Mean-Shift Clustering

Mean shift finds clusters without being told how many there are: every point climbs uphill on the estimated density until it reaches a peak (a mode), and points that reach the same mode form a cluster.

Implement mean_shift(X, bandwidth, tol=1e-5, max_iter=300):

1. Start a copy of every point. Repeatedly move each copy to the Gaussian-weighted mean of the original points, with weights $\exp(-\lVert x - c\rVert^2 / (2h^2))$, until every copy moves less than tol (or max_iter is reached).
2. Merge modes: scan the converged points in order. A point joins the first existing centre within bandwidth / 2; otherwise it becomes a new centre.
3. Return (centres, labels), with centres as an array in order of creation.