Semi-supervised clustering for de-duplication

Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the same physical entity in the same cluster and putting records corresponding to different physical entities into different clusters. We introduce a framework which we call promise correlation clustering. Given a complete graph $G$ with the edges labelled $0$ and $1$, the goal is to find a clustering that minimizes the number of $0$ edges within a cluster plus the number of $1$ edges across different clusters (or correlation loss). The optimal clustering can also be viewed as a complete graph $G^*$ with edges corresponding to points in the same cluster being labelled $0$ and other edges being labelled $1$. Under the promise that the edge difference between $G$ and $G^*$ is "small", we prove that finding the optimal clustering (or $G^*$) is still NP-Hard. [Ashtiani et. al, 2016] introduced the framework of semi-supervised clustering, where the learning algorithm has access to an oracle, which answers whether two points belong to the same or different clusters. We further prove that even with access to a same-cluster oracle, the promise version is NP-Hard as long as the number queries to the oracle is not too large ($o(n)$ where $n$ is the number of vertices). Given these negative results, we consider a restricted version of correlation clustering. As before, the goal is to find a clustering that minimizes the correlation loss. However, we restrict ourselves to a given class $\mathcal F$ of clusterings. We offer a semi-supervised algorithmic approach to solve the restricted variant with success guarantees.