PCA Feature Selection and Adaboost.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ans =\n",
      "\n",
      "   2.1244e-13\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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NV0kSEhJox9I3JCRpEG2hkSx3amGZSqXas2ePXq/Pyclpa2ubM2eOUqnkHqqp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\nQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clear all\n",
    "load RunTimeData.mat\n",
    "[coeff,score,~,~,explained_data] = pca(data);\n",
    "projdata = data*coeff(:,1:2);\n",
    "subplot(121), plot(projdata(:,1),projdata(:,2),'x') , title('Built-in')\n",
    "[eigvec, eigval] = eig(cov(data));\n",
    "pca_data = (eigvec(:,end-1:end)'*data')';   % pca_data = data*eigvec(:,end-1:end)\n",
    "subplot(122), plot(pca_data(:,1),pca_data(:,2),'x') , title('My implementation')\n",
    "sum(sum(abs((bsxfun(@minus,data,mean(data,1)))-score*coeff')))        % should give 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA feature selection and AdaBoost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### prepare data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "clear all; clc; \n",
    "load('MEGdata.mat')  \n",
    "\n",
    "idx1 = find(VideoClass==1);\n",
    "idx2 = find(VideoClass==2);\n",
    "\n",
    "data = double( MEGdata([idx1;idx2],:,:));\n",
    "class = double (VideoClass([idx1;idx2]));\n",
    "\n",
    "\n",
    "N = size(class,1);     % Number of samples\n",
    "Ntest = 50;\n",
    "Ntrain = N - Ntest;\n",
    "\n",
    "idx = randperm(N);      \n",
    "trndata = double( data(idx(1:Ntrain),:,:));\n",
    "trnclass = double ( class(idx(1:Ntrain)));\n",
    "\n",
    "NumOfClasses = length(unique(trnclass));\n",
    "\n",
    "\n",
    "testdata = double( data(idx(Ntrain+1:end),:,:) );\n",
    "testclass = double( class(idx(Ntrain+1:end)));\n",
    "\n",
    "trn_feature = [mean(trndata,3) var(trndata,0,3)];\n",
    "test_feature = [mean(testdata,3) var(testdata,0,3)];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### pca feature selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "% [eigvec_trn, eigval_trn] = eig(cov(trn_feature));\n",
    "% [eigvec_test, eigval_test] = eig(cov(test_feature));\n",
    "\n",
    "[coeff_trn,~,~,~,explained_trn] = pca(trn_feature);\n",
    "[coeff_test,~,~,~,explained_test] = pca(test_feature);\n",
    "trn_feature_hat = trn_feature*coeff_trn(:,1:25);\n",
    "test_feature_hat = test_feature*coeff_test(:,1:25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AdaBoost\n",
    "- Adaboost algorithm using WLSQ (Weighted Least Squares) classifier as base classifier. The weighted least square fit is given by\n",
    "\n",
    "$$\n",
    "\\beta = (X^TWX)^{-1} X^TWy\n",
    "$$\n",
    "\n",
    "where $W$ is diagonal matrix containing data importance weights, $X$ is a matrix containing data training samples and 1 on it's rows, and $y$ is a vector of values 1 and -1 indicating class label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 5;  % boosting round (Number of base learners)\n",
    "w = 1/Ntrain * ones(1,Ntrain);  % initialize weights\n",
    "W = diag(w);                    % diagonal weight matrix\n",
    "beta = zeros(size(trn_feature_hat,2),L);\n",
    "err = 0.1*ones(1,L);    % error rate for each base learners\n",
    "\n",
    "% Training Phase\n",
    "for j=1:L   % for all base learners\n",
    "\n",
    "    % randomly draw X_j from X with probability w_j\n",
    "    randIdx = randsrc(Ntrain,1,[1:Ntrain;w]);\n",
    "    X = trn_feature_hat(randIdx,:);\n",
    "\n",
    "    %true_y = -1*ones(1,Ntrain);     % true class labels\n",
    "    true_trn_y = trnclass(randIdx)';\n",
    "    true_trn_y(true_trn_y==2) = -1;     % Class 1 -> 1, Class2 -> -1\n",
    "    beta(:,j) = ((X'*W*X)\\X')*W*true_trn_y';\n",
    "    predicted_y = sign(X*beta(:,j));\n",
    "    err(j) = sum(w(true_trn_y~=predicted_y'));\n",
    "    if err(j) <= 0 || err(j)>0.5\n",
    "       break; \n",
    "    else\n",
    "        % adjust weights for missclassfified patterns (to increase their importance)\n",
    "        w(true_trn_y~=predicted_y') = w(true_trn_y~=predicted_y')*(1-err(j))/err(j);\n",
    "        w = w./sum(w);  % normalize probabilities\n",
    "        W = diag(w);\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "% Testing Phase\n",
    "predicted_ensemble_y = zeros(Ntest,L);\n",
    "for j=1:L\n",
    "    predicted_ensemble_y(:,j) = sign(test_feature_hat*beta(:,j));\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aggregating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "predicted_test_y = zeros(Ntest,1);\n",
    "for i=1:Ntest\n",
    "    predicted_test_y(i,:) = sign(sum(log((1-err)./err).*predicted_ensemble_y(i,:)));\n",
    "end\n",
    "\n",
    "true_test_y =  testclass;\n",
    "true_test_y(true_test_y==2) = -1;\n",
    "\n",
    "TestPredAcc = mean(predicted_test_y==true_test_y)"
   ]
  }
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