Task: Question Answering
Input (English): Initially, we experimented with a graph-based community detection algorithm that maximizes cluster modularity BIBREF20 , but we found no simple way to constrain this method to produce a specific number of equally-sized clusters. The brute force approach of enumerating all possible cluster assignments is intractable given the large search space ( INLINEFORM0 possible assignments). We devise a simple clustering algorithm to approximate this process. First, we initialize with random cluster assignments and define “cluster strength” to be the relative difference between “intra-group” Euclidean distance and “inter-group” Euclidean distance. Then, we iteratively propose random exchanges of memberships, only accepting these proposals when the cluster strength increases, until convergence. To evaluate the quality of the computationally-derived clusters against those of Calvino, we measure cluster purity BIBREF21 : given a set of predicted clusters INLINEFORM1 and ground-truth clusters INLINEFORM2 that both partition a set of INLINEFORM3 data points, INLINEFORM4 
 Question: Which clustering method do they use to cluster city description embeddings?
Output (English):  We devise a simple clustering algorithm to approximate this process. First, we initialize with random cluster assignments and define “cluster strength” to be the relative difference between “intra-group” Euclidean distance and “inter-group” Euclidean distance. Then, we iteratively propose random exchanges of memberships, only accepting these proposals when the cluster strength increases, until convergence.