MATLAB 中 SVM 实现

直接上代码

main.m



%% Initialize data

clear, clc, close all;

load('data.mat');

y(y == 0) = -1;

% X_train = X(1:35, :);

% y_train = y(1:35);

% X_test = X(36:51, :);

% y_test = y(36:51);

%% Visualize data

% jhplotdata(X_train, y_train);

%% Training a SVM(Support Vector Machine) Classifier

C = 10;

svm = jhsvmtrain(X, y, C, 'Linear');

result = jhsvmtest(svm, X);

fprintf('Accuracy: %f\n', mean(double(result.y_pred == y)));

jhplotdata(X, y);

hold on;

x1_min = min(X(:, 1)) - 1;

x1_max = max(X(:, 1)) + 1;

x2_min = min(X(:, 2)) - 1;

x2_max = max(X(:, 2)) + 1;

[XX, YY] = meshgrid(x1_min:0.02:x1_max, x2_min:0.02:x2_max);

Z = jhsvmtest(svm, [XX(:) YY(:)]);

Z = reshape(Z.y_pred, size(XX));

contour(XX, YY, Z);

hold off;

jhsvmtrain.m



function [model] = jhsvmtrain(X, y, C, kernel_type)

%% 函数的核心就是对拉格朗日对偶式的二次规划问题, 通过返回的alpha得到我们需要的支持向量

% convert the primal problem to a dual problem, the dual problem is written

% below.

% the number of training examples.

m = length(y);

% NOTE!! The following two statements, which represent the

% target function, are fixed cause our target function is fixed.

H = y * y' * jhkernels(X', X', kernel_type);

f = -ones(m, 1);

A = [];

b = [];

Aeq = y';

beq = 0;

lb = zeros(m, 1);

% C is the regularization parameter which means that our model has already

% taken the error into the consideration.

ub = C * ones(m, 1);

alphas0 = zeros(m, 1);

epsilon = 1e-8;

options = optimset('LargeScale', 'off', 'Display', 'off');

alphas1 = quadprog(H, f, A, b, Aeq, beq, lb, ub, alphas0, options);

logic_vector = abs(alphas1) > epsilon;

model.vec_x = X(logic_vector, :);

model.vec_y = y(logic_vector);

model.alphas = alphas1(logic_vector);

end

jhsvmtest.m



function result = jhsvmtest(model, X)

% 在svmTrain中我们主要计算的就是那几个支持向量, 对应的, 核心就是alpha

% 现在有了alpha, 我们通过公式可以轻而易举地计算出w, 我们还不知道b的值, 也即是超平面偏差的值

% 所有先将我们的支持向量代入到公式中, 计算出一个临时的w

% 对于一直的支持向量来说, 我们已经知道了它的label, 所有可以计算出b, 将超平面拉过来, 再将这个b运用到测试集中即可

% 带入公式w = \sum_{i=1}^{m}\alpha^{(i)}y^{(i)}x^{(i)}^Tx

% x是输入需要预测的值

tmp = (model.alphas' .* model.vec_y' * jhkernels(model.vec_x', model.vec_x', 'Linear'))';

% 计算出偏差, 也就是超平面的截距

total_bias = model.vec_y - tmp;

bias = mean(total_bias);

% 我们已经得到了apha, 因为w是由alpha表示的, 所以通过alpha可以计算出w

% w = sum(alpha .* y_sv)*kernel(x_sv, x_test)

% 其中y_sv是sv的标签, x_sv是sv的样本, x_test是需要预测的数据

w = (model.alphas' .* model.vec_y' * jhkernels(model.vec_x', X', 'Linear'))';

result.w = w;

result.y_pred = sign(w + bias);

result.b = bias;

end

jhkernel.m



function K = jhkernels(X1, X2, kernel_type)

switch lower(kernel_type)

    case 'linear'

        K = X1' * X2;

    case 'rbf'

        K = X1' * X2;

        fprintf("I am sorry about that the rbg kernel is not implemented yet, here we still use the linear kernel to compute\n");

end

end

jhplotdata.m



function jhplotdata(X, y, caption, labelx, labely, color1, color2)

if ~exist('caption', 'var') || isempty(caption)

   caption = 'The relationship between X1 and X2';

end

if ~exist('labelx', 'var') || isempty(labelx)

   labelx = 'X1';

end

if ~exist('labely', 'var') || isempty(labely)

   labely = 'X2';

end

if ~exist('color1', 'var') || isempty(color1)

   color1 = 'r';

end

if ~exist('color2', 'var') || isempty(color2)

   color2 = 'r';

end

% JHPLOTDATA is going to plot two dimentional data

positive = find(y == 1);

negative = find(y == -1);

plot(X(positive, 1), X(positive, 2), 'ro', 'MarkerFace', color1);

hold on;

plot(X(negative, 1), X(negative, 2), 'bo', 'MarkerFace', color2);

title(caption);

xlabel(labelx);

ylabel(labely);

legend('Positive Data', 'Negative Data');

hold off;

end

巴特西

SVM 之 MATLAB 实现代码

MATLAB 中 SVM 实现

直接上代码

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