Answer: (iv) k-Means

Partitioning clustering methods partition $n$ data objects into $k$ clusters (where $k$ is given in advance) such that each object belongs to the cluster whose centroid (mean) is nearest to it. k-Means is the classic partitioning algorithm:

1. Choose $k$ initial centroids (one per cluster).
2. Assign each object to the cluster of its nearest centroid.
3. Recompute each cluster's centroid as the mean of its member objects.
4. Repeat steps 2–3 until the centroids stop changing.

Input: k, dataset D
Repeat until centroids converge:
    assign each x ∊ D to cluster of nearest centroid
    recompute each centroid = mean of its cluster

Why the others are wrong:

• (i) Apriori — an association-rule mining algorithm (frequent itemset generation), not a clustering method.
• (ii) ID3 — a decision tree classifier.
• (iii) Naïve Bayes — a probabilistic classifier, not a clustering method.

Hence the partitioning clustering method among the options is k-Means.