# Understanding the kdist graph used to select DBSCAN epsilon parameter

I need to use DBSCAN for my research and am having trouble understanding the kdist graph used to select the epsilon parameter - specifically, I do not understand what is happening behind the scenes and what is being presented on the X axis. I am using R and the DBSCAN library.

I am currently just trying to understand the help presented in the documentation when I run the following code:

help(KNNdistplot)


This is the sample code:

data(iris)
iris <- as.matrix(iris[,1:4])

kNNdist(iris, k=4, search="kd")
kNNdistplot(iris, k=4)
## the knee is around a distance of .5


Which produces the following output:

My questions:

1. The 'iris' object is a matrix containing four columns of 150 observations. I am very confused as to what 'distance' the algorithm is calculating given the number of columns present. Which one is it using? When I think of distance, I think of calculating the distance between two points (in my case, typically lat/long) using the standard formula:

$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Which is clearly not what's going on here as when I test the kNNdist function on a subset of the iris matrix containing only one column, it still produces a result. Is there another definition of 'neighbor' that I am just completely not understanding here?

1. I also do not understand the X axis - what does 'Points (sample) sorted by distance' mean?

2. The data set that I ultimately need to run DBSCAN on is spatial (lat/long) - does this change how epsilon would be calculated?

3. My background is in geography, and I'm slowly starting to move towards the more quantitative side of things, so I tend to think spatially. When this package is referring to 'neighbor', what exactly do they mean? I tend to think of neighbors as points nearby in space, i.e. lat/long that are close together.

Thanks in advance for any help. I'm sure this is probably a simple concept that is flying about 10,000 feet above my head.