Machine learning 第7周编程作业 SVM

1.Gaussian Kernel

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
%
%
 
m=length(x1)
sum=0
for i=1:m,
  sum=sum-((x1(i)-x2(i))^2)
endfor
 
sim=exp(sum/(2*sigma^2))
 
% =============================================================
 
end

　　

2.Example Dataset 3

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))
%
steps=[0.01,0.03,0.1,0.3,1,3,10,30];
minerror=Inf;
minC=Inf;
minsigma=Inf;
 
for i=1:length(steps),
  for j=1:length(steps),
    curc=steps(i);
    cursigma=steps(j);
    model=svmTrain(X,y,curc,@(x1,x2)gaussianKernel(x1,x2,cursigma));
    predictions=svmPredict(model,Xval);
    error=mean(double(predictions~=yval));
    if(error<minerror)
       minerror=error;
       minC=curc;
       minsigma=cursigma;
    end
  endfor
endfor
 
C=minC;
sigma=minsigma;
 
% =========================================================================
 
end

　　

3.Vocabulary List

function word_indices = processEmail(email_contents)
%PROCESSEMAIL preprocesses a the body of an email and
%returns a list of word_indices
%   word_indices = PROCESSEMAIL(email_contents) preprocesses
%   the body of an email and returns a list of indices of the
%   words contained in the email.
%
 
% Load Vocabulary
vocabList = getVocabList();
 
% Init return value
word_indices = [];
 
% ========================== Preprocess Email ===========================
 
% Find the Headers ( \n\n and remove )
% Uncomment the following lines if you are working with raw emails with the
% full headers
 
% hdrstart = strfind(email_contents, ([char(10) char(10)]));
% email_contents = email_contents(hdrstart(1):end);
 
% Lower case
email_contents = lower(email_contents);
 
% Strip all HTML
% Looks for any expression that starts with < and ends with > and replace
% and does not have any < or > in the tag it with a space
email_contents = regexprep(email_contents, '<[^<>]+>', ' ');
 
% Handle Numbers
% Look for one or more characters between 0-9
email_contents = regexprep(email_contents, '[0-9]+', 'number');
 
% Handle URLS
% Look for strings starting with http:// or https://
email_contents = regexprep(email_contents, ...
                           '(http|https)://[^\s]*', 'httpaddr');
 
% Handle Email Addresses
% Look for strings with @ in the middle
email_contents = regexprep(email_contents, '[^\s]+@[^\s]+', 'emailaddr');
 
% Handle $ sign
email_contents = regexprep(email_contents, '[$]+', 'dollar');
 
% ========================== Tokenize Email ===========================
 
% Output the email to screen as well
fprintf('\n==== Processed Email ====\n\n');
 
% Process file
l = 0;
 
while ~isempty(email_contents)
 
    % Tokenize and also get rid of any punctuation
    [str, email_contents] = ...
       strtok(email_contents, ...
              [' @$/#.-:&*+=[]?!(){},''">_<;%' char(10) char(13)]);
 
    % Remove any non alphanumeric characters
    str = regexprep(str, '[^a-zA-Z0-9]', '');
 
    % Stem the word
    % (the porterStemmer sometimes has issues, so we use a try catch block)
    try str = porterStemmer(strtrim(str));
    catch str = ''; continue;
    end;
 
    % Skip the word if it is too short
    if length(str) < 1
       continue;
    end
 
    % Look up the word in the dictionary and add to word_indices if
    % found
    % ====================== YOUR CODE HERE ======================
    % Instructions: Fill in this function to add the index of str to
    %               word_indices if it is in the vocabulary. At this point
    %               of the code, you have a stemmed word from the email in
    %               the variable str. You should look up str in the
    %               vocabulary list (vocabList). If a match exists, you
    %               should add the index of the word to the word_indices
    %               vector. Concretely, if str = 'action', then you should
    %               look up the vocabulary list to find where in vocabList
    %               'action' appears. For example, if vocabList{18} =
    %               'action', then, you should add 18 to the word_indices
    %               vector (e.g., word_indices = [word_indices ; 18]; ).
    %
    % Note: vocabList{idx} returns a the word with index idx in the
    %       vocabulary list.
    %
    % Note: You can use strcmp(str1, str2) to compare two strings (str1 and
    %       str2). It will return 1 only if the two strings are equivalent.
    %
 
    for idx=1:length(vocabList),
      if(strcmp(vocabList{idx},str)==1)
         word_indices=[word_indices;idx];
      end
    endfor
 
    % =============================================================
 
    % Print to screen, ensuring that the output lines are not too long
    if (l + length(str) + 1) > 78
        fprintf('\n');
        l = 0;
    end
    fprintf('%s ', str);
    l = l + length(str) + 1;
 
end
 
% Print footer
fprintf('\n\n=========================\n');
 
end

　　

4.emailFeatures

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 ..];
%
%
 
     for i=1:length(word_indices),
       x(word_indices(i))=1;
     endfor
 
% =========================================================================
 
end