Low-rank Matrix Completion using Alternating Minimization(MCAM-numpy)

• The repository reproducing algorithm in the paper, Low-rank Matrix Completion using Alternating Minimization.

  • I reproduce the Algorithm 2(AltMinComplete) only. Because, Algorithm 1 is not for matrix completion problem, but for matrix sensing problem.

• In this repository, I used numpy to implement the paper.

• The meanings of parameters.
  ```
  m: The number of row of the matrix
  n: The number of column of the matrix
  p: samling probability
  omega: the observed set omega. if entries are given, 1 else 0.
  cardinality_of_omega: The cardinality of set omega.

M: The matrix to recover.
X: The solution of AM.

k: The rank of the matrix.
T: The number of iteration
mu: coherence

- How to init and run

virtualenv .venv -p python3
. .venv/bin/activate
pip install -r requirements.txt
python run.py

- The example of result(console)

RANK of M : 2
|U_hat-U|_F/|U|_F: 1.4007495010575732

t( 0): 7.056300795604675e-17
t( 1): 8.023918248411439e-17
t( 2): 6.838685255066973e-17
t( 3): 7.616046824035152e-17
t( 4): 6.07257413689918e-17

RANK of X : 2
TRAIN RMSE : 1.9046232036157855e-17
TEST RMSE : 6.635452802602127e-18
|X-M|_F/|M|_F : 4.614953476853536e-16
```