Representational Similarity Analysis tutorial

Dataset

• from Woo et al., 2014, Nat Comms (download: https://cocoanlab.github.io/pdfs/Woo_2014_NatComms.pdf)
• N = 59
• There were two types of tasks, and in each task, there were two conditions (2 x 2 design)
• -- Physical pain task (Heat, Warmth conditions)
• -- Social pain task (Rejection, Friends conditions)

Analysis plan

1. Computing RDMs for each participant, for each region (4 ROIs: aINS, dACC, S2/dpINS, TPJ and 1 whole-brain mask), and visualize the average RDMs (the whole-brain mask was created using neurosynth [10/04/2013] with the a priori terms, 'pain', 'emotion', and 'social'; the union of forward and reverse inference maps at q < .1, FDR corrected)
2. Comparing brain (4 ROIs and whole-brain masks) and model RDMs -- We will use four model RDMs to test: heat vs. others (HO), rejection vs. others (RO), physical vs. social (PS), aversive vs. non-aversive (AN)
3. Statistical inference: Using each brian mask, we will do statistical inference for four models above

Key research question:

Step 1: Computing and visualizing RDMs

Basic setup

Reading data for ROI masks

Computing RDMs for each region and for each individual

Visualize mean RDMs

figure;

set(gcf, 'position', [1 740 1487 215], 'color', 'w')

for i = 1:numel(roi)

if i == 1, disp('Representational Dissimilarity Matrices'); end

subplot(1,5,i);

imagesc(mean(roi{i}.rdms,3));

colorbar;

roi{i}.name(strfind(roi{i}.name, '_')) = ' ';

title(roi{i}.name);

set(gca, 'xticklabel', conditions, 'XTickLabelRotation', 90, 'yticklabel', conditions);

end

Representational Dissimilarity Matrices

Step 2: Comparing brain and model RDMs

Creating model RDMs

% 1. Pain vs. others

model{1}.rdms = [0 1 1 1;1 0 0 0;1 0 0 0;1 0 0 0];

model{1}.name = 'pain vs others';

% 2. Rejection vs. others

model{2}.rdms = [0 0 1 0;0 0 1 0;1 1 0 1;0 0 1 0];

model{2}.name = 'rejection vs others';

% 3. physical vs. social

model{3}.rdms = [0 0 1 1;0 0 1 1;1 1 0 0;1 1 0 0];

model{3}.name = 'physical vs social';

% 4. aversive (pain and rejection) vs. nonaversive (warmth and friend)

model{4}.rdms = [0 1 0 1;1 0 1 0;0 1 0 1;1 0 1 0];

model{4}.name = 'aversive vs nonaversive';

figure;

set(gcf, 'position', [1 755 1135 200], 'color', 'w')

for i = 1:numel(model)

if i == 1, disp('Model Representational Dissimilarity Matrices'); end

subplot(1,4,i);

imagesc(model{i}.rdms);

colorbar;

title(model{i}.name);

set(gca, 'xtick', 1:4, 'ytick', 1:4);

set(gca, 'xticklabel', conditions, 'XTickLabelRotation', 90, 'yticklabel', conditions);

end

Model Representational Dissimilarity Matrices

Comparing the ROI RDMs with the model RDMs

Visualize the relationships among the regions and models using MDS (multidimensional scaling) and t-SNE

rdm_model = 1-r_models;

Y = mdscale(rdm_model,4);

figure;

set(gcf, 'position', [1 605 1141 350])

subplot(1,3,1);

imagesc(r_models);

set(gca, 'xtick', 1:7, 'ytick', 1:7, 'xticklabel', rdms.names, 'XTickLabelRotation', 90, 'yticklabel', rdms.names);

colorbar;

title('Model RDM correlation (Kendall''s tau a)');

subplot(1,3,2);

for i = 1:size(Y,1)

for j = 1:size(Y,1)

if i ~= j

if rdm_model(i,j) ~= 0

h = line([Y(i,1), Y(j,1)], [Y(i,2), Y(j,2)], 'linewidth', (2-rdm_model(i,j))*3, 'color', [.5 .5 .5 .1]);

end

end

end

end

hold on;

scatter(Y(:,1), Y(:,2), 100, 'r', 'filled');

short_name = {'S2/dpINS', 'aINS', 'dACC', 'TPJ', 'whole', 'HO', 'RO', 'PS', 'AN'};

text(Y(:,1)+.05, Y(:,2)+.05, short_name, 'Rotation', 45, 'fontsize', 15)

set(gca, 'xlim', [-0.5 1.3], 'ylim', [-0.6 0.9]);

axis off;

title('MDS');

subplot(1,3,3);

rng(135); % used a fixed seed (an arbitrary number) for reproducibility

Y = tsne(rdms.flatten_dat','Algorithm','exact','Distance','correlation', 'Perplexity', 5);

for i = 1:size(Y,1)

for j = 1:size(Y,1)

if i ~= j

if rdm_model(i,j) ~= 0

h = line([Y(i,1), Y(j,1)], [Y(i,2), Y(j,2)], 'linewidth', (2-rdm_model(i,j))*3, 'color', [.5 .5 .5 .1]);

end

end

end

end

hold on;

scatter(Y(:,1), Y(:,2), 100, 'r', 'filled');

text(Y(:,1)+10, Y(:,2)+10, short_name, 'Rotation', 45, 'fontsize', 15);

set(gca, 'xlim', get(gca, 'xlim')+[0 50], 'ylim', get(gca, 'ylim')+[0 50]);

title('tSNE')

axis off;

disp('HO: Heat vs. Others, RO: Rejection vs. Others, PS: Physical vs. Social, AN: Aversive vs. Non-aversive');

HO: Heat vs. Others, RO: Rejection vs. Others, PS: Physical vs. Social, AN: Aversive vs. Non-aversive

Step 3: Statistical inference

Prep for bootstrap tests

Run bootstrap tests

Plot the results

figure;

set(gcf, 'position', [1 701 1669 254]);

for roi_i = 1:numel(roi)

y = [roi{roi_i}.bootmean_HO roi{roi_i}.bootmean_RO roi{roi_i}.bootmean_PS roi{roi_i}.bootmean_AN];

e = [roi{roi_i}.bootste_HO roi{roi_i}.bootste_RO roi{roi_i}.bootste_PS roi{roi_i}.bootste_AN];

p = [roi{roi_i}.bootP_HO roi{roi_i}.bootP_RO roi{roi_i}.bootP_PS roi{roi_i}.bootP_AN];

subplot(1, numel(roi), roi_i);

bar_wani_2016(y, e, .8, 'errbar_width', 0, 'ast', p, 'use_samefig', 'ylim', [-.6 1]);

patch(get(gca, 'xlim'), roi{roi_i}.noise_ceiling, [.7 .7 .7]);

title(roi{roi_i}.name);

ylabel('correlation (Kendall''s tau a)');

xticklabels(model_names);

end

Conclusion