We consider the problem of clustering partially labeled data from a minimal number of randomly chosen pairwise comparisons between the items. We introduce an efficient local algorithm based on a power iteration of the non-backtracking operator and study its performance on a generative model. For the case of two clusters, we give bounds on the classification error and show that a small error can be achieved from O(n) randomly chosen measurements, where n is the number of items in the dataset. Our algorithm is therefore efficient both in terms of time and space complexities. We also investigate numerically the performance of the algorithm on synthetic and real-world data.