densub {admmDensestSubmatrix}

densub

Description

Iteratively solves the convex optimization problem using ADMM.

Usage

densub(G, m, n, tau = 0.35, gamma = 6/(sqrt(m * n) * (q - p)),
  opt_tol = 1e-04, maxiter, quiet = TRUE)

Arguments

G

sampled binary matrix

m

number of rows in dense submatrix

n

number of columns in dense submatrix

tau

penalty parameter for equality constraint violation

gamma

l_1 regularization parameter

opt_tol

stopping tolerance in algorithm

maxiter

maximum number of iterations of the algorithm to run

quiet

toggles between displaying intermediate statistics

Details

min |X|_* + gamma* |Y|_1 + 1_Omega_W (W) + 1_Omega_Q (Q) + 1_Omega_Z (Z)

s.t X - Y = 0, X = W, X = Z,

where Omega_W (W), Omega_Q (Q), Omega_Z (Z) are the sets: Omega_W = {W in R^MxN | e^TWe = mn}

Omega_Q = {Q in R^MxN | Projection of Q on not N = 0}

Omega_Z = {Z in R^MxN | Z_ij <= 1 for all (i,j) in M x N}

Omega_Q = {Q in R^MxN | Projection of Q on not N = 0}

Omega_Z = {Z in R^MxN | Z_ij <= 1 for all (i,j) in M x N}

1_S is the indicator function of the set S in R^MxN such that 1_S(X) = 0 if X in S and +infinity otherwise

Value

Rank one matrix with mn nonzero entries, matrix Y that is used to count the number of disagreements between G and X