Principled Graph Matching Algorithms for Integrating Multiple Data   Sources
  This paper explores combinatorial optimization for problems of max-weight graph matching on multi-partite graphs, which arise in integrating multiple data sources. Entity resolution-the data integration problem of performing noisy joins on structured data-typically proceeds by first hashing each record into zero or more blocks, scoring pairs of records that are co-blocked for similarity, and then matching pairs of sufficient similarity. In the most common case of matching two sources, it is often desirable for the final matching to be one-to-one (a record may be matched with at most one other); members of the database and statistical record linkage communities accomplish such matchings in the final stage 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 ER problem from Bing significantly larger than typically found in the literature, 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. 
Duo Zhang and Benjamin I. P. Rubinstein and Jim Gemmell
cs.DB cs.LG stat.ML