Another approach for testing Matrix completion

sparse_mc_test.cpp

#include <mlpack/core.hpp>
#include <mlpack/core/optimizers/parallel_sgd/parallel_sgd.hpp>
#include <mlpack/core/optimizers/parallel_sgd/decay_policies/constant_step.hpp>
#include <mlpack/core/optimizers/parallel_sgd/sparse_mc_function.hpp>

using namespace std;
using namespace mlpack::optimization;
int main()
{
  size_t numRows, numCols;
  numCols = numRows = 10; // A square matrix
  size_t degree = 2;
  arma::sp_mat inputMat(numRows, numCols);
  // Alternating columns with +1 and -1, at 2 consecutive positions.
  for(size_t i = 0; i < numCols; ++i)
  {
    int val = (i % 2) ? 1 : -1;
    inputMat.at(i, i) = val;
    inputMat.at((i + 2) % numRows, i) = val;
  }
  cout << arma::mat(inputMat) << endl;
  SparseMCLossFunction f(inputMat, 1e-6, degree);
  ConstantStep decayPolicy(0.2);
  size_t batchSize = std::ceil((float) (2 * numRows) / omp_get_max_threads());
  ParallelSGD<ConstantStep> s(1e5, batchSize, 
      1e-5, decayPolicy);

  arma::mat iterate(degree, numCols + numRows);
  double initial = 0;
  for(size_t i = 0; i < f.NumFunctions(); ++i)
  {
    initial += f.Evaluate(iterate, i);
  }
  cout << "Initial objective : " << initial << endl;

  s.Optimize(f, iterate);

  double final = 0;
  for(size_t i = 0; i < f.NumFunctions(); ++i)
  {
    final += f.Evaluate(iterate, i);
  }
  cout << "Final objective : " << final << endl;
  arma::mat gen(arma::trans(iterate.cols(0, numRows - 1)) *
      iterate.cols(numRows, numRows + numCols - 1));

  cout << gen << endl;
}

stdout

#############################################################################################
i    , i
i + 2, i (Same row evidence)
#############################################################################################
λ mlpack_spike/hogwild ∴ g++ sparse_mc_test.cpp -O2 -std=c++11 -Wall -larmadillo -lmlpack -fopenmp -g
λ mlpack_spike/hogwild ∴ ./a.out
  -1.0000        0        0        0        0        0        0        0  -1.0000        0
        0   1.0000        0        0        0        0        0        0        0   1.0000
  -1.0000        0  -1.0000        0        0        0        0        0        0        0
        0   1.0000        0   1.0000        0        0        0        0        0        0
        0        0  -1.0000        0  -1.0000        0        0        0        0        0
        0        0        0   1.0000        0   1.0000        0        0        0        0
        0        0        0        0  -1.0000        0  -1.0000        0        0        0
        0        0        0        0        0   1.0000        0   1.0000        0        0
        0        0        0        0        0        0  -1.0000        0  -1.0000        0
        0        0        0        0        0        0        0   1.0000        0   1.0000

Initial objective : 18
Final objective : 8.30448e-05
  -0.9987  -0.9370  -0.9928  -0.9345  -0.9903  -0.9332  -0.9930  -0.9326  -0.9990  -0.9409
   1.0650   0.9992   1.0587   0.9966   1.0560   0.9952   1.0589   0.9945   1.0654   1.0004
  -1.0023  -0.9404  -0.9965  -0.9380  -0.9939  -0.9367  -0.9966  -0.9360  -1.0027  -0.9443
   1.0672   1.0013   1.0609   0.9986   1.0582   0.9972   1.0611   0.9965   1.0676   1.0054
  -1.0083  -0.9460  -1.0024  -0.9435  -0.9998  -0.9422  -1.0025  -0.9415  -1.0086  -0.9499
   1.0695   1.0035   1.0633   1.0009   1.0606   0.9995   1.0635   0.9987   1.0700   1.0076
  -1.0081  -0.9458  -1.0022  -0.9433  -0.9996  -0.9420  -1.0023  -0.9413  -1.0084  -0.9497
   1.0707   1.0046   1.0645   1.0020   1.0618   1.0006   1.0646   0.9999   1.0712   1.0088
  -1.0021  -0.9402  -0.9963  -0.9378  -0.9937  -0.9364  -0.9964  -0.9358  -1.0025  -0.9441
   1.0711   1.0049   1.0648   1.0023   1.0621   1.0009   1.0650   1.0002   1.0715   0.9998

#############################################################################################
i    , i
i + 1, i
i + 3, i
i + 5, i (Same column evidence)
#############################################################################################
λ mlpack_spike/hogwild ∴ ./a.out
  -1.0000        0        0        0        0   1.0000        0   1.0000        0   1.0000
  -1.0000   1.0000        0        0        0        0  -1.0000        0  -1.0000        0
        0   1.0000  -1.0000        0        0        0        0   1.0000        0   1.0000
  -1.0000        0  -1.0000   1.0000        0        0        0        0  -1.0000        0
        0   1.0000        0   1.0000  -1.0000        0        0        0        0   1.0000
  -1.0000        0  -1.0000        0  -1.0000   1.0000        0        0        0        0
        0   1.0000        0   1.0000        0   1.0000  -1.0000        0        0        0
        0        0  -1.0000        0  -1.0000        0  -1.0000   1.0000        0        0
        0        0        0   1.0000        0   1.0000        0   1.0000  -1.0000        0
        0        0        0        0  -1.0000        0  -1.0000        0  -1.0000   1.0000

Initial objective : 152
Final objective : 0.000190717
  -1.0019   0.9986  -0.9992   1.0003  -0.9989   1.0012  -0.9992   0.9986  -1.0014   0.9984
  -1.0010   0.9978  -0.9983   0.9994  -0.9980   1.0003  -0.9983   0.9977  -1.0005   0.9975
  -1.0038   1.0005  -1.0011   1.0022  -1.0007   1.0031  -1.0011   1.0005  -1.0033   1.0003
  -1.0006   0.9974  -0.9979   0.9990  -0.9976   0.9999  -0.9979   0.9973  -1.0001   0.9971
  -1.0030   0.9998  -1.0003   1.0015  -1.0000   1.0024  -1.0003   0.9997  -1.0026   0.9996
  -1.0009   0.9977  -0.9982   0.9994  -0.9979   1.0003  -0.9982   0.9976  -1.0005   0.9975
  -1.0024   0.9991  -0.9997   1.0008  -0.9994   1.0017  -0.9997   0.9991  -1.0019   0.9989
  -1.0034   1.0002  -1.0008   1.0019  -1.0004   1.0028  -1.0008   1.0002  -1.0030   1.0000
  -1.0009   0.9976  -0.9982   0.9993  -0.9978   1.0002  -0.9982   0.9976  -1.0004   0.9974
  -1.0028   0.9996  -1.0001   1.0012  -0.9998   1.0021  -1.0001   0.9995  -1.0023   0.9993