# Unique Jaccardian Distance?

Hi I have a dataset that could be simulated using:

set.seed(123)
v1 <- rbinom(10000, 1, .2)
v2 <- rbinom(10000, 1, .3)
v3 <- rbinom(10000, 1, .25)
v4 <- rbinom(10000, 1, .5)
v5 <- rbinom(10000, 1, .35)
v6 <- rbinom(10000, 1, .2)
v7 <- rbinom(10000, 1, .3)
v8 <- rbinom(10000, 1, .25)
v9 <- rbinom(10000, 1, .5)
v10<- rbinom(10000, 1, .35)
dats <- data.frame(v1,v2,v3,v4,v5,v6,v7,v8,v9,v10)


I am working on using Jaccard distance to create a distance structure as follows:

dat.jac <- philentropy::distance(dats, method = "jaccard")


So here is my question: As these are binary variables, that means there is at most 2^10 = 1024 unique groups. Does this mean that I have over-represented data since I have well over 1024 points? Another way to ask this is do I need to calculate the Jaccard distance of unique observations and use the counts of observations as weights, or can I just calculate the Jaccard distance of each observation (row) to get the distance matrix? In terms of programming, which of the following should I proceed with?

dat.jac <- philentropy::distance(dats, method = "jaccard")


or

dat.jac <- philentropy::distance(unique(dats), method = "jaccard")


My goal is to use the distance matrix in hierarchical clustering using the following code:

dist.jac.mat<- as.matrix(dist.jac)
dist.jac.mat[is.na(dist.jac.mat)] <- 0
hc <- hclust(as.dist(dist.jac.mat), method = "single")
fviz_nbclust(dats, FUN = hcut, diss = as.dist(dist.jac.mat), k.max = 15,
nboot = 250, method = "silhouette")