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 ?
