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Matrix Completion on Co-Manifolds (308536)

Keywords: Matrix completion, co-manifold learning, missing data imputation

Imputation of missing data is usually performed as a pre-processing step for downstream tasks. We propose to solve the missing data imputation problem with co-manifold learning which carries out joint dimension reduction on the rows and columns of a data matrix. We perform co-clustering in the missing data setting to estimate the complete matrix from a partially observed matrix. The estimation runs at different scales which is achieved by encoding the pair of joint cost parameters along the rows and columns at different values. Based on the collection of those estimated complete matrices, a new multi-scale distance is defined to to estimate the row and column pairwise distances of the complete data matrix. Then those missing entries are filled in based on the new multi-scale distances. Numerical experiments demonstrate the utility of our imputation procedure.