Matrix Completion with Deterministic Sampling: Theories and Methods

In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning validity prevalent assumption that is randomly chosen according to probabilistic model. To break through limits random sampling, we explore in this paper problem real-valued matrix completion under setup deterministic sampling. We propose two conditions, isomeric condition and relative well-conditionedness, for guaranteeing an arbitrary be recoverable from a sampling entries. It provable proposed conditions are weaker than uniform and, most importantly, it also necessary completions partial matrices identifiable. Equipped with these new tools, prove collection theorems recovery well convex/nonconvex completion. Among other things, study detail Schatten quasi-norm induced method termed dictionary pursuit (IsoDP), show IsoDP exhibits distinct behaviors absent traditional bilinear programs.