Finding nearest matching points - r

Question

What I would like to do is for the red points find the nearest equivalent blue dot on the other side of the abline (i.e. 1,5 find 5,1).
Data:
https://1drv.ms/f/s!Asb7WztvacfOuesIq4evh0jjvejZ4Q
Edit: to open data do readRDS("path/to/data")
So what I have tried is to find the difference between the x and y coordinates, rank them and then find the min value going down the ranks for both x and y. The results and pretty bad. The thing I'm struggling with is finding a way to find nearest match of tuples.
My attempt:
find_nearest <- function(query, subject){
weight_df <- data.frame(ID=query$ID)
#find difference of first, then second, rank and find match in both going from top to bottom
tmp_df <- query
for(i in 1:nrow(subject)){
first_order <- order(abs(query$mean_score_n-subject$mean_score_n[i]))
second_order <- order(abs(query$mean_score_p-subject$mean_score_p[i]))
tmp_df$order_1[first_order] <- seq(1, nrow(tmp_df))
tmp_df$order_2[second_order] <- seq(1, nrow(tmp_df))
weight_df[,i+1] <- tmp_df$order_1 + tmp_df$order_2
}
rownames(weight_df) <- weight_df$ID
weight_df$ID <- NULL
print(dim(weight_df))
nearest_match <- list()
count <- 1
subject_ids <- NA
query_ids <- NA
while(ncol(weight_df) > 0 & count <= ncol(weight_df)){
pos <- which(weight_df == min(weight_df, na.rm = TRUE), arr.ind = TRUE)
if(length(unique(rownames(pos))) > 1){
for(i in nrow(pos)){
#if subject/query already used then mask and find another
if(subject$ID[pos[i,2]] %in% subject_ids){
weight_df[pos[i,1],pos[i,2]] <- NA
}else if(query$ID[pos[i,1]] %in% query_ids){
weight_df[pos[i,1],pos[i,2]] <- NA
}else{
subject_ids <- c(subject_ids, subject$ID[pos[i,2]])
query_ids <- c(query_ids, query$ID[pos[i,1]])
nearest_match[[count]] <- data.frame(query=query[pos[i,1],]$ID, subject=subject[pos[i,2],]$ID)
#mask
weight_df[pos[i,1],pos[i,2]] <- NA
count <- count + 1
}
}
}else if(nrow(pos) > 1){
#if subject/query already used then mask and find another
if(subject$ID[pos[1,2]] %in% subject_ids){
weight_df[pos[1,1],pos[1,2]] <- NA
}else if(query$ID[pos[1,1]] %in% query_ids){
weight_df[pos[1,1],pos[1,2]] <- NA
}else{
subject_ids <- c(subject_ids, subject$ID[pos[1,1]])
query_ids <- c(query_ids, query$ID[pos[1,1]])
nearest_match[[count]] <- data.frame(query=query[pos[1,1],]$ID, subject=subject[pos[1,2],]$ID)
#mask
weight_df[pos[1,1],pos[1,2]] <- NA
count <- count + 1
}
}else{
#if subject/query already used then mask and find another
if(subject$ID[pos[2]] %in% subject_ids){
weight_df[pos[1],pos[2]] <- NA
}else if(query$ID[pos[1]] %in% query_ids){
weight_df[pos[1],pos[2]] <- NA
}else{
subject_ids <- c(subject_ids, subject$ID[pos[2]])
query_ids <- c(query_ids, query$ID[pos[1]])
nearest_match[[count]] <- data.frame(query=query[pos[1],]$ID, subject=subject[pos[2],]$ID)
#mask
weight_df[pos[1],pos[2]] <- NA
count <- count + 1
}
}
}
out <- plyr::ldply(nearest_match, rbind)
out <- merge(out, data.frame(subject=subject$ID,
mean_score_p_n=subject$mean_score_p,
mean_score_n_n= subject$mean_score_n), by="subject", all.x=TRUE)
out <- merge(out, data.frame(query=query$ID,
mean_score_p_p=query$mean_score_p,
mean_score_n_p= query$mean_score_n), by="query", all.x=TRUE)
return(out)
}
Edit: is this what the solution looks like for you?
ggplot() +
geom_point(data=B[out,], aes(x=mean_score_p, y= mean_score_n, color="red")) +
geom_point(data=A, aes(x=mean_score_p, y=mean_score_n, color="blue")) +
geom_abline(intercept = 0, slope = 1)

Answer 1

Let
query <- readRDS("query.dms")
subject <- readRDS("subject.dms")
kA <- nrow(subject)
kB <- nrow(query)
A <- as.matrix(subject[, 2:3])
B <- as.matrix(query[, 2:3])
where we want to find the closest "reverse" point (row) in B to each point in A.
Solution permitting non-unique results
Then, assuming that you are using the Euclidean distance,
D <- as.matrix(dist(rbind(A, B[, 2:1])))[(1 + kA):(kA + kB), 1:kA]
unname(apply(D, 2, which.min))
# [1] 268 183 350 284 21 360 132 287 100 298 58 56 170 70 47 305 353
# [18] 43 266 198 58 215 198 389 412 321 255 181 79 340 292 268 198 54
# [35] 390 38 376 47 19 94 244 18 168 201 160 194 114 247 287 273 182
# [52] 87 94 87 192 63 160 244 101 298 62
are the corresponding row numbers in B. The trick was to switch the coordinates of the points in B by using B[, 2:1].
Solution with unique results
out <- vector("numeric", length = kA)
colnames(D) <- 1:ncol(D)
rownames(D) <- 1:nrow(D)
while(any(out == 0))
for(i in 1:nrow(D)) {
aux <- apply(D, 2, which.min)
if(i %in% aux) {
win <- which(aux == i)[which.min(D[i, aux == i])]
out[as.numeric(names(win))] <- as.numeric(rownames(D)[i])
D <- D[-i, -win, drop = FALSE]
}
}
out
# [1] 268 183 350 284 21 360 132 213 100 298 22 56 170 70 128 305 353
# [18] 43 266 198 58 215 294 389 412 321 255 181 79 340 292 20 347 54
# [35] 390 38 376 47 19 94 73 18 168 201 160 194 114 247 287 273 182
# [52] 87 365 158 192 63 211 244 101 68 62
whereas
all(table(res) == 1)
# [1] TRUE
confirms uniqueness. The solution is not the most efficient, but on your dataset it takes only a couple of seconds. It takes some time because it keeps going over all the available points in B checking if it is the closest one to any of the points in A. If so, the corresponding point in B is assigned to the closest one in A. Then both the point in A and the point in B are eliminated from the distance matrix. The loop goes until every point in A has some match in B.