  Factoring a matrix into two low rank matrices is at the heart of many
problems. The problem of matrix completion especially uses it to decompose a
sparse matrix into two non sparse, low rank matrices which can then be used to
predict unknown entries of the original matrix. We present a scalable and
decentralized approach in which instead of learning two factors for the
original input matrix, we decompose the original matrix into a grid blocks,
each of whose factors can be individually learned just by communicating
(gossiping) with neighboring blocks. This eliminates any need for a central
server. We show that our algorithm performs well on both synthetic and real
datasets.
