Choose a Clustering Strategy After Closure Merges Families

Your pairwise classifier is good (pairwise precision 0.97 at a chosen threshold). After you merge accepted pairs by transitive closure, an audit finds one cluster of 190 records that contains about 45 different real people, many sharing a surname and a street. Another cluster has two real customers merged by a single weak link between a father and a son who share a first name and an address.

1. Explain with arithmetic why closure amplified a small number of false links.
2. Compare three alternative strategies (average-linkage hierarchical clustering, pivot clustering, a higher closure threshold) on what each fixes and what each costs.
3. Which evaluation numbers would you use to choose, and what would you watch in the largest components?
4. Is a better clustering algorithm the only fix?