NON-NEGATIVE MATRIX FACTORIZATION OF CLUSTERED DATA WITH MISSING VALUES

We propose the approximation-theoretic technique of optimal recovery for imputing missing values in clustered data, specifically for non-negative matrix factorization (NMF), and develop an algorithm for implementation. Under certain geometric conditions, we prove tight upper bounds on NMF relative error, which is the first bound of this type for missing values. Experiments on image data and biological data show that this technique performs as well as or better than other imputation techniques that account for local structure.