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Source coding is the canonical problem of data compression in informationtheory. In a locally encodable source coding, each compressed bit depends ononly few bits of the input. In this paper, we show that a recently popularmodel of semi-supervised clustering is equivalent to locally encodable sourcecoding. In this model, the task is to perform multiclass labeling of unlabeledelements. At the beginning, we can ask in parallel a set of simple queries toan oracle who provides (possibly erroneous) binary answers to the queries. Thequeries cannot involve more than two (or a fixed constant number of) elements.Now the labeling of all the elements (or clustering) must be performed based onthe noisy query answers. The goal is to recover all the correct labelings whileminimizing the number of such queries. The equivalence to locally encodablesource codes leads us to find lower bounds on the number of queries required ina variety of scenarios. We provide querying schemes based on pairwise `samecluster' queries - and pairwise AND queries and show provable performanceguarantees for each of the schemes.

Semisupervised Clustering by Queries and Locally Encodable Source Coding