I refer to this MPML message and to the associated conversation, in particular to the interesting comments made by Aldo Vitagliano, author of Solex orbit simulator, about the difficulty to see a cluster of KBOs.
I do not know the answer but this prompted me to look at the KBO's orbit parameter distribution. What follows next is an exercise ... so I do not claim that it is correct!
I used the Web service made available by MPC to look for KBOs characterized by:
250 AU < a < 1000 AU
I found this list:
Then I used the R package to produce a hierarchical cluster as follows:
1) I scaled the above table so that every column has mean 0 and variance 1.
2) I calculated the distance between any two rows (manhattan distance).
3) I submitted the scaled table to the function hclust choosing clustering method complete.
4) I used a further R function ( see rect.hclust ) to display colored rectangles at different height: the purpose is to help visualize the various clusters at different levels.
I do not know, whether these clusters have a statistical significance or not.
The left cluster maybe interesting: in fact, it consistently maintains its shape even when you cut the dendogram at a level where the second big cluster gets split into 5 subgroups.
The left cluster contains asteroid 2012 VP113 plus other 4 even more similar asteroids.
From now on I will refer to this cluster as "cluster 2" as opposed to "cluster1" made by all other KBOs without further distinctions.
A nice R function is cutree: you can tag the original table with a further column i.e. the cluster where it is supposed to belong. By doing this, you can use, for example, the function ggpairs of the GGally library to make a set of plots like these:
- in the diagonal, you can see the density distribution, each cluster being given a different color. Cluster 2 is coloured in blue.
- above the diagonal: you can see the correlation between pairs of parameters, with cluster detail and total as well.
- below the diagonal: you can see a scatter plot diagram of each pair of parameters, again the colour represents a cluster.
.... and, if you are interested in a specifc plot, you can make it alone with the ggplot function.
- let's see a scatter plot of orbital parameters a and w where we add the name of the asteroids
- finally, let's see the density distribution of orbital parameter w