Coursera Machine Learning 第七周 quiz Programming Exercise 6: Support Vector Machines

gaussianKernel.m

function sim = gaussianKernel(x1, x2, sigma)
%RBFKERNEL returns a radial basis function kernel between x1 and x2
%   sim = gaussianKernel(x1, x2) returns a gaussian kernel between x1 and x2
%   and returns the value in sim

% Ensure that x1 and x2 are column vectors
x1 = x1(:); x2 = x2(:);

% You need to return the following variables correctly.
sim = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the similarity between x1
%               and x2 computed using a Gaussian kernel with bandwidth
%               sigma
%
%
SSq = sum((x1-x2).^2);


Temp1  = SSq / (2 * sigma^2);
sim=exp(-Temp1);





% =============================================================
    
end

dataset3Params.m

function [C, sigma] = dataset3Params(X, y, Xval, yval)
%EX6PARAMS 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] = EX6PARAMS(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))
%
C_try=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];
sigma_try=[0.01; 0.03; 0.1; 0.3; 1; 3; 10; 30];

for i=1:length(C_try)
    C=C_try(i);
    for j=1:length(sigma_try)
        sigma=sigma_try(j);
        model= svmTrain(X, y, C, @(x1, x2) gaussianKernel(x1, x2, sigma)); 
        predictions = svmPredict(model,Xval);

        error(j) = mean(double(predictions ~= yval));

% Accumulating error from i=1:m
        if (j==1)
            error_j=error(j);
        else
            error_j=[error_j; error(j)];
        end
    end
    if (i==1)
        error_i=error_j;
    else
        error_i=[error_i error_j];
    end            
    
end

% Display the error_i in matrix
error_i

% Locate the index of the minimum value in matrix error_i
[r,c]=find(error_i==min(min(error_i)));

% Optimum C and sigma are identified from the matrix above
C=C_try(c);
sigma=sigma_try(r);

% Optimum value of C and sigma are:
%C=1;
%sigma=0.1;






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

end

processEmail.m

function sim = gaussianKernel(x1, x2, sigma)
%RBFKERNEL returns a radial basis function kernel between x1 and x2
%   sim = gaussianKernel(x1, x2) returns a gaussian kernel between x1 and x2
%   and returns the value in sim

% Ensure that x1 and x2 are column vectors
x1 = x1(:); x2 = x2(:);

% You need to return the following variables correctly.
sim = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the similarity between x1
%               and x2 computed using a Gaussian kernel with bandwidth
%               sigma
%
%
SSq = sum((x1-x2).^2);


Temp1  = SSq / (2 * sigma^2);
sim=exp(-Temp1);





% =============================================================
    
end

emailFeatures.m

function x = emailFeatures(word_indices)
%EMAILFEATURES takes in a word_indices vector and produces a feature vector
%from the word indices
%   x = EMAILFEATURES(word_indices) takes in a word_indices vector and 
%   produces a feature vector from the word indices. 

% Total number of words in the dictionary
n = 1899;

% You need to return the following variables correctly.
x = zeros(n, 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return a feature vector for the
%               given email (word_indices). To help make it easier to 
%               process the emails, we have have already pre-processed each
%               email and converted each word in the email into an index in
%               a fixed dictionary (of 1899 words). The variable
%               word_indices contains the list of indices of the words
%               which occur in one email.
% 
%               Concretely, if an email has the text:
%
%                  The quick brown fox jumped over the lazy dog.
%
%               Then, the word_indices vector for this text might look 
%               like:
%               
%                   60  100   33   44   10     53  60  58   5
%
%               where, we have mapped each word onto a number, for example:
%
%                   the   -- 60
%                   quick -- 100
%                   ...
%
%              (note: the above numbers are just an example and are not the
%               actual mappings).
%
%              Your task is take one such word_indices vector and construct
%              a binary feature vector that indicates whether a particular
%              word occurs in the email. That is, x(i) = 1 when word i
%              is present in the email. Concretely, if the word 'the' (say,
%              index 60) appears in the email, then x(60) = 1. The feature
%              vector should look like:
%
%              x = [ 0 0 0 0 1 0 0 0 ... 0 0 0 0 1 ... 0 0 0 1 0 ..];
%
%
k = length(word_indices);  
for i = 1:k,  
    if(x(word_indices(i)) == 0)  
        x(word_indices(i)) = x(word_indices(i)) + 1;  
    end  
end  







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

end