Deep-Union Completion

Large amounts of missing data are becoming increasingly ubiquitous in modern high-dimensional datasets. Unfortunately, classical completion methods like low-rank, high-rank, or deep matrix completion (LRMC/HRMC/DMC) are often unable to handle real data that does not fall under their respective models. Here we propose a novel completion strategy that generalizes all these models. The main idea is to find a Union of Subspaces (UoS) that can fit a non-linear embedding of the original data, and complete the data according to this latent UoS. This embedding is obtained through a novel pseudo-completion layer in a deep architecture, and the UoS structure is identified in closed-form through an intermediate clustering layer. Our design reduces the exponential memory requirements that are typically induced by uneven patterns of missing data. We give exact details of our architecture, model, loss functions, and training strategy. Our experiments on over 10 real datasets show that our method consistently outperforms the state-of-the-art accuracy by more than a staggering 40%.