SVM.zip_svm 分割_svm 分类_svm正样本_正例

function [model] = svmTrain(X, Y, C, kernelFunction, ... tol, max_passes) %SVMTRAIN Trains an SVM classifier using a simplified version of the SMO %algorithm. % [model] = SVMTRAIN(X, Y, C, kernelFunction, tol, max_passes) trains an % SVM classifier and returns trained model. X is the matrix of training % examples. Each row is a training example, and the jth column holds the % jth feature. Y is a column matrix containing 1 for positive examples % and 0 for negative examples. C is the standard SVM regularization % parameter. tol is a tolerance value used for determining equality of % floating point numbers. max_passes controls the number of iterations % over the dataset (without changes to alpha) before the algorithm quits. % % Note: This is a simplified version of the SMO algorithm for training % SVMs. In practice, if you want to train an SVM classifier, we % recommend using an optimized package such as: % % LIBSVM (http://www.csie.ntu.edu.tw/~cjlin/libsvm/) % SVMLight (http://svmlight.joachims.org/) % % if ~exist('tol', 'var') || isempty(tol) tol = 1e-3; end if ~exist('max_passes', 'var') || isempty(max_passes) max_passes = 5; end % Data parameters m = size(X, 1); n = size(X, 2); % Map 0 to -1 Y(Y==0) = -1; % Variables alphas = zeros(m, 1); b = 0; E = zeros(m, 1); passes = 0; eta = 0; L = 0; H = 0; % Pre-compute the Kernel Matrix since our dataset is small % (in practice, optimized SVM packages that handle large datasets % gracefully will _not_ do this) % % We have implemented optimized vectorized version of the Kernels here so % that the svm training will run faster. if strcmp(func2str(kernelFunction), 'linearKernel') % Vectorized computation for the Linear Kernel % This is equivalent to computing the kernel on every pair of examples K = X*X'; elseif strfind(func2str(kernelFunction), 'gaussianKernel') % Vectorized RBF Kernel % This is equivalent to computing the kernel on every pair of examples X2 = sum(X.^2, 2); K = bsxfun(@plus, X2, bsxfun(@plus, X2', - 2 * (X * X'))); K = kernelFunction(1, 0) .^ K; else % Pre-compute the Kernel Matrix % The following can be slow due to the lack of vectorization K = zeros(m); for i = 1:m for j = i:m K(i,j) = kernelFunction(X(i,:)', X(j,:)'); K(j,i) = K(i,j); %the matrix is symmetric end end end % Train fprintf('\nTraining ...'); dots = 12; while passes < max_passes, num_changed_alphas = 0; for i = 1:m, % Calculate Ei = f(x(i)) - y(i) using (2). % E(i) = b + sum (X(i, :) * (repmat(alphas.*Y,1,n).*X)') - Y(i); E(i) = b + sum (alphas.*Y.*K(:,i)) - Y(i); if ((Y(i)*E(i) < -tol && alphas(i) < C) || (Y(i)*E(i) > tol && alphas(i) > 0)), % In practice, there are many heuristics one can use to select % the i and j. In this simplified code, we select them randomly. j = ceil(m * rand()); while j == i, % Make sure i \neq j j = ceil(m * rand()); end % Calculate Ej = f(x(j)) - y(j) using (2). E(j) = b + sum (alphas.*Y.*K(:,j)) - Y(j); % Save old alphas alpha_i_old = alphas(i); alpha_j_old = alphas(j); % Compute L and H by (10) or (11). if (Y(i) == Y(j)), L = max(0, alphas(j) + alphas(i) - C); H = min(C, alphas(j) + alphas(i)); else L = max(0, alphas(j) - alphas(i)); H = min(C, C + alphas(j) - alphas(i)); end if (L == H), % continue to next i. continue; end % Compute eta by (14). eta = 2 * K(i,j) - K(i,i) - K(j,j); if (eta >= 0), % continue to next i. continue; end % Compute and clip new value for alpha j using (12) and (15). alphas(j) = alphas(j) - (Y(j) * (E(i) - E(j))) / eta; % Clip alphas(j) = min (H, alphas(j)); alphas(j) = max (L, alphas(j)); % Check if change in alpha is significant if (abs(alphas(j) - alpha_j_old) < tol), % continue to next i. % replace anyway alphas(j) = alpha_j_old; continue; end % Determine value for alpha i using (16). alphas(i) = alphas(i) + Y(i)*Y(j)*(alpha_j_old - alphas(j)); % Compute b1 and b2 using (17) and (18) respectively. b1 = b - E(i) ... - Y(i) * (alphas(i) - alpha_i_old) * K(i,j)' ... - Y(j) * (alphas(j) - alpha_j_old) * K(i,j)'; b2 = b - E(j) ... - Y(i) * (alphas(i) - alpha_i_old) * K(i,j)' ... - Y(j) * (alphas(j) - alpha_j_old) * K(j,j)'; % Compute b by (19). if (0 < alphas(i) && alphas(i) < C), b = b1; elseif (0 < alphas(j) && alphas(j) < C), b = b2; else b = (b1+b2)/2; end num_changed_alphas = num_changed_alphas + 1; end end if (num_changed_alphas == 0), passes = passes + 1; else passes = 0; end fprintf('.'); dots = dots + 1; if dots > 78 dots = 0; fprintf('\n'); end if exist('OCTAVE_VERSION') fflush(stdout); end end fprintf(' Done! \n\n'); % Save the model idx = alphas > 0; model.X= X(idx,:); model.y= Y(idx); model.kernelFunction = kernelFunction; model.b= b; model.alphas= alphas(idx); model.w = ((alphas.*Y)'*X)'; end