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Clustering Via Crowdsourcing

In recent years, crowdsourcing, aka human aided computation has emerged as an effective platform for solving problems that are considered complex for machines alone. Using human is time-consuming and costly due to monetary compensations. Therefore, a crowd based algorithm must judiciously use any information computed through an automated process, and ask minimum number of questions to the crowd adaptively. One such problem which has received significant attention is {\em entity resolution}. Formally, we are given a graph $G=(V,E)$ with unknown edge set $E$ where $G$ is a union of $k$ (again unknown, but typically large $O(n^α)$, for $α>0$) disjoint cliques $G_i(V_i, E_i)$, $i =1, \dots, k$. The goal is to retrieve the sets $V_i$s by making minimum number of pair-wise queries $V \times V\to\{\pm1\}$ to an oracle (the crowd). When the answer to each query is correct, e.g. via resampling, then this reduces to finding connected components in a graph. On the other hand, when crowd answers may be incorrect, it corresponds to clustering over minimum number of noisy inputs. Even, with perfect answers, a simple lower and upper bound of $Θ(nk)$ on query complexity can be shown. A major contr