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Fig4_HarmonicStability.m
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Fig4_HarmonicStability.m
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%% Experiment 12: Noise Stability Ananlysis
%% Perturbation:
rng('shuffle','twister');
U_Scales_Noise = struct('scale',[],'noise_sigma',[],'UU_diag_SC_vs_SCnoisy_all',[],'all_combo_diagonals',[]);
std_multiplier_list = 0:2.5e-4:1;
var_multiplier_list = std_multiplier_list.^2;
k_multipliers = length(std_multiplier_list);
scale = 200;
filename = sprintf('MICA_schaefer%d_SCFC_struct.mat',scale);
load(filename);
n_subjects = length(MICA);
nroi = length(MICA(1).SC);
SC_all = zeros(nroi,nroi, n_subjects);
for i = 1:n_subjects
SC = MICA(i).SC;
SC = SC./norm(SC,'fro');
SC_all(:,:,i) = SC;
end
SC_template = mean(SC_all,3);
[~, SC_U_template, SC_ev_template] = graph_laplacian(SC_template, 'normalized');
UU_diag_SC_vs_SCnoisy_all = ones(n_subjects, nroi, k_multipliers);
for k = 2:k_multipliers
disp(k);
r = makedist('Rician','s',0,'sigma',std_multiplier_list(k));
noise_mat = random(r,[nroi, nroi]);
noise_mat = (triu(noise_mat,1) + triu(noise_mat,1)').*~eye(nroi);
for i = 1:n_subjects
SC = SC_all(:,:,i);
[L_SC, SC_U_sub, ~] = graph_laplacian(SC, 'normalized');
SC_U_sub_matched = match_eigs(SC_U_sub, SC_U_template);
SC_noisy = (SC + noise_mat);
SC_noisy = SC_noisy./norm(SC_noisy, 'fro');
[L_SC_noisy, SC_noisy_U_sub, ~] = graph_laplacian(SC_noisy, 'normalized');
SC_noisy_U_sub_matched2Sub = match_eigs(SC_noisy_U_sub, SC_U_sub_matched);
UU_diag_SC_vs_SCnoisy_all(i,:,k) = abs(diag(SC_U_sub_matched' * SC_noisy_U_sub_matched2Sub));
end
end
save(sprintf('U_Scale-%d_RicianNoise_VFinal.mat',scale),'UU_diag_SC_vs_SCnoisy_all','std_multiplier_list','var_multiplier_list','k_multipliers' ,'SC_template','SC_U_template','SC_ev_template');
%% Similarity by regime
% load(sprintf('PreComputed_Data/U_Scale-200_RicianNoise_VFinal.mat',scale))
n_subjects = 50;
% % From EV Regime Consensus:
int_range = 1:26;
deg_range = 27:187;
seg_range = 188:214;
int_color = [0.3, 0.9, 0.9];
deg_color = [0.9, 0.9, 0.3];
seg_color = [0.9, 0.3, 0.9];
mean_SC_weight = mean(nonzeros(triu(SC_template,1)));
k_multipliers = 201;
Perturb_Int = zeros(n_subjects, k_multipliers);
Perturb_Deg = zeros(n_subjects, k_multipliers);
Perturb_Seg = zeros(n_subjects, k_multipliers);
for k = 1:k_multipliers
Perturb_Int(:,k) = mean(UU_diag_SC_vs_SCnoisy_all(:, int_range,k),2);
Perturb_Deg(:,k) = mean(UU_diag_SC_vs_SCnoisy_all(:, deg_range,k),2);
Perturb_Seg(:,k) = mean(UU_diag_SC_vs_SCnoisy_all(:, seg_range,k),2);
end
FIG = figure();
hold on;
plot_iqr(std_multiplier_list(1:k_multipliers), Perturb_Int, 'median', int_color, true, 0.8);
plot_iqr(std_multiplier_list(1:k_multipliers), Perturb_Deg, 'median', deg_color, true, 0.8);
plot_iqr(std_multiplier_list(1:k_multipliers), Perturb_Seg, 'median', seg_color, true, 0.8);
xline(mean_SC_weight, 'k--', 'Mean SC weight' ,'LineWidth',2);
hold off;
box on;
axis square;
xlim([0, std_multiplier_list(k_multipliers)]);
title('Network Perturbation');
xlabel('Rician Sigma');
ylabel('Perturbation Similarity');
set(FIG, 'Position',[1,49,1920,955]);
%% Compute Stability as linear approximation of initial slope
nroi = 214;
customFit = fittype('m*x + 1', 'independent', 'x', 'dependent', 'y');
options = fitoptions('Method', 'NonlinearLeastSquares', ...
'StartPoint', [0], ... % initial guess for [a, b]
'Lower', [-Inf], ... % lower bounds for [a, b]
'Upper', [0]); % upper bounds for [a, b]
k = 5; %Use first 5 perturbations for linear fit
x = std_multiplier_list(1:k)';
max_dPS_dP_lin = zeros(50,214);
for sub = 1:50
for i = 1:nroi
F0 = fit(x, squeeze(UU_diag_SC_vs_SCnoisy_all(sub,i,1:k)), customFit, options);
max_dPS_dP_lin(sub,i) = F0.m;
end
end
%% Visualize Stability Across Harmonics:
nroi = 214;
n_subjects = 50;
scale = 200;
[~, ~, ev_deriv] = find_ev_IntDegSeg(SC_ev_template,'1deriv');
% % From EV Regime Consensus:
int_range = 1:26;
deg_range = 27:187;
seg_range = 188:214;
int_color = [0.3, 0.9, 0.9];
deg_color = [0.9, 0.9, 0.3];
seg_color = [0.9, 0.3, 0.9];
deriv_color = [0.5 .2 .8];
lw = 2;
X = 1:214;
FIG = figure();
t = tiledlayout(1,1);
ax1 = axes(t);
hold on;
p1 = plot_iqr(X(int_range),max_dPS_dP_lin(:,int_range), 'median', int_color, true,0.8);
p2 = plot_iqr(X(deg_range),max_dPS_dP_lin(:,deg_range), 'median', deg_color, true,0.8);
p3 = plot_iqr(X(seg_range),max_dPS_dP_lin(:,seg_range), 'median', seg_color, true,0.8);
p1.LineWidth = lw;
p2.LineWidth = lw;
p3.LineWidth = lw;
xline(int_range(end)+0.5, 'k--', 'LineWidth',lw);
xline(deg_range(end)+0.5, 'k--', 'LineWidth',lw);
ax1.Box = 'off';
ax1.XLim = [0 220];
axis square;
hold off;
ax2 = axes(t);
p4 = plot(ax2, 1:nroi, ev_deriv);
p4.Color = deriv_color;
p4.LineWidth = 3;
ax2.YAxisLocation = 'right';
ax2.YColor = deriv_color;
ax2.Box = 'off';
ax2.Color = 'none';
set(ax2, 'XTickLabel',[]);
ax2.XLim = [0 220];
axis square;
set(FIG, 'Position',[1,49,1920,955]);
ax1.YLabel = ylabel('Perturbation Derivative Maximum');
ax2.YLabel = ylabel('Eigenvalue Derivative');
title('Stability of Harmonics');
xlabel({'','Eigenmode Index'})
%% Stability vs Gap-Spectrum Histogram and Scatter Plot
r = zeros(50,1); p = r; sz = 20;
r_int = zeros(50,1); p_int = r;
r_deg = zeros(50,1); p_deg = r;
r_seg = zeros(50,1); p_seg = r;
FIG = figure(); hold on;
for i = 1:n_subjects
[r(i), p(i)] = corr(ev_deriv, max_dPS_dP_lin(i,:)');
[r_int(i), p_int(i)] = corr(ev_deriv(int_range), max_dPS_dP_lin(i,int_range)');
[r_deg(i), p_deg(i)] = corr(ev_deriv(deg_range), max_dPS_dP_lin(i,deg_range)');
[r_seg(i), p_seg(i)] = corr(ev_deriv(seg_range), max_dPS_dP_lin(i,seg_range)');
scatter(ev_deriv(int_range), max_dPS_dP_lin(i,int_range)', 30,'filled', 'MarkerFaceColor', int_color, 'MarkerEdgeColor','k');
scatter(ev_deriv(deg_range), max_dPS_dP_lin(i,deg_range)', 30,'filled', 'MarkerFaceColor', deg_color, 'MarkerEdgeColor','k');
scatter(ev_deriv(seg_range), max_dPS_dP_lin(i,seg_range)', 30,'filled', 'MarkerFaceColor', seg_color, 'MarkerEdgeColor','k');
end
% % Template Derivative:
ev_deriv_rep = repmat(ev_deriv,50,1);
X = [ones(size(ev_deriv_rep)), ev_deriv_rep]; % Design matrix
max_dPS_dP_transpose = max_dPS_dP_lin';
b = X \ max_dPS_dP_transpose(:); % Regression coefficients (b0, b1)
LRfit = X * b; % Fitted values
p1 = plot(ev_deriv_rep, LRfit, 'k--','LineWidth',lw);
hold off;
axis square;
box on;
title('All Subjects dLambda vs dPS');
xlabel('EV Deriv');
ylabel('dPS/dP');
set(FIG, 'Position',[1,49,1920,955]);
ylim([-1200, 0])
%
% % % Scatter of just the median:
sz = 200;
median_max_dPS_dP = median(max_dPS_dP_lin)';
% median_max_dPS_dP = median(max_dPS_dP)';
[r_med, p_med] = corr(ev_deriv, median_max_dPS_dP);
cmap = summer(3);
FIG = figure();
% h = histogram(r);
h = histogram(r, 0.5:0.02:0.75); xlim([0.5, 0.75]);
ylim([0,15]);
p5 = xline(mean(r), 'k--');%,sprintf('mean=%0.2f', mean(r)));
p5.LineWidth = lw;
h.FaceColor = cmap(2,:);
axis square;
set(FIG, 'Position',[1,49,1920,955]);
title('Histogram of individual correlations');
xlabel("Pearson's Correlation");
ylabel('Subject Count');
%% Some extra plots...
% % Plots for median stability per regime:
%
% FIG = figure(); hold on;
% X = [ones(length(int_range),1), ev_deriv(int_range)];
% b = X \ median_max_dPS_dP(int_range);
% LRfit = X * b; % Fitted values
% p1 = plot(ev_deriv(int_range), LRfit, ':','Color', [0 0 0],'LineWidth',lw);
% scatter(ev_deriv(int_range),median_max_dPS_dP(int_range), sz,'filled', 'MarkerFaceColor',int_color,'MarkerEdgeColor','k');
% hold off;
% axis square;
% box on;
% title('INT Median dLambda vs dPS');
% xlabel('EV Deriv');
% ylabel('dPS/dP');
% set(FIG, 'Position',[1,49,1920,955]);
% % ylim([-500, 0]);
%
% FIG = figure(); hold on;
% X = [ones(length(deg_range),1), ev_deriv(deg_range)];
% b = X \ median_max_dPS_dP(deg_range);
% LRfit = X * b; % Fitted values
% p1 = plot(ev_deriv(deg_range), LRfit, ':','Color', [0 0 0],'LineWidth',lw);
% scatter(ev_deriv(deg_range),median_max_dPS_dP(deg_range), sz,'filled', 'MarkerFaceColor',deg_color,'MarkerEdgeColor','k');
% hold off;
% axis square;
% box on;
% title('DEG Median dLambda vs dPS');
% xlabel('EV Deriv');
% ylabel('dPS/dP');
% set(FIG, 'Position',[1,49,1920,955]);
% % ylim([-3000, 0]);
%
% FIG = figure(); hold on;
% X = [ones(length(seg_range),1), ev_deriv(seg_range)];
% b = X \ median_max_dPS_dP(seg_range);
% LRfit = X * b; % Fitted values
% p1 = plot(ev_deriv(seg_range), LRfit, ':','Color', [0 0 0],'LineWidth',lw);
% scatter(ev_deriv(seg_range), median_max_dPS_dP(seg_range), sz,'filled', 'MarkerFaceColor',seg_color,'MarkerEdgeColor','k');
% hold off;
% axis square;
% box on;
% title('SEG Median dLambda vs dPS');
% xlabel('EV Deriv');
% ylabel('dPS/dP');
% set(FIG, 'Position',[1,49,1920,955]);
% % ylim([-2000, 0]);
% % Violin Plots per subject-wise harmonic stability vs regime
% data2plot = [r_int, r_deg, r_seg];
%
% FIG = figure();
% violinplot(data2plot,{'INT','DEG','SEG'}, 'ViolinColor',[int_color; deg_color; seg_color]);
%
% box on;
%
% title('Subject Correlations Perturbation vs Regime');
% ylabel("Pearson's correlation");
% ylim([0 1]);
% fig_width = 3.75; fig_height = 1.45;
% pbaspect([fig_width, fig_height, 1]);
% set(FIG, 'Position',[1,49,1920,955]);