gradingPCA.m

function [trainedClassifier, validationAccuracy,classificationTree] = gradingPCA(trainingData)
% trainClassifier(trainingData)
%  returns a trained classifier and its accuracy.
%  This code recreates the classification model trained in
%  Classification Learner app.
%
%   Input:
%       trainingData: the training data of same data type as imported
%        in the app (table or matrix).
%
%   Output:
%       trainedClassifier: a struct containing the trained classifier.
%        The struct contains various fields with information about the
%        trained classifier.
%
%       trainedClassifier.predictFcn: a function to make predictions
%        on new data. It takes an input of the same form as this training
%        code (table or matrix) and returns predictions for the response.
%        If you supply a matrix, include only the predictors columns (or
%        rows).
%
%       validationAccuracy: a double containing the accuracy in
%        percent. In the app, the History list displays this
%        overall accuracy score for each model.
%
%  Use the code to train the model with new data.
%  To retrain your classifier, call the function from the command line
%  with your original data or new data as the input argument trainingData.
%
%  For example, to retrain a classifier trained with the original data set
%  T, enter:
%    [trainedClassifier, validationAccuracy] = trainClassifier(T)
%
%  To make predictions with the returned 'trainedClassifier' on new data T,
%  use
%    yfit = trainedClassifier.predictFcn(T)
%
%  To automate training the same classifier with new data, or to learn how
%  to programmatically train classifiers, examine the generated code.

% Auto-generated by MATLAB on 04-Dec-2016 22:35:57


% Extract predictors and response
% This code processes the data into the right shape for training the
% classifier.
inputTable = trainingData;
predictorNames = {'neurodens', 'gndens', 'gliodens', 'astrodens'};
predictors = inputTable(:, predictorNames);
response = inputTable.tissue;
isCategoricalPredictor = [false, false, false, false];

% Apply a PCA to the predictor matrix.
% Run PCA on numeric predictors only. Categorical predictors are passed through PCA untouched.
isCategoricalPredictorBeforePCA = isCategoricalPredictor;
numericPredictors = predictors(:, ~isCategoricalPredictor);
numericPredictors = table2array(varfun(@double, numericPredictors));
% 'inf' values have to be treated as missing data for PCA.
numericPredictors(isinf(numericPredictors)) = NaN;
[pcaCoefficients, pcaScores, ~, ~, explained, pcaCenters] = pca(...
    numericPredictors, ...
    'Centered', true);
% Keep enough components to explain the desired amount of variance.
explainedVarianceToKeepAsFraction = 87/100;
numComponentsToKeep = find(cumsum(explained)/sum(explained) >= explainedVarianceToKeepAsFraction, 1);
pcaCoefficients = pcaCoefficients(:,1:numComponentsToKeep);
predictors = [array2table(pcaScores(:,1:numComponentsToKeep)), predictors(:, isCategoricalPredictor)];
isCategoricalPredictor = [false(1,numComponentsToKeep), true(1,sum(isCategoricalPredictor))];

% Train a classifier
% This code specifies all the classifier options and trains the classifier.
classificationTree = fitctree(...
    predictors, ...
    response, ...
    'SplitCriterion', 'gdi', ...
    'MaxNumSplits', 100, ...
    'Surrogate', 'off', ...
    'ClassNames', {'HIGH'; 'INTER'});

% Create the result struct with predict function
predictorExtractionFcn = @(t) t(:, predictorNames);
pcaTransformationFcn = @(x) [ array2table(bsxfun(@minus, table2array(varfun(@double, x(:, ~isCategoricalPredictorBeforePCA))), pcaCenters) * pcaCoefficients), x(:,isCategoricalPredictorBeforePCA) ];
treePredictFcn = @(x) predict(classificationTree, x);
trainedClassifier.predictFcn = @(x) treePredictFcn(pcaTransformationFcn(predictorExtractionFcn(x)));

% Add additional fields to the result struct
trainedClassifier.RequiredVariables = {'neurodens', 'gndens', 'gliodens', 'astrodens'};
trainedClassifier.PCACenters = pcaCenters;
trainedClassifier.PCACoefficients = pcaCoefficients;
trainedClassifier.ClassificationTree = classificationTree;
trainedClassifier.About = 'This struct is a trained classifier exported from Classification Learner R2016a.';
trainedClassifier.HowToPredict = sprintf('To make predictions on a new table, T, use: \n  yfit = c.predictFcn(T) \nreplacing ''c'' with the name of the variable that is this struct, e.g. ''trainedClassifier''. \n \nThe table, T, must contain the variables returned by: \n  c.RequiredVariables \nVariable formats (e.g. matrix/vector, datatype) must match the original training data. \nAdditional variables are ignored. \n \nFor more information, see <a href="matlab:helpview(fullfile(docroot, ''stats'', ''stats.map''), ''appclassification_exportmodeltoworkspace'')">How to predict using an exported model</a>.');

% Extract predictors and response
% This code processes the data into the right shape for training the
% classifier.
inputTable = trainingData;
predictorNames = {'neurodens', 'gndens', 'gliodens', 'astrodens'};
predictors = inputTable(:, predictorNames);
response = inputTable.tissue;
isCategoricalPredictor = [false, false, false, false];

% Perform cross-validation
KFolds = 20;
cvp = cvpartition(response, 'KFold', KFolds);
% Initialize the predictions and scores to the proper sizes
validationPredictions = response;
numObservations = size(predictors, 1);
numClasses = 2;
validationScores = NaN(numObservations, numClasses);
for fold = 1:KFolds
    trainingPredictors = predictors(cvp.training(fold), :);
    trainingResponse = response(cvp.training(fold), :);
    foldIsCategoricalPredictor = isCategoricalPredictor;
    
    % Apply a PCA to the predictor matrix.
    % Run PCA on numeric predictors only. Categorical predictors are passed through PCA untouched.
    isCategoricalPredictorBeforePCA = foldIsCategoricalPredictor;
    numericPredictors = trainingPredictors(:, ~foldIsCategoricalPredictor);
    numericPredictors = table2array(varfun(@double, numericPredictors));
    % 'inf' values have to be treated as missing data for PCA.
    numericPredictors(isinf(numericPredictors)) = NaN;
    [pcaCoefficients, pcaScores, ~, ~, explained, pcaCenters] = pca(...
        numericPredictors, ...
        'Centered', true);
    % Keep enough components to explain the desired amount of variance.
    explainedVarianceToKeepAsFraction = 87/100;
    numComponentsToKeep = find(cumsum(explained)/sum(explained) >= explainedVarianceToKeepAsFraction, 1);
    pcaCoefficients = pcaCoefficients(:,1:numComponentsToKeep);
    trainingPredictors = [array2table(pcaScores(:,1:numComponentsToKeep)), trainingPredictors(:, foldIsCategoricalPredictor)];
    foldIsCategoricalPredictor = [false(1,numComponentsToKeep), true(1,sum(foldIsCategoricalPredictor))];
    
    % Train a classifier
    % This code specifies all the classifier options and trains the classifier.
    classificationTree = fitctree(...
        trainingPredictors, ...
        trainingResponse, ...
        'SplitCriterion', 'gdi', ...
        'MaxNumSplits', 100, ...
        'Surrogate', 'off', ...
        'ClassNames', {'HIGH'; 'INTER'});
    
    % Create the result struct with predict function
    pcaTransformationFcn = @(x) [ array2table(bsxfun(@minus, table2array(varfun(@double, x(:, ~isCategoricalPredictorBeforePCA))), pcaCenters) * pcaCoefficients), x(:,isCategoricalPredictorBeforePCA) ];
    treePredictFcn = @(x) predict(classificationTree, x);
    validationPredictFcn = @(x) treePredictFcn(pcaTransformationFcn(x));
    
    % Add additional fields to the result struct
    
    % Compute validation predictions and scores
    validationPredictors = predictors(cvp.test(fold), :);
    [foldPredictions, foldScores] = validationPredictFcn(validationPredictors);
    
    % Store predictions and scores in the original order
    validationPredictions(cvp.test(fold), :) = foldPredictions;
    validationScores(cvp.test(fold), :) = foldScores;
end

correctPredictions = strcmp(validationPredictions, response);
validationAccuracy = sum(correctPredictions)/length(correctPredictions);