title: What exactly the ROC curve can tell us or can be inferred?
body: <p>I wrote some codes to run a linear discriminant analysis based classification:</p>
  
  <pre><code>%% Construct a LDA classifier with selected features and ground truth information
  LDAClassifierObject                     = ClassificationDiscriminant.fit(featureSelcted, groundTruthGroup, 'DiscrimType', 'linear');
  LDAClassifierResubError                 = resubLoss(LDAClassifierObject);
  </code></pre>
  
  <p>Thus, I can get</p>
  
  <pre><code>Resubstitution Error of LDA (Training Error): 1.7391e-01
  Resubstitution Accuracy of LDA: 82.61%
  Confusion Matrix of LDA:
      14     3
       1     5
  </code></pre>
  
  <p>Then I run a ROC analysis for the LDA classifier:</p>
  
  <pre><code>% Predict resubstitution response of LDA classifier
  [LDALabel, LDAScore]                    = resubPredict(LDAClassifierObject);
  
  % Fit probabilities for scores (the groundTruthGroup contains lables either 'Good' or 'Bad')
  [FPR, TPR, Thr, AUC, OPTROCPT]      = perfcurve(groundTruthGroup(:,1), LDAScore(:,1), 'Good');
  </code></pre>
  
  <p>I have got:</p>
  
  <pre><code>OPTROCPT =
  
      0.1250    0.8667
  </code></pre>
  
  <p>Therefore, we can get:</p>
  
  <pre><code>Accuracy of LDA after ROC analysis: 86.91%
  Confusion Matrix of LDA after ROC analysis:
      13     1
       2     7
  </code></pre>
  
  <p>My questions are:</p>
  
  <ol>
  <li><p>After ROC analysis we obtained a better accuracy, when we report the accuracy of the classifier, which value we should use? What exactly the ROC curve can tell us or can be inferred? Can we say after ROC analysis we found a better accuracy of the LDA classifier?</p></li>
  <li><p>Why the ROC can produce a better accuracy for the classifier, but the original ClassificationDiscriminant.fit can't?</p></li>
  <li><p>I have also done a cross validation for the LDA classifier, like</p>
  
  <p>cvLDAClassifier                     = crossval(LDAClassifierObject, 'leaveout', 'on');</p></li>
  </ol>
  
  <p>Then how to get the ROC analysis for the cross validation? '<code>resubPredict</code>' method seems only accept 'discriminant object' as input, then how can we get the scores?</p>
  
  <p>4.. <code>classperf</code> function of Matlab is very handy to gather all the information of the classifier, like</p>
  
  <pre><code>%% Get the performance of the classifier
  LDAClassifierPerformace                 = classperf(groundTruthGroup, resubPredict(LDAClassifierObject));
  </code></pre>
  
  <p>However, anyone knows how to gather these information such as accuracy, FPR, etc. for the cross validation results?</p>
  
  <p>Thanks very much. I am really looking forward to see the reply to above questions. </p>
  
  <p>A.</p>