# Principled Graph Matching Algorithms for Integrating Multiple Data Sources

arXiv: https://arxiv.org/abs/1402.0282 · HTML: https://mlsanity.com/paper/1402.0282/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2014.

## Built on by (most cited first, 1 of 1)

- [Multidimensional Assignment Problem for multipartite entity resolution](https://mlsanity.com/paper/2112.03346/) (2021)

## Abstract (arXiv)

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.