Seeded k-means with fixed seed points

Cluster with a few labeled seeds that never move

Seeded k-means (Basu, Banerjee and Mooney, 2002) starts each cluster from the mean of its labeled seeds. During the iterations, seeded points keep their label, and unlabeled points are assigned to their nearest centroid.

Implement seeded_kmeans(X, seeds, k, iters=100).

• X is (N, d). seeds is (N,) with class indices 0..k-1 for seeded points and -1 for unlabeled points.
• Initialize each centroid as the mean of its seeded points.
• Repeat: assign each unlabeled point to its nearest centroid (seeded points keep their label), then recompute each centroid as the mean of its assigned points. Stop when no label changes or after iters rounds.
• Return (labels, centroids). labels is an integer array of length N, and centroids is (k, d).

Constraints

• Every class 0..k-1 must have at least one seed. Otherwise raise ValueError.
• A seed value outside -1..k-1 raises ValueError.
• Shapes must be consistent. Otherwise raise ValueError.
• k >= 1 and iters >= 1.
• Do not modify the inputs.

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