Nearest centroid classifier

The problem, from first principles

01-knn predicts by comparing a query against every training point — accurate, but the prediction cost grows with the size of the training set. Nearest centroid asks whether that's really necessary: if a class's points cluster together, a single summary point per class (its centroid) might capture "what this class looks like" well enough to skip comparing against every individual training example.

From theory to code

Implement nearest_centroid_fit(input, labels), which returns one centroid per class, and nearest_centroid_predict(model, queries), which assigns each query to its nearest centroid's class. Reuse 01-knn's pairwise_distances — don't recompute distances by hand.

Constraints

• nearest_centroid_fit returns {"classes": ..., "centroids": array (n_classes, n_features)}, one centroid row per distinct class, in the same order as classes.
• A centroid is the mean feature vector of that class's own training rows.
• nearest_centroid_predict returns one predicted class per row of queries, the class of the nearest centroid (Euclidean distance).
• Ties broken toward the lower class label (whichever np.argmin returns first).

Hints

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