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ICURC.m
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ICURC.m
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function [C,U_pinv,R, ICURC_time] = ICURC(X_Omega_UR, I_ccs, J_ccs, r, params_ICURC)
%Return the CUR components of result of solved Matrix Completion problem
%under Cross-Concentrated Sampling (CCS).
%
%Inputs:
% X_Omega_ccs - observed data matrix based on CCS sampling model
% I_ccs - row indices of the selected row submatrix
% J_ccs - column indices of the selected column submatrix
% r : rank of targt X
% params_ICURC - parameter structure containing the following fields:
% TOL,max_ite - stopping crICURC_iteria
% defaults = 1e-4 (TOL), 500 (mxitr)
% eta - step size
% default = [1, 1, 1] for [eta_C, eat_R, era_U], step sizes for
% updating C, R, and U respectively
% steps_are1 - if all step sizes are 1
% default = true
%Outputs:
% C, U_pinv, R - The CUR components of recovered X
% ICURC_time -Function execution time
% ICURC_ite - Number of ICURC_iterations required
if(~exist('params_ICURC','var'))
params_ICURC=struct();
end
params_ICURC = SetDefaultParams_ICURC(params_ICURC);
eta=params_ICURC.eta;
fprintf('using stepsize eta_C = %f.\n', eta(1));
fprintf('using stepsize eta_R = %f.\n', eta(2));
fprintf('using stepsize eta_U = %f.\n', eta(3));
TOL=params_ICURC.TOL;
max_ite=params_ICURC.max_ite;
steps_are1=params_ICURC.steps_are1;
%This step is to extract observed C, U, and R
Obs_U = X_Omega_UR(I_ccs, J_ccs);
Obs_C = X_Omega_UR(:, J_ccs);
Obs_R = X_Omega_UR(I_ccs, :);
C_size = size(Obs_C);
R_size = size(Obs_R);
all_row_ind = 1:C_size(1);
all_col_ind = 1:R_size(2);
I_ccs_comp = setdiff(all_row_ind, I_ccs);
J_ccs_comp = setdiff(all_col_ind, J_ccs);
C = Obs_C(I_ccs_comp, :);
R = Obs_R(:, J_ccs_comp);
%C and R are C_obs\U, R_obs\U.
Smp_C = C ~= 0;
Smp_R = R ~= 0;
Smp_U = Obs_U ~= 0;
L_obs_only_row = R;
L_obs_only_col = C;
L_obs_only_U = Obs_U;
Omega_row = find(Smp_R);
Omega_col = find(Smp_C);
Omega_U = find(Smp_U);
L_obs_row_vec = L_obs_only_row(Omega_row);
L_obs_col_vec = L_obs_only_col(Omega_col);
L_obs_U_vec = L_obs_only_U(Omega_U);
normC_obs = norm(L_obs_col_vec,'fro');
normU_obs = norm(L_obs_U_vec,'fro');
normR_obs = norm(L_obs_row_vec,'fro');
col_row_norm_sum = normC_obs + normU_obs + normR_obs;
%Initializing U
U = Obs_U;
[u,s,v] = svd(U);
u = u(:, 1:r);
v = v(:, 1:r);
s = s(1:r, 1:r);
U = u*s*v';
%Calculating error
% New_Error = (norm(R(Omega_row) - L_obs_row_vec,'fro') + ...
% norm(C(Omega_col)- L_obs_col_vec, 'fro') + ...
% norm(U(Omega_U)- L_obs_U_vec))/col_row_norm_sum;
%If all step sizes are 1
if steps_are1
fprintf('running ICURC with stepsize all equal to 1\n');
fct_time = tic;
for ICURC_ite = 1:max_ite
ite_itme = tic;
R = u*(u'*R);
C = C*v*v';
New_Error = (norm(R(Omega_row) - L_obs_row_vec,'fro') + ...
norm(C(Omega_col)- L_obs_col_vec, 'fro') + ...
norm(U_i(Omega_U)- L_obs_U_vec))/col_row_norm_sum;
if New_Error < TOL || ICURC_ite == max_ite
ICURC_time = toc(fct_time);
R(Omega_row) = L_obs_row_vec;
C(Omega_col) = L_obs_col_vec;
U(Omega_U) = L_obs_U_vec;
Final_C = zeros(C_size);
Final_R = zeros(R_size);
Final_C(I_ccs_comp, :) = C;
Final_R(:, J_ccs_comp) = R;
Final_C(I_ccs, :) = U;
Final_R(:, J_ccs) = U;
C = Final_C;
R = Final_R;
[u,s,v] = svd(U);
u = u(:, 1:r);
v = v(:, 1:r);
s = s(1:r, 1:r);
U_pinv = v*pinv(s)*u';
fprintf('ICURC finished in %d iterations, final error: %e, total runtime: %f \n', ICURC_ite, New_Error, ICURC_time);
return
end
%Updating R, C, and U
R(Omega_row) = L_obs_row_vec;
C(Omega_col) = L_obs_col_vec;
U(Omega_U) = L_obs_U_vec;
[u,s,v] = svd(U);
u = u(:, 1:r);
v = v(:, 1:r);
s = s(1:r, 1:r);
U = u*s*v';
fprintf('Iteration %d: error: %e, timer: %f \n', ICURC_ite, New_Error, toc(ite_itme));
end
%If all step sizes are not 1
else
fprintf('running ICURC with given stepsizes \n');
step_c = eta(1);
step_r = eta(2);
step_u = eta(3);
fct_time = tic;
for ICURC_ite = 1:max_ite
ite_itme = tic;
R = u*(u'*R);
C = C*v*v';
New_Error = (norm(R(Omega_row) - L_obs_row_vec,'fro') + ...
norm(C(Omega_col)- L_obs_col_vec, 'fro') + ...
norm(U(Omega_U)- L_obs_U_vec))/col_row_norm_sum;
if New_Error < TOL || ICURC_ite == max_ite
ICURC_time = toc(fct_time);
R(Omega_row) = L_obs_row_vec;
C(Omega_col) = L_obs_col_vec;
U(Omega_U) = L_obs_U_vec;
Final_C = zeros(C_size);
Final_R = zeros(R_size);
Final_C(I_ccs_comp, :) = C;
Final_R(:, J_ccs_comp) = R;
Final_C(I_ccs, :) = U;
Final_R(:, J_ccs) = U;
C = Final_C;
R = Final_R;
[u,s,v] = svd(U);
u = u(:, 1:r);
v = v(:, 1:r);
s = s(1:r, 1:r);
U_pinv = v*pinv(s)*u';
fprintf('ICURC finished in %d iterations, final error: %e, total runtime: %f \n', ICURC_ite, New_Error, ICURC_time);
return
end
%Updating R, C, and U
R(Omega_row) = (1 - step_r)*R(Omega_row) + step_r*(L_obs_row_vec);
C(Omega_col) = (1 - step_c)*C(Omega_col) + step_c*(L_obs_col_vec);
U(Omega_U) = (1 - step_u)*U(Omega_U) + step_u*(L_obs_U_vec);
[u,s,v] = svd(U);
u = u(:, 1:r);
v = v(:, 1:r);
s = s(1:r, 1:r);
U = u*s*v';
fprintf('Iteration %d: error: %e, timer: %f \n', ICURC_ite, New_Error, toc(ite_itme));
end
end
end