tutorial_matlab/matlab_reliability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# MVPA MEG Tutorial (Matlab): RDMs and reliability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "[Tutorial starting page](https://github.com/m-guggenmos/megmvpa/).\n",
    "\n",
    "**Goal of this tutorial:** compute representational dissimilarity matrices (RDMs) and the intersession-reliability for RDMs for the example of Support Vector Machine classification.\n",
    "\n",
    "## Tutorial\n",
    "\n",
    "We set a seed, in order to make analyses reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rng(10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's load some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "root = ''; % This is the /path/to the directory containing the data.\n",
    "           % We leave it empty here, because the data is located in the current directory.\n",
    "\n",
    "% Load data and trial labels for the two sessions of participant 01\n",
    "\n",
    "% Session 1\n",
    "load(fullfile(root, 'data01_sess1.mat'));\n",
    "load(fullfile(root, 'labels01_sess1.mat'));\n",
    "sessions(1).data = data01_sess1;\n",
    "sessions(1).labels = labels01_sess1;\n",
    "% Session 2\n",
    "load(fullfile(root, 'data01_sess2.mat'));\n",
    "load(fullfile(root, 'labels01_sess2.mat'));\n",
    "sessions(2).data = data01_sess2;\n",
    "sessions(2).labels = labels01_sess2;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we set some parameters. Only the number of permutations and the number of pseudo-trials are free parameters. The number of conditions, sensors, time points and sessions are derived from the data (i.e., from the `sessions` variable above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "% Parameters\n",
    "n_perm = 20;  % number of permutations\n",
    "n_pseudo = 5;  % number of pseudo-trials\n",
    "n_conditions = length(unique(sessions(1).labels));\n",
    "n_sensors = size(sessions(1).data, 2);\n",
    "n_time = size(sessions(1).data, 3);\n",
    "n_sessions = length(sessions);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The analytic logic is contained in a nested for loop, with loops for the number of sessions, number of permutations, number of timepoints, number of conditions, and number of conditions again. Overall, the logic contains 5 crucial steps:\n",
    "1. Compute pseudo-trials for the training and test data\n",
    "2. Whiten the training data (here using the Epoch method, which is recommended in our manuscript)\n",
    "3. Fit the classifier to the training data\n",
    "4. Predict samples from the test data\n",
    "5. Compute the dissimilarity (here classification accuracy) for the current condition pair and store in RDM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "% pre-load mechanism, for convenience\n",
    "preload_RDM = true;\n",
    "if preload_RDM\n",
    "    load(fullfile(root, 'result_reliability.mat'))\n",
    "else\n",
    "    RDM = nan(n_sessions, n_perm, n_conditions, n_conditions, n_time);\n",
    "    for s = 1:n_sessions\n",
    "\n",
    "        fprintf('Session %g / %g\\n', s, n_sessions)\n",
    "\n",
    "        X = sessions(s).data;\n",
    "        y = sessions(s).labels;\n",
    "        \n",
    "        conditions = unique(y);\n",
    "        n_trials = histc(y, conditions);\n",
    "\n",
    "        for f = 1:n_perm\n",
    "            fprintf('\\tPermutation %g / %g\\n', f, n_perm)\n",
    "            \n",
    "            % precompute permutations\n",
    "            ind_pseudo_train = nan(n_conditions, n_conditions, 2*(n_pseudo-1));\n",
    "            ind_pseudo_test = nan(n_conditions, n_conditions, 2);\n",
    "            labels_pseudo_train = nan(n_conditions, n_conditions, 2*(n_pseudo-1));\n",
    "            labels_pseudo_test = nan(n_conditions, n_conditions, 2);\n",
    "            for c1 = 1:n_conditions\n",
    "                range_c1 = (c1-1)*(n_pseudo-1)+1:c1*(n_pseudo-1);\n",
    "                for c2 = 1:n_conditions\n",
    "                    range_c2 = (c2-1)*(n_pseudo-1)+1:c2*(n_pseudo-1);\n",
    "                    ind_pseudo_train(c1, c2, 1:2*(n_pseudo - 1)) = [range_c1 range_c2];\n",
    "                    ind_pseudo_test(c1, c2, :) = [c1 c2];\n",
    "                    labels_pseudo_train(c1, c2, 1:2*(n_pseudo - 1)) = ...\n",
    "                        [conditions(c1)*ones(1, n_pseudo - 1) conditions(c2)*ones(1, n_pseudo - 1)];\n",
    "                    labels_pseudo_test(c1, c2, :) = conditions([c1 c2]);\n",
    "                end\n",
    "            end              \n",
    "            train_indices = cell(1, n_conditions*(n_pseudo-1));\n",
    "            test_indices = cell(1, n_conditions);\n",
    "            for c1 = 1:n_conditions  % separate permutation for each class\n",
    "                prm_ = randperm(n_trials(c1));                \n",
    "                prm = cell(1, n_pseudo);\n",
    "                splitsize = n_trials(c1) / n_pseudo;\n",
    "                for i = 1:n_pseudo\n",
    "                    idxs = floor(round((i-1)*splitsize)):floor(round((i)*splitsize))-1;\n",
    "                    prm{i} = prm_(idxs + 1);\n",
    "                end                                \n",
    "                ind = cellfun(@(x)x+sum(n_trials(1:c1-1)), prm, 'UniformOutput', 0);\n",
    "                xrange = (c1-1)*(n_pseudo-1)+1:c1*(n_pseudo-1);\n",
    "                for i = 1:length(xrange)\n",
    "                    train_indices{xrange(i)} = ind{i};\n",
    "                end\n",
    "                test_indices{c1} = ind{end};\n",
    "            end                                \n",
    "\n",
    "            % 1. Compute pseudo-trials for training and test\n",
    "            Xpseudo_train = nan(length(train_indices), n_sensors, n_time);\n",
    "            Xpseudo_test = nan(length(test_indices), n_sensors, n_time);\n",
    "            for i = 1:length(train_indices)\n",
    "                Xpseudo_train(i, :, :) = mean(X(train_indices{i}, :, :), 1);\n",
    "            end\n",
    "            for i = 1:length(test_indices)\n",
    "                Xpseudo_test(i, :, :) = mean(X(test_indices{i}, :, :), 1);\n",
    "            end\n",
    "\n",
    "\n",
    "            % 2. Whitening using the Epoch method\n",
    "            sigma_conditions = reshape(squeeze(labels_pseudo_train(1, :, n_pseudo:end))', 1, []);\n",
    "            sigma_ = nan(n_conditions, n_sensors, n_sensors);\n",
    "            for c = 1:n_conditions\n",
    "                % compute sigma for each time point, then average across time\n",
    "                tmp_ = nan(n_time, n_sensors, n_sensors);\n",
    "                for t = 1:n_time\n",
    "                    tmp_(t, :, :) = cov1para(Xpseudo_train(sigma_conditions==c, :, t));\n",
    "                end\n",
    "                sigma_(c, :, :) = mean(tmp_, 1);\n",
    "            end\n",
    "            sigma = squeeze(mean(sigma_, 1));  % average across conditions\n",
    "            sigma_inv = sigma^-0.5;\n",
    "            for t = 1:n_time\n",
    "                Xpseudo_train(:, :, t) = squeeze(Xpseudo_train(:, :, t)) * sigma_inv;\n",
    "                Xpseudo_test(:, :, t) = squeeze(Xpseudo_test(:, :, t)) * sigma_inv;\n",
    "            end\n",
    "\n",
    "            for t = 1:n_time\n",
    "                for c1 = 1:n_conditions-1\n",
    "                    for c2 = c1+1:n_conditions                        \n",
    "                        % 3. Fit the classifier using training data\n",
    "                        data_train = Xpseudo_train(ind_pseudo_train(c1, c2, :), :, t);\n",
    "                        y_train = squeeze(labels_pseudo_train(c1, c2, :));\n",
    "                        model_svm = svmtrain(y_train, data_train, '-c 1 -q 0 -t 0');\n",
    "\n",
    "                        % 4. Compute predictions using test data\n",
    "                        data_test = Xpseudo_test(ind_pseudo_test(c1, c2, :), :, t);\n",
    "                        y_train = squeeze(labels_pseudo_test(c1, c2, :));\n",
    "                        predictions = svmpredict(y_train, data_test, model_svm, '-q 0 -t 0');\n",
    "\n",
    "                        % 5. Compute dissimilarity and store in RDM\n",
    "                        dissimilarity = mean(predictions == y_train) - 0.5;\n",
    "                        RDM(s, f, c1, c2, t) = mean(dissimilarity);\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    % average across permutations\n",
    "    RDM = squeeze(nanmean(RDM, 2));\n",
    "    save(fullfile(root, 'result_reliability.mat'), 'RDM')\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After computing the RDMs for each session and each timepoint, let's take a look at the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at the structure of `RDM`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans =\n",
      "\n",
      "     2     9     9   111\n",
      "\n"
     ]
    }
   ],
   "source": [
    "size(RDM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable `RDM` contains a #conditions x #conditions = 9x9 RDM for 2 sessions and 111 time points (note that the time resolution is 10 ms).\n",
    "\n",
    "Now we compute two the session-to-session reliability of RDMs in two ways: pattern reliability and sum-of-squares[SSQ] reliability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reliability_pattern = nan(1, n_time);\n",
    "reliability_ssq = nan(1, n_time);\n",
    "for t = 1:n_time\n",
    "    d1_ = squeeze(RDM(1, :, :, t));\n",
    "    d1 = d1_(~isnan(d1_));\n",
    "    d2_ = squeeze(RDM(2, :, :, t));\n",
    "    d2 = d2_(~isnan(d2_));\n",
    "    reliability_pattern(t) = corr(d1, d2);\n",
    "    reliability_ssq(t) = 1 - sqrt(sum((d1-d2).^2))/sqrt(sum(d1.^2+d2.^2));\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot across time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA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\nSUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure;\n",
    "hold on\n",
    "plot(-100:10:1001, reliability_pattern, 'linewidth', 2)\n",
    "plot(-100:10:1001, reliability_ssq, 'linewidth', 2)\n",
    "xlim([-100 1000])\n",
    "xlabel('Time [ms]')\n",
    "ylabel('Reliability')\n",
    "legend('Pattern', 'SSQ')\n",
    "box on"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see, that the reliability is generally more noisy compared to classification accuracy, since it is based on only two samples: session1 and session2. In addition, we can anticipate that SSQ reliability will be higher than pattern reliability for classification. In fact, the low pattern reliability is a specific problem of classification and is due to the loss of information, when computing the binary correctness of predictions."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "codemirror_mode": "octave",
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-matlab",
   "name": "matlab",
   "version": "0.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}