Description Usage Arguments Value References Examples
Let's assume an ideal matrix M with (m\times n) entries with rank r and we are given a partially observed matrix M\_E which contains many missing entries. Matrix reconstruction  or completion  is the task of filling in such entries. OptSpace is an efficient algorithm that reconstructs M from E=O(rn) observed elements with relative root mean square error (RMSE)
RMSE ≤ C(α)√{nr/E}
1 
A 
an (n\times m) matrix whose missing entries should be flaged as NA. 
ropt 

niter 
maximum number of iterations allowed. 
tol 
stopping criterion for reconstruction in Frobenius norm. 
showprogress 
a logical value; 
a named list containing
an (n \times r) matrix as left singular vectors.
an (r \times r) matrix as singular values.
an (m \times r) matrix as right singular vectors.
a vector containing reconstruction errors at each successive iteration.
keshavan_matrix_2010ROptSpace
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  ## Parameter Settings
n = 1000;
m = 100;
r = 3;
tolerance = 1e7
eps = 10*r*log10(n)
## Generate a matrix with given data
U = matrix(rnorm(n*r),nrow=n)
V = matrix(rnorm(m*r),nrow=m)
Sig = diag(r)
M0 = U%*%Sig%*%t(V)
## Set some entries to be NA with probability eps/sqrt(m*n)
E = 1  ceiling(matrix(rnorm(n*m),nrow=n)  eps/sqrt(m*n))
M_E = M0
M_E[(E==0)] = NA
## Create a noisy version
noiselevel = 0.1
M_E_noise = M_E + matrix(rnorm(n*m),nrow=n)*noiselevel
## Use OptSpace for reconstruction
res1 = OptSpace(M_E,tol=tolerance)
res2 = OptSpace(M_E_noise,tol=tolerance)
## Compute errors for both cases using Frobenius norm
err_clean = norm(res1$X%*%res1$S%*%t(res1$Y)M0,'f')/sqrt(m*n)
err_noise = norm(res2$X%*%res2$S%*%t(res2$Y)M0,'f')/sqrt(m*n)
## print out the results
m1 = sprintf('RMSE without noise : %e',err_clean)
m2 = sprintf('RMSE with noise of %.2f : %e',noiselevel,err_noise)
print(m1)
print(m2)

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