Calinski-Harabasz index

Intermediate Netflix, Spotify+5

The problem, from first principles

A good clustering has tight clusters that sit far from one another. The Calinski-Harabasz index (also called the variance ratio criterion) makes that precise: it compares between-cluster dispersion with within-cluster dispersion, each scaled by its degrees of freedom. Higher means a better-defined partition.

Implement calinski_harabasz_index(X, labels).

B = Σ_k n_k ‖c_k − c‖², where c_k are cluster centroids and c is the overall mean.
W = Σ_k Σ_{x in cluster k} ‖x − c_k‖².
Return (B / (k − 1)) / (W / (n − k)).

Constraints

Fewer than two clusters, or as many clusters as points, raises ValueError.
If W is zero, return inf.

Hints

Open one at a time. Each gives away a little more than the last.

Hint 1

Compute the overall mean once, then each cluster's centroid and size with a boolean mask.

Hint 2

Squared distances are cheaper to sum than distances here. np.sum((A - B) ** 2) works on the whole cluster at once.

Keywords

classical-mlunsupervisedclusteringevaluation

Python

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