Suppose I have a data of 1000 random values ranging from 0 to 100, I want to detect clusters in the data with numbers near to each other. I decide how near, for example not more than 2.5 of difference to each other. I don't pre-settle the ammount of clusters (I want to detect them!) and I don't settle central values from which to pick the 2.5 numbers as in threshold. Is this possible to do?
The number of cluster resulting can be any number, even 1 cluster or 1000 clusters, it's all up to the 2.5 or the difference that I select.
This is easy.
Sort the values increasingly. Every time two successive values are spaced by more than $2.5$ units, split.