SVMs

代价函数

支持向量机做的全部事情，就是极小化参数向量θ范数的平方，或者说长度的平方。
内积θ‘ x^((i))而变成了p^((i))⋅∥θ∥。
p^((i))用来表示这是第 i个训练样本在参数向量θ上的投影。

核函数

可视化数据集

改变惩罚系数C

C= 1

C= 1000

当C不是非常非常大的时候，它可以忽略掉一些异常点的影响，得到更好的决策界。

SVM with Gaussian

设置适当的C和sigma

function [C, sigma] = dataset3Params(X, y, Xval, yval)
%DATASET3PARAMS returns your choice of C and sigma for Part 3 of the exercise
%where you select the optimal (C, sigma) learning parameters to use for SVM
%with RBF kernel
%   [C, sigma] = DATASET3PARAMS(X, y, Xval, yval) returns your choice of C and 
%   sigma. You should complete this function to return the optimal C and 
%   sigma based on a cross-validation set.
%

% You need to return the following variables correctly.
C = 1;
sigma = 0.3;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the optimal C and sigma
%               learning parameters found using the cross validation set.
%               You can use svmPredict to predict the labels on the cross
%               validation set. For example, 
%                   predictions = svmPredict(model, Xval);
%               will return the predictions on the cross validation set.
%
%  Note: You can compute the prediction error using 
%        mean(double(predictions ~= yval))
%
para_c = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30];
para_s = para_c;
error = 10;


for i=1:length(para_c)
    for j=1:length(para_c)
        model = svmTrain(X, y, para_c(i), @(x1, x2) gaussianKernel(x1, x2, para_s(j)));
        predict = svmPredict(model, Xval);
        cur = mean(double(predict ~= yval));
        if cur < error
            error = cur;
            C = para_c(i);
            sigma = para_s(j);
        end
    end
end





% =========================================================================

end