#' mapper2D function
#'
#' This function uses a filter function f: X -> R^2 on a data set X that has n rows (observations) and k columns (variables).
#'
#' @param distance_matrix an n x n matrix of pairwise dissimilarities
#' @param filter_values a list of two length n vector of real numbers
#' @param num_intervals a vector of two positive integers
#' @param percent_overlap a number between 0 and 100 specifying how much adjacent intervals should overlap
#' @param num_bins_when_clustering a positive integer that controls whether points in the same level set end up in the same cluster
#'
#' @return An object of class \code{TDAmapper} which is a list of items named \code{adjacency} (adjacency matrix for the edges), \code{num_vertices} (integer number of vertices), \code{level_of_vertex} (vector with \code{level_of_vertex[i]} = index of the level set for vertex i), \code{points_in_vertex} (list with \code{points_in_vertex[[i]]} = vector of indices of points in vertex i), \code{points_in_level} (list with \code{points_in_level[[i]]} = vector of indices of points in level set i, and \code{vertices_in_level} (list with \code{vertices_in_level[[i]]} = vector of indices of vertices in level set i.
#'
#' @author Paul Pearson, \email{pearsonp@@hope.edu}
#' @references \url{https://github.com/paultpearson/TDAmapper}
#' @seealso \code{\link{mapper1D}}
#' @keywords mapper2D
#'
#' @examples
#' m2 <- mapper2D(
#' distance_matrix = dist(data.frame( x=2*cos(1:100), y=sin(1:100) )),
#' filter_values = list( 2*cos(1:100), sin(1:100) ),
#' num_intervals = c(5,5),
#' percent_overlap = 50,
#' num_bins_when_clustering = 10)
#' \dontrun{
#' library(igraph)
#' g2 <- graph.adjacency(m2$adjacency, mode="undirected")
#' plot(g2, layout = layout.auto(g2) )
#' }
#' @export
#'
mapper2D <- function(
distance_matrix = dist(data.frame( x=2*cos(1:100), y=sin(1:100) )),
filter_values = list( 2*cos(1:100), sin(1:100) ),
num_intervals = c(5,5),
percent_overlap = 50,
num_bins_when_clustering = 10
) {
# initialize variables
vertex_index <- 0
# indexed from 1 to the number of vertices
level_of_vertex <- c()
points_in_vertex <- list()
# filter_values_in_vertex <- list() # just use filter_values[points_in_vertex[[i]]]
# indexed from 1 to the number of levels
points_in_level <- list()
vertices_in_level <- list()
# filter_values_in_level <- list() # just use filter_values[points_in_level[[i]]]
filter_min_1 <- min(filter_values[[1]])
filter_max_1 <- max(filter_values[[1]])
filter_min_2 <- min(filter_values[[2]])
filter_max_2 <- max(filter_values[[2]])
interval_length_1 <- (filter_max_1 - filter_min_1) / (num_intervals[1] - (num_intervals[1] - 1) * percent_overlap/100 )
interval_length_2 <- (filter_max_2 - filter_min_2) / (num_intervals[2] - (num_intervals[2] - 1) * percent_overlap/100 )
step_size_1 <- interval_length_1 * (1 - percent_overlap/100)
step_size_2 <- interval_length_2 * (1 - percent_overlap/100)
num_levels <- num_intervals[1] * num_intervals[2]
# level_index_matrix <- matrix(1:num_levels, num_intervals[1], num_intervals[2])
#
# Given any sequential index i in 1:num_levels,
# you can get the ordered pair index (row_index,col_index) by
# row_index <- which(level_index_matrix == i, arr.ind=TRUE)[1]
# col_index <- which(level_index_matrix == i, arr.ind=TRUE)[2]
#
# Given any ordered pair index (row_index,col_index),
# you can get the sequential index i in 1:num_levels by
# i <- level_index_matrix[row_index,col_index]
# Given any sequential index i in 1:num_levels,
# "row_index" = level_indices_1[i]
# "col_index" = level_indices_2[i]
level_indices_1 <- rep(1:num_intervals[1], num_intervals[2])
level_indices_2 <- rep(1:num_intervals[2], each=num_intervals[1])
# begin mapper main loop
for (level in 1:num_levels) {
level_1 <- level_indices_1[level]
level_2 <- level_indices_2[level]
min_value_in_level_1 <- filter_min_1 + (level_1 - 1) * step_size_1
min_value_in_level_2 <- filter_min_2 + (level_2 - 1) * step_size_2
max_value_in_level_1 <- min_value_in_level_1 + interval_length_1
max_value_in_level_2 <- min_value_in_level_2 + interval_length_2
points_in_level_logical <-
(min_value_in_level_1 <= filter_values[[1]]) &
(min_value_in_level_2 <= filter_values[[2]]) &
(filter_values[[1]] <= max_value_in_level_1) &
(filter_values[[2]] <= max_value_in_level_2)
num_points_in_level <- sum(points_in_level_logical)
points_in_level[[level]] <- which(points_in_level_logical==TRUE)
if (num_points_in_level == 0) {
print('Level set is empty')
vertices_in_level[[level]] <- -1 # Bertrand Michel's suggestion for empty levels: use flag -1
next
}
if (num_points_in_level == 1) {
print('Level set has only one point')
num_vertices_in_level <- 1
cluster_indices_within_level <- c(1)
vertices_in_level[[level]] <- vertex_index + (1:num_vertices_in_level)
}
if (num_points_in_level > 1) {
# use as.matrix() to put the distance matrix in square form,
# and as.dist() to put it in vector form
# This could probably use some optimization...
level_distance_matrix <- as.dist(as.matrix(distance_matrix)[points_in_level_logical,points_in_level_logical])
level_max_distance <- max(level_distance_matrix)
# use R's hclust (provided by stats or fastcluster)
# in place of Matlab's linkage function.
level_hcluster_ouput <- hclust(level_distance_matrix,method="single")
heights <- level_hcluster_ouput$height
cutoff <- cluster_cutoff_at_first_empty_bin(heights, level_max_distance, num_bins_when_clustering)
# use as.vector() to get rid fo the names for the vector entries
cluster_indices_within_level <- as.vector( cutree(level_hcluster_ouput, h=cutoff) )
num_vertices_in_level <- max( cluster_indices_within_level )
vertices_in_level[[level]] <- vertex_index + (1:num_vertices_in_level)
# points_in_level[[level]] and cluster_indices_within_level have the same length.
# heights has length 1 less than points_in_level[[level]] and cluster_indices_within_level
# print(heights)
# print(points_in_level[[level]])
# print(cluster_indices_within_level)
}
for (j in 1:num_vertices_in_level) {
vertex_index <- vertex_index + 1
# points_in_level_logical is a logical vector, so use which(points_in_level_logical==TRUE) to convert it to a numerical vector of indices
#nodeset <- which(points_in_level_logical==TRUE)[cluster_indices_within_level == j]
level_of_vertex[vertex_index] <- level
points_in_vertex[[vertex_index]] <- which(points_in_level_logical==TRUE)[cluster_indices_within_level == j]
#points_in_vertex[[vertex_index]] <- nodeset
#filter_values_in_vertex[[vertex_index]] <- filter_values[nodeset]
}
} # end mapper main loop
# Note: num_vertices = vertex index.
# Create the adjacency matrix for the graph, starting with a matrix of zeros
adja <- mat.or.vec( vertex_index, vertex_index )
for (i in 1:num_intervals[1]) {
for (j in 2:num_intervals[2]) {
# For adjacent level sets L_{i,j} and L_{i,j-1}, get the sequential index values k1 and k2
k1 <- which( (level_indices_1 == i) & (level_indices_2 == j) )
k2 <- which( (level_indices_1 == i) & (level_indices_2 == j-1))
# check that both level sets are nonemtpy
if ( (vertices_in_level[[k1]][1] != -1) & (vertices_in_level[[k2]][1] != -1) ) {
for (v1 in vertices_in_level[[k1]]) {
for (v2 in vertices_in_level[[k2]]) {
# return 1 if the intersection is nonempty
adja[v1,v2] <- ( length(intersect(points_in_vertex[[v1]],
points_in_vertex[[v2]])) > 0 )
adja[v2,v1] <- adja[v1,v2]
}
}
}
} # end part 1 of constructing adjacency matrix
}
for (j in 1:num_intervals[2]) {
for (i in 2:num_intervals[1]) {
# For adjacent level sets L_{i,j} and L_{i-1,j}, get the sequential index values k1 and k2
k1 <- which( (level_indices_1 == i) & (level_indices_2 == j) )
k2 <- which( (level_indices_1 == i-1) & (level_indices_2 == j))
# check that both level sets are nonemtpy
if ( (vertices_in_level[[k1]][1] != -1) & (vertices_in_level[[k2]][1] != -1) ) {
for (v1 in vertices_in_level[[k1]]) {
for (v2 in vertices_in_level[[k2]]) {
# return 1 if the intersection is nonempty
adja[v1,v2] <- ( length(intersect(points_in_vertex[[v1]],
points_in_vertex[[v2]])) > 0 )
adja[v2,v1] <- adja[v1,v2]
}
}
}
} # end part 2 of constructing adjacency matrix
}
mapperoutput <- list(adjacency = adja,
num_vertices = vertex_index,
level_of_vertex = level_of_vertex,
points_in_vertex = points_in_vertex,
#filter_values_in_vertex = filter_values_in_vertex,
points_in_level = points_in_level,
vertices_in_level = vertices_in_level
)
class(mapperoutput) <- "TDAmapper"
return(mapperoutput)
} # end mapper2D function
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