10 fold cross-validation in one-against-all SVM (using LibSVM)

Solution 1:

Mainly there are two reasons we do cross-validation:

• as a testing method which gives us a nearly unbiased estimate of the generalization power of our model (by avoiding overfitting)
• as a way of model selection (eg: find the best C and gamma parameters over the training data, see this post for an example)

For the first case which we are interested in, the process involves training k models for each fold, and then training one final model over the entire training set. We report the average accuracy over the k-folds.

Now since we are using one-vs-all approach to handle the multi-class problem, each model consists of N support vector machines (one for each class).

The following are wrapper functions implementing the one-vs-all approach:

function mdl = libsvmtrain_ova(y, X, opts)
    if nargin < 3, opts = ''; end

    %# classes
    labels = unique(y);
    numLabels = numel(labels);

    %# train one-against-all models
    models = cell(numLabels,1);
    for k=1:numLabels
        models{k} = libsvmtrain(double(y==labels(k)), X, strcat(opts,' -b 1 -q'));
    end
    mdl = struct('models',{models}, 'labels',labels);
end

function [pred,acc,prob] = libsvmpredict_ova(y, X, mdl)
    %# classes
    labels = mdl.labels;
    numLabels = numel(labels);

    %# get probability estimates of test instances using each 1-vs-all model
    prob = zeros(size(X,1), numLabels);
    for k=1:numLabels
        [~,~,p] = libsvmpredict(double(y==labels(k)), X, mdl.models{k}, '-b 1 -q');
        prob(:,k) = p(:, mdl.models{k}.Label==1);
    end

    %# predict the class with the highest probability
    [~,pred] = max(prob, [], 2);
    %# compute classification accuracy
    acc = mean(pred == y);
end

And here are functions to support cross-validation:

function acc = libsvmcrossval_ova(y, X, opts, nfold, indices)
    if nargin < 3, opts = ''; end
    if nargin < 4, nfold = 10; end
    if nargin < 5, indices = crossvalidation(y, nfold); end

    %# N-fold cross-validation testing
    acc = zeros(nfold,1);
    for i=1:nfold
        testIdx = (indices == i); trainIdx = ~testIdx;
        mdl = libsvmtrain_ova(y(trainIdx), X(trainIdx,:), opts);
        [~,acc(i)] = libsvmpredict_ova(y(testIdx), X(testIdx,:), mdl);
    end
    acc = mean(acc);    %# average accuracy
end

function indices = crossvalidation(y, nfold)
    %# stratified n-fold cros-validation
    %#indices = crossvalind('Kfold', y, nfold);  %# Bioinformatics toolbox
    cv = cvpartition(y, 'kfold',nfold);          %# Statistics toolbox
    indices = zeros(size(y));
    for i=1:nfold
        indices(cv.test(i)) = i;
    end
end

Finally, here is simple demo to illustrate the usage:

%# laod dataset
S = load('fisheriris');
data = zscore(S.meas);
labels = grp2idx(S.species);

%# cross-validate using one-vs-all approach
opts = '-s 0 -t 2 -c 1 -g 0.25';    %# libsvm training options
nfold = 10;
acc = libsvmcrossval_ova(labels, data, opts, nfold);
fprintf('Cross Validation Accuracy = %.4f%%\n', 100*mean(acc));

%# compute final model over the entire dataset
mdl = libsvmtrain_ova(labels, data, opts);

Compare that against the one-vs-one approach which is used by default by libsvm:

acc = libsvmtrain(labels, data, sprintf('%s -v %d -q',opts,nfold));
model = libsvmtrain(labels, data, strcat(opts,' -q'));

Solution 2:

It may be confusing you that one of the two questions is not about LIBSVM. You should try to adjust this answer and ignore the other.

You should select the folds, and do the rest exactly as the linked question. Assume the data has been loaded into data and the labels into labels:

n = size(data,1);
ns = floor(n/10);
for fold=1:10,
    if fold==1,
        testindices= ((fold-1)*ns+1):fold*ns;
        trainindices = fold*ns+1:n;
    else
        if fold==10,
            testindices= ((fold-1)*ns+1):n;
            trainindices = 1:(fold-1)*ns;
        else
            testindices= ((fold-1)*ns+1):fold*ns;
            trainindices = [1:(fold-1)*ns,fold*ns+1:n];
         end
    end
    % use testindices only for testing and train indices only for testing
    trainLabel = label(trainindices);
    trainData = data(trainindices,:);
    testLabel = label(testindices);
    testData = data(testindices,:)
    %# train one-against-all models
    model = cell(numLabels,1);
    for k=1:numLabels
        model{k} = svmtrain(double(trainLabel==k), trainData, '-c 1 -g 0.2 -b 1');
    end

    %# get probability estimates of test instances using each model
    prob = zeros(size(testData,1),numLabels);
    for k=1:numLabels
        [~,~,p] = svmpredict(double(testLabel==k), testData, model{k}, '-b 1');
        prob(:,k) = p(:,model{k}.Label==1);    %# probability of class==k
    end

    %# predict the class with the highest probability
    [~,pred] = max(prob,[],2);
    acc = sum(pred == testLabel) ./ numel(testLabel)    %# accuracy
    C = confusionmat(testLabel, pred)                   %# confusion matrix
end