我对使用自定义距离函数计算距离矩阵感兴趣。此函数应考虑空间数据和两个控制变量。此距离可以是欧几里得距离。详细信息如下：
我有一个卖家和买家的数据。这个空间数据集包含城市、坐标、购买数量和两个控制变量。我想应用一个层次聚类来确定“地理市场”。为此，我想计算一个考虑了我提到的两个控制变量的距离矩阵。
我试过这样做，但我不确定我是否正确使用对象W。

# Sample data (because is private info).
set.seed(123)
n <- 100
cities <- c("City1", "City2", "City3", "City4", "City5")
seller_city <- sample(cities, n, replace = TRUE)
buyer_city <- sample(cities, n, replace = TRUE)
seller_coords <- data.frame(lon = rnorm(n, -80, 1), lat = rnorm(n, 40, 1))
buyer_coords <- data.frame(lon = rnorm(n, -80, 1), lat = rnorm(n, 40, 1))
quantity <- rpois(n, 10)
var1 <- rnorm(n, 0, 1) #First control variable.
var2 <- rnorm(n, 0, 1) #Second control variable.
df <- data.frame(seller_city, buyer_city, seller_coords, buyer_coords, quantity, var1, var2)

# Compute distance matrix
city_dist <- distm(x =df[,c("lon", "lat")] ,
                             y = df[,c("lon.1", "lat.1")])
city_dist <- (city_dist - mean(city_dist)) / sd(city_dist) #Normalising, because its units differ to the control variables.
var_dist <- as.matrix(dist(df %>% select(var1, var2)))
var_dist <- (var_dist - mean(var_dist)) / sd(var_dist) #Normalising, because its units differ to the control variables.
W <- city_dist + var_dist # sum up

# Perform hierarchical clustering
hc <- hclust(as.dist(W), 
             method = "ward.D2")

其思想是用以下公式计算城市 i 和 j 之间的距离：

其中，x 是经度，y 是纬度，v1 是控制变量1，并且 v2 是控制变量2。