/
show_pca_plots.m
executable file
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show_pca_plots.m
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function show_pca_plots()
clc;
close all;
clear
%% Select case
%case_num = 1; % Case P1
%case_num = 2; % Case P2
case_num = 3; % small instance
if case_num == 1
N = 5000000; d = 100; r = 5;
elseif case_num == 2
N = 500000; d = 1000; r = 5;
elseif case_num == 3
N = 100000; d = 100; r = 5;
else
end
%% Define parameters
maxepoch = 100;
tolgradnorm = 1e-8;
%% Generate data
fprintf('generating data ... ');
x_sample = randn(d, N);
x_sample = diag(exprnd(2, d , 1))*x_sample;
x_sample = x_sample - repmat(mean(x_sample,2),1,size(x_sample,2));
%cond(x_sample)
fprintf('done.\n');
% Iput data as cell
data.x = mat2cell(x_sample, d, ones(N, 1)); %
%% Obtain solution
coeff = pca(x_sample');
x_star = coeff(:,1:r);
f_sol = -0.5/N*norm(x_star'*x_sample, 'fro')^2;
fprintf('f_sol: %.16e, cond = %.2f\n', f_sol, cond(x_sample));
%% Set manifold
problem.M = grassmannfactory(d, r);
problem.ncostterms = N;
problem.d = d;
problem.data = data;
%% Define problem definitions
problem.cost = @cost;
function f = cost(U)
f = -0.5*norm(U'*x_sample, 'fro')^2;
f = f/N;
end
problem.egrad = @egrad;
function g = egrad(U)
g = - x_sample*(x_sample'*U);
g = g/N;
end
problem.partialegrad = @partialegrad;
function g = partialegrad(U, indices)
len = length(indices);
x_sample_batchsize = x_sample(:,indices);
g = - x_sample_batchsize*(x_sample_batchsize'*U);
g = g/len;
end
problem.ehess = @ehess;
function gdot = ehess(U, Udot)
gdot = - x_sample*(x_sample'*Udot);
gdot = gdot/N;
end
problem.partialehess = @partialehess;
function gdot = partialehess(U, Udot, indices, square_hess_diag)
len = length(indices);
x_sub_sample = x_sample(:, indices);
gdot = - x_sub_sample * (x_sub_sample' * Udot);
gdot = gdot/len;
end
% % Consistency checks
% checkgradient(problem)
% pause;
% % Consistency checks
% checkhessian(problem)
% pause;
%% Run algorithms
% Initialize
Uinit = problem.M.rand();
% Run RSD
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
[~, ~, infos_sd, ~] = steepestdescent_mod(problem, Uinit, options);
% Run RCG
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
[~, ~, infos_cg, ~] = conjugategradient_mod(problem, Uinit, options);
% Run RLBFGS
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
[~, ~, infos_lbfgs] = lbfgs_mod(problem, Uinit, options);
% Run RSVRG
clear options;
inner_repeat = 5;
options.verbosity = 1;
options.batchsize = floor(N/100);
options.update_type = 'svrg';
options.stepsize = 0.001;
options.stepsize_type = 'fix';
options.stepsize_lambda = 0;
options.tolgradnorm = tolgradnorm;
options.boost = 0;
options.svrg_type = 2; % effective only for R-SVRG variants
options.maxinneriter = inner_repeat * N;
options.transport = 'ret_vector';
options.maxepoch = floor(maxepoch / (1 + inner_repeat)) * 2;
[~, ~, infos_svrg, ~] = Riemannian_svrg(problem, Uinit, options);
% Run RTR (basic)
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
options.samp_hess_init_size = N;
[~, ~, infos_tr, ~] = subsampled_rtr(problem, Uinit, options);
% Run Sub-sampled Hessian TR
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
options.samp_hess_scheme = 'fix';
options.samp_hess_init_size = floor(N/100);
options.useExp = true;
[~, ~, infos_subHtr_fix, ~] = subsampled_rtr(problem, Uinit, options);
% Run Sub-sampled Hessian & Gradient TR
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
options.samp_hess_scheme = 'fix';
options.samp_hess_init_size = floor(N/100);
options.samp_grad_scheme = 'fix';
options.samp_grad_init_size = floor(N/10);
options.useExp = true;
[~, ~, infos_subHGtr_fix, ~] = subsampled_rtr(problem, Uinit, options);
%% calculate optimality gap
optgap_sd = abs([infos_sd.cost] - f_sol);
optgap_cg = abs([infos_cg.cost] - f_sol);
optgap_lbfgs = abs([infos_lbfgs.cost] - f_sol);
optgap_svrg = abs([infos_svrg.cost] - f_sol);
optgap_tr = abs([infos_tr.cost] - f_sol);
optgap_subHtr_fix = abs([infos_subHtr_fix.cost] - f_sol);
optgap_subHGtr_fix = abs([infos_subHGtr_fix.cost] - f_sol);
%% Plots
fs = 20;
line_color = {[255, 128, 0], [76, 153, 0], [255,0,255], [204, 204, 0], [0, 0, 255], [255, 0, 0], [255, 0, 0]};
titlestr = sprintf('PCA Problme: N=%d, d=%d, r=%d', N, d, r);
% Optimality gap (Train loss - optimum) vs. oracle calls
figure;
semilogy([infos_sd.oraclecalls], optgap_sd,'-','LineWidth',2, 'Color', line_color{1}/255); hold on;
semilogy([infos_cg.oraclecalls], optgap_cg, '-','LineWidth',2, 'Color', line_color{2}/255); hold on;
semilogy([infos_lbfgs.oraclecalls], optgap_lbfgs,'-','LineWidth',2, 'Color', line_color{3}/255); hold on;
semilogy([infos_svrg.oraclecalls], optgap_svrg,'-','LineWidth',2, 'Color', line_color{4}/255); hold on;
semilogy([infos_tr.oraclecalls], optgap_tr,'-','LineWidth',2, 'Color', line_color{5}/255); hold on;
semilogy([infos_subHtr_fix.oraclecalls], optgap_subHtr_fix,'-','LineWidth',2, 'Color', line_color{6}/255); hold on;
semilogy([infos_subHGtr_fix.oraclecalls], optgap_subHGtr_fix,'-.','LineWidth',2, 'Color', line_color{7}/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'Oracle calls','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Optimality gap','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('RSD', 'RCG', 'RLBFGS','RSVRG', 'RTR','Sub-H-RTR', 'Sub-HG-RTR');
title(titlestr)
% Optimality gap (Train loss - optimum) vs. processing time [sec]
figure;
semilogy([infos_sd.time], optgap_sd,'-','LineWidth',2, 'Color', line_color{1}/255); hold on;
semilogy([infos_cg.time], optgap_cg, '-','LineWidth',2, 'Color', line_color{2}/255); hold on;
semilogy([infos_lbfgs.time], optgap_lbfgs,'-','LineWidth',2, 'Color', line_color{3}/255); hold on;
semilogy([infos_svrg.time], optgap_svrg,'-','LineWidth',2, 'Color', line_color{4}/255); hold on;
semilogy([infos_tr.time], optgap_tr,'-','LineWidth',2, 'Color', line_color{5}/255); hold on;
semilogy([infos_subHtr_fix.time], optgap_subHtr_fix,'-','LineWidth',2, 'Color', line_color{6}/255); hold on;
semilogy([infos_subHGtr_fix.time], optgap_subHGtr_fix,'-.','LineWidth',2, 'Color', line_color{7}/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'Time [sec]','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Optimality gap','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('RSD', 'RCG', 'RLBFGS','RSVRG', 'RTR','Sub-H-RTR', 'Sub-HG-RTR');
title(titlestr)
end