This repository contains Python and Matlab implementations for R2RILS as described in J. Bauch, B. Nadler and P. Zilber (2021), available in SIMODS or arXiv, as well as simple demos demonstrating the usage of the Python and Matlab implementations.
The entry point to run R2RILS is a function with the same name which expects the following parameters:
- required arguments:
- X: input matrix to complete. This should be a numpy array of dimensions m x n.
- omega: a mask matrix. 1 on observed entries, 0 otherwise.
- rank: the target rank.
- optional arguments:
- max_iter: maximal number of iterations.
- LSQR solver arguments:
- lsqr_col_norm: if True, normalize columns of LSQR matrix.
- lsqr_max_iter: maximal number of iterations of LSQR solver.
- lsqr_tol: tolerance of LSQR solver.
- lsqr_smart_tol: should increase LSQR's accuracy according to the current quality of the objective.
- lsqr_smart_obj_min: minimal objective to start smart tolerance from.
- initialization arguments:
- init_option: 0 for SVD initialization, 1 for random, 2 for user-defined.
- init_U: in case init_option==2, use this matrix to initialize U.
- init_V: in case init_option==2, use this matrix to initialize V.
- weight of previous estimate arguments:
- weight_previous_estimate: different averaging weight for the previous estimate of U, V.
- weight_from_iter: iteration number to start the different weighting from.
- weight_every_iter: use different use different averaging when iter_num % weight_every_iter < 2.
- early stopping arguments (see paper for exact definitions):
- early_stopping_rmse_abs: eps for absolute difference between X_hat and X (RMSE), -1 for disabled.
- early_stopping_rel: eps for relative difference of X_hat between iterations, -1 for disabled.
- early_stopping_rmse_rel: eps for relative difference of RMSE between iterations, -1 for disabled.
This method returns X_hat - R2RILS estimate for X0, and a convergence flag which indicates if the algorithm converged.
The entry point for running R2RILS in Matlab is again a function bearing the same name
which expects the following parameters:
- X: matrix with observed entries in the set omega.
- omega: array of pairs (i,j) indicating which entries are observed.
- rank: the target rank.
- opts: an optional meta-veraible, encapsulates the options detailed in the python implementation above.
This method returns [X_hat, U_hat, lambda_hat, V_hat, observed_RMSE, iter, convergence_flag] where:
- X_hat: rank r approximation of X0.
- U_hat: matrix of left singular vectors of X_hat.
- lambda_hat: singular values of X_hat.
- V_hat: matrix of right singular vectors of X_hat.
- observed_RMSE: the RMSE of X_hat on the observed entires of X0.
- iter: final iteration number of the algorithm.
- convergence_flag: incdicating whether the algorithm converged.