Calculate the weighted distance from a modified distance matrix

Question

I got a modified distance matrix where I want to use the transformed (normalized) distance in the creation of a variable. Below, I have some code that produces an example data.

set.seed(12)

size <- sample(100:1000, 7)
var <- c("V3", "V4", "V5", "V6", "V7", "V8", "V9")
dist <- matrix(runif(100), nrow = 7, ncol = 7)
diag(dist) <- 0

df <- as.data.frame(cbind(var, size, dist))

This leads to a dataset looking like this:

  var size                  V3                V4                 V5                V6                V7                 V8                V9
1  V3  549                   0 0.264918377622962  0.787836347473785 0.439429325051606 0.941087544662878   0.97763589094393 0.774718186818063
2  V4  445  0.0228777434676886                 0 0.0978530396241695 0.669819295872003 0.693911424372345  0.197649595327675 0.394586439244449
3  V5  435 0.00832482660189271 0.457607151241973                  0 0.240883231163025 0.843702238984406  0.844225987326354 0.361513090785593
4  V6  346   0.392697197152302 0.540707547217607  0.217823043232784                 0 0.384644460165873 0.0950279189273715 0.421090044546872
5  V7  958   0.813880559289828 0.665679829893634  0.267943592974916 0.882756386883557                 0  0.381151003297418 0.322011524345726
6  V8  273    0.37624845537357 0.112698937533423  0.504767951788381 0.814063254510984  0.58848182996735                  0 0.552160830702633
7  V9  552   0.380812183720991  0.21836716751568  0.188586926786229 0.633264608215541 0.530477509833872  0.152623838977888                 0

The data consists of several variables indicating on the distance between the var and different points, where the column called V3 , V4 , and so on, is the other point, ie var == V4 distance to V5 is denoted by the column called V5 . Size denotes the size.

What I want to do is to calculate the weighted sum of distance , where the distance is weighted according to the size of the other point. See the formula below:

where Si is the size of unit i , (the variable is called size ). Di is the normalized distance between one point (ie column var3 , var4 , var5 ...) to the i th point, and the summation is over all k units.

For example, Di can be the distance from the given point V3 to V4 ( 0.264918377622962 ), and then the Si is the size of var == V4 (ie 445 )

How do I perform this calculation when my data looks like this?

Thanks!

Answer 1

Perhaps this is what you are looking for?

Working column-wise, we divide the size of each point by its distance from the column representing the point in question (1:7). Obviously we exclude the diagonal. Summing the result gives us the weighted size for that point

set.seed(12)

size <- sample(100:1000, 7)
var <- c("V3", "V4", "V5", "V6", "V7", "V8", "V9")
dist <- matrix(runif(49), nrow = 7, ncol = 7)
diag(dist) <- 0

df <- as.data.frame(cbind(var, size, dist))

df$WS <- sapply(seq(nrow(df)), 
         function(i) sum(as.numeric(as.character((df[[2]][-i]))) / 
                         as.numeric(as.character(df[[i + 2]][-i]))))

df$WS
#> [1] 75937.840 10052.202 13876.181  6011.826  4144.254 13099.493  7330.831

^{Created on 2020-11-13 by the reprex package (v0.3.0)}