A X B Cross-validation.

To implement a nested cross-validation like 5 times 2-fold cross-validation in MATLAB, you'll need to manually loop through the outer and inner folds. The idea is to repeat a 2-fold cross-validation 5 times. This approach involves splitting your data into two halves, training on one half and testing on the other, and then swapping the roles of the halves. This process is repeated 5 times with different random partitions.

Here’s how you can implement this in MATLAB and obtain the confusion matrix for each run:

% Load your dataset
load fisheriris % Example dataset
X = meas; % Features
y = species; % Labels
% Define the number of outer repetitions and inner folds
outerRepeats = 5;
innerFolds = 2;
% Initialize variables to store results
confusionMatrices = cell(outerRepeats, innerFolds);
accuracies = zeros(outerRepeats, innerFolds);
% Outer loop for repetitions
for outer = 1:outerRepeats
    % Create a partition for 2-fold cross-validation
    cv = cvpartition(y, 'KFold', innerFolds);
    
    % Inner loop for 2-fold cross-validation
    for inner = 1:innerFolds
        % Get the training and test indices for the current fold
        trainIdx = training(cv, inner);
        testIdx = test(cv, inner);
        
        % Split the data into training and test sets for this fold
        XTrain = X(trainIdx, :);
        yTrain = y(trainIdx, :);
        XTest = X(testIdx, :);
        yTest = y(testIdx, :);
        
        % Train the model on the training set
        model = fitcknn(XTrain, yTrain);
        
        % Test the model on the test set
        predictions = predict(model, XTest);
        
        % Calculate the confusion matrix for the current fold
        confMat = confusionmat(yTest, predictions);
        confusionMatrices{outer, inner} = confMat;
        
        % Calculate accuracy for the current fold
        accuracies(outer, inner) = sum(predictions == yTest) / length(yTest);
        
        % Display results for the current fold
        fprintf('Outer %d, Inner %d Accuracy: %.2f%%\n', outer, inner, accuracies(outer, inner) * 100);
    end
end
% Calculate the average accuracy across all repetitions and folds
averageAccuracy = mean(accuracies(:));
fprintf('Average Accuracy: %.2f%%\n', averageAccuracy * 100);
% Display one of the confusion matrices as an example
disp('Example Confusion Matrix:');
disp(confusionMatrices{1, 1});

Explanation:

Outer Loop: Run the 2-fold cross-validation outerRepeats times. This simulates different random splits to ensure robustness.
Inner Loop: Perform 2-fold cross-validation, where you alternate between two halves of the data for training and testing.
Model Training and Testing: Train the model on the training set and evaluate it on the test set for each fold.
Confusion Matrix and Accuracy: Calculate and store the confusion matrix and accuracy for each fold. You can access each confusion matrix from confusionMatrices.
Average Accuracy: Calculate the average accuracy over all runs and folds to get an overall performance measure.