Recovery of Partially Observed Data Appearing in Clusters

We propose a matrix completion algorithm for matrices where the columns appear in clusters. The algorithm estimates the similarity between every pair of points using partial distances, computed from the entries of their commonly observed indices. It is shown that the similarity matrix can be reliably estimated from partial distances, and used to aid the recovery process. It is observed that the proposed algorithm with the estimated similarity matrix performs very well for wellseparated clusters where the coherence of the difference between columns from different clusters is low. The method is also successful in reconstructing images from under-sampled Fourier data.