In the multi-ellipsoidal algorithm, a cluster must have a minimum of ndim+1 member points. This means that two widely separated modes will not be split into separate clusters if one mode has only a few points.
For example, in 2-d, here is how two modes are separated when the lower peak has 3 points:
On a later iteration, one of the 3 points in the lower peak is discarded due to having the lowest likelihood. At that point, the separation looks like:
Possible Solution 1: "Freeze" bounding ellipsoid for clusters that have ndim + 1 points. That ellipsoid will be used until all its points disappear. A little distatesful because it makes the ellipsoid decomposition "stateful": You can't just look at a set of points and see how the bounding ellipsoids will look - the answer depends on previous iterations.
Possible solution 2: Relax requirement of clusters having ndim + 1 points. Would expand ellipsoid dimensions to fulfill a target volume. May lead to oversplitting into too many ellipsoids.
DBSCAN for mode identification might help with this. (If DBSCAN identifies a mode, always split, even if there are <= ndim points.)
A good test case to see how big a problem this is would be two N-d gaussians of different heights.
In the multi-ellipsoidal algorithm, a cluster must have a minimum of ndim+1 member points. This means that two widely separated modes will not be split into separate clusters if one mode has only a few points.
For example, in 2-d, here is how two modes are separated when the lower peak has 3 points:
On a later iteration, one of the 3 points in the lower peak is discarded due to having the lowest likelihood. At that point, the separation looks like:
Possible Solution 1: "Freeze" bounding ellipsoid for clusters that have ndim + 1 points. That ellipsoid will be used until all its points disappear. A little distatesful because it makes the ellipsoid decomposition "stateful": You can't just look at a set of points and see how the bounding ellipsoids will look - the answer depends on previous iterations.
Possible solution 2: Relax requirement of clusters having ndim + 1 points. Would expand ellipsoid dimensions to fulfill a target volume. May lead to oversplitting into too many ellipsoids.
DBSCAN for mode identification might help with this. (If DBSCAN identifies a mode, always split, even if there are <= ndim points.)
A good test case to see how big a problem this is would be two N-d gaussians of different heights.