# Clustering sets of bounded points

That's a clustering problem.

How can we clusterize a union of clusters that are bounded boxes in N dimensions.

More explicitly, the data is generated the following way: $$N$$ is an arbitrary integer being the number of dimensions $$k$$ is the number of clusters For $$i$$ from $$1$$ to $$k$$, we define the $$i$$th cluster as :

For $$d$$ from $$1$$ to $$N$$, draw $$m_{i, d}$$ and $$M_{i, d}$$ the bounds of the cluster $$i$$ on dimension $$d$$. Then, draw a random number of points $$x = (x_1, ..., x_N)$$ in $$\mathbb{R}^N$$ such that, for all $$d$$, $$m_{i, d} < x_d < M_{i, d}$$

So the data is a union of clusters that are bounded boxes in $$N$$ dimensions.

The number of clusters is unknown and possibly large (up to 10.000).

So far, I tried density based clustering algorithm like DBSCAN and HDBSCAN but the problem is that it's hard to define distances on this dataset, I have some variable that are much larger than the others and the algorithm use the bigger variable more often. I tried to normalize the data but it didn't help that much.

As the data is very structure (bounded boxes), I think there might be better algorithm that would exploit that.

How can we clusterize datas of this type ?

• Why are distances hard to define? Commented Nov 11, 2019 at 13:53