Consistent Collective Matrix Completion under Joint Low Rank Structure

Consistent Collective Matrix Completion under Joint Low Rank Structure: Supplementary Material

Graph Matrix Completion in Presence of Outliers

Matrix completion problem has gathered a lot of attention in recent years. In the matrix completion problem, the goal is to recover a low-rank matrix from a subset of its entries. The graph matrix completion was introduced based on the fact that the relation between rows (or columns) of a matrix can be modeled as a graph structure. The graph matrix completion problem is formulated by adding the...

Co-Regularized Collective Matrix Factorization for Joint Matrix Completion

Collective matrix factorization (CMF) is a popular technique for joint matrix completion. However, it relies on a strong assumption that matrices share a common low-rank structure, which may not be easily satisfied in practice. To lift this limitation, this paper introduces a novel joint matrix completion method based on a relaxed assumption. Specifically, we allow the matrix structures to be d...

Low Permutation-rank Matrices: Structural Properties and Noisy Completion

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming that the underlying matrix has low rank, or is well-approximated by a low rank matrix. In this paper, we propose a richer model based on what we term the “permu...

Matrix Completion Under Monotonic Single Index Models

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is distorted by a (typically unknown) nonlinear transformation. This paper addresses the challenge of matrix completion in the face of such nonlinearities. Given a f...