDPT"`, `"FAIR"`,
#' `"SL_MIDPT"`, `"SL_FAIR"` or `"SUGGEST"` (SL stands for sliding). `"SUGGEST"` uses
#' ANNs best guess.
#' @param approx use approximate nearest neighbors. All NN up to a distance of
#' a factor of `(1 + approx) eps` may be used. Some actual NN may be omitted
#' leading to spurious clusters and noise points. However, the algorithm will
#' enjoy a significant speedup.
#' @param decreasing logical; sort in decreasing order?
#' @param ... additional parameters are passed on.
#' @return An object of class `sNN` (subclass of [kNN] and [NN]) containing a list
#' with the following components:
#' \item{id }{a matrix with ids. }
#' \item{dist}{a matrix with the distances. }
#' \item{shared }{a matrix with the number of shared nearest neighbors. }
#' \item{k }{number of `k` used. }
#'
#' @author Michael Hahsler
#' @references R. A. Jarvis and E. A. Patrick. 1973. Clustering Using a
#' Similarity Measure Based on Shared Near Neighbors. _IEEE Trans. Comput._
#' 22, 11 (November 1973), 1025-1034.
#' \doi{10.1109/T-C.1973.223640}
#' @keywords model
#' @examples
#' data(iris)
#' x <- iris[, -5]
#'
#' # finding kNN and add the number of shared nearest neighbors.
#' k <- 5
#' nn <- sNN(x, k = k)
#' nn
#'
#' # shared nearest neighbor distribution
#' table(as.vector(nn$shared))
#'
#' # explore neighborhood of point 10
#' i <- 10
#' nn$shared[i,]
#'
#' plot(nn, x)
#'
#' # apply a threshold to create a sNN graph with edges
#' # if more than 3 neighbors are shared.
#' nn_3 <- sNN(nn, kt = 3)
#' plot(nn_3, x)
#'
#' # get an adjacency list for the shared nearest neighbor graph
#' adjacencylist(nn_3)
#' @export
sNN <- function(x,
k,
kt = NULL,
jp = FALSE,
sort = TRUE,
search = "kdtree",
bucketSize = 10,
splitRule = "suggest",
approx = 0) {
if (missing(k))
k <- x$k
if (inherits(x, "kNN")) {
if (k != x$k) {
if (ncol(x$id) < k)
stop("kNN object does not contain enough neighbors!")
if (!x$sort)
x <- sort.kNN(x)
x$id <- x$id[, 1:k]
x$dist <- x$dist[, 1:k]
x$k <- k
}
} else
x <-
kNN(
x,
k,
sort = FALSE,
search = search,
bucketSize = bucketSize,
splitRule = splitRule,
approx = approx
)
x$shared <- SNN_sim_int(x$id, as.logical(jp[1]))
x$sort_shared <- FALSE
class(x) <- c("sNN", "kNN", "NN")
if (sort)
x <- sort.sNN(x)
x$kt <- kt
if (!is.null(kt)) {
if (kt > k)
stop("kt needs to be less than k.")
rem <- x$shared < kt
x$id[rem] <- NA
x$dist[rem] <- NA
x$shared[rem] <- NA
}
x
}
#' @rdname sNN
#' @export
sort.sNN <- function(x, decreasing = TRUE, ...) {
if (!is.null(x$sort_shared) && x$sort_shared)
return(x)
if (is.null(x$shared))
stop("Unable to sort. Number of shared neighbors is missing.")
if (ncol(x$id) < 2) {
x$sort <- TRUE
x$sort_shared <- TRUE
return(x)
}
## sort first by number of shared points (decreasing) and break ties by id (increasing)
k <- ncol(x$shared)
o <- sapply(
1:nrow(x$shared),
FUN =
function(i)
order(k - x$shared[i, ], x$id[i, ], decreasing = !decreasing)
)
for (i in 1:ncol(o)) {
x$shared[i, ] <- x$shared[i, ][o[, i]]
x$dist[i, ] <- x$dist[i, ][o[, i]]
x$id[i, ] <- x$id[i, ][o[, i]]
}
x$sort <- FALSE
x$sort_shared <- TRUE
x
}
#' @rdname sNN
#' @export
print.sNN <- function(x, ...) {
cat(
"shared-nearest neighbors for ",
nrow(x$id),
" objects (k=",
x$k,
", kt=",
ifelse(is.null(x$kt), "NULL", x$kt),
").",
"\n",
sep = ""
)
cat("Available fields: ", paste(names(x), collapse = ", "), "\n", sep = "")
}
```

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