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This paper explores combinatorial optimization for problems of max-weight graph matching on multi-partite graphs, which arise in integrating multiple data sources. In the most common two-source case, it is often desirable for the final matching to be one-to-one; the database and statistical record linkage communities accomplish this by weighted bipartite graph matching on similarity scores. Such matchings are intuitively appealing: they leverage a natural global property of many real-world entity stores-that of being nearly deduped-and are known to provide significant improvements to precision and recall. Unfortunately, unlike the bipartite case, exact max-weight matching on multi-partite graphs is known to be NP-hard. Our two-fold algorithmic contributions approximate multi-partite max-weight matching: our first algorithm borrows optimization techniques common to Bayesian probabilistic inference; our second is a greedy approximation algorithm. In addition to a theoretical guarantee on the latter, we present comparisons on a real-world entity resolution problem from Bing significantly larger than typically found in the literature, on publication data, and on a series of synthetic problems. Our results quantify significant improvements due to exploiting multiple sources, which are made possible by global one-to-one constraints linking otherwise independent matching sub-problems. We also discover that our algorithms are complementary: one being much more robust under noise, and the other being simple to implement and very fast to run.

Principled Graph Matching Algorithms for Integrating Multiple Data Sources