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

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

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

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