主要有两个原因我们做
cross-validation：
>作为一种测试方法,使我们几乎无偏估计我们的模型的泛化力(通过避免过度拟合)
>作为model selection的一种方式(例如：在训练数据中找到最佳的C和gamma参数,参见this post的一个例子)
对于我们感兴趣的第一种情况,该过程涉及对每个折叠训练k个模型,然后在整个训练集中训练一个最终模型.
我们报告平均精度在k折.
现在,由于我们使用一对一的方法来处理多类问题,每个模型由N个支持向量机(每个类一个)组成.
以下是实现一对一的方法的封装函数：
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
并且这里是支持交叉验证的功能：
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
最后,这里是简单的演示来说明用法：
%# 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);
将其与由libsvm默认使用的一对一方法进行比较：
acc = libsvmtrain(labels, data, sprintf('%s -v %d -q',opts,nfold));
model = libsvmtrain(labels, data, strcat(opts,' -q'));