Coursera machine learning week 7 assignment answers – Andrew Ng

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
  %
  %
  sim = exp(-1*sum(abs(x1-x2).^2)/(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))
  %
  %% %%%%%%%%%% WORKING: SOLUTION1 %%%%%%%%%%
  % C_list     = [0.01 0.03 0.1 0.3 1 3 10 30]';
  % sigma_list = [0.01 0.03 0.1 0.3 1 3 10 30]';
  %
  % prediction_error = zeros(length(C_list), length(sigma_list));
  % for i = 1:length(C_list)
  %     for j = 1: length(sigma_list)
  %         C_test = C_list(i);
  %         sigma_test = sigma_list(j);
  %         model = svmTrain(X, y, C_test, @(x1, x2) gaussianKernel(x1, x2, sigma_test));
  %         predictions = svmPredict(model, Xval);
  %         prediction_error(i,j) = mean(double(predictions ~= yval));
  %     end
  % end
  %
  % % Finding row and col corresponding to min(prediction_error)
  % [values, row_index]=min(prediction_error);
  % [~ ,col] = min(values);
  % row = row_index(col);
  %
  % % C and sigma corresponding to min(prediction_error)
  % C = C_list(row);
  % sigma = sigma_list(col);
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %% %%%%%%%%%% WORKING: SOLUION 2 %%%%%%%%%%%%%%
  C_list     = [0.01 0.03 0.1 0.3 1 3 10 30]';
  sigma_list = [0.01 0.03 0.1 0.3 1 3 10 30]';
  prediction_error = zeros(length(C_list), length(sigma_list));
  result = zeros(length(C_list)+length(sigma_list),3);
  row = 1;
  for i = 1:length(C_list)
      for j = 1: length(sigma_list)
          C_test = C_list(i);
          sigma_test = sigma_list(j);
          model = svmTrain(X, y, C_test, @(x1, x2) gaussianKernel(x1, x2, sigma_test));
          predictions = svmPredict(model, Xval);
          prediction_error(i,j) = mean(double(predictions ~= yval));
          result(row,:) = [prediction_error(i,j), C_test, sigma_test];
          row = row + 1;
      end
  end
  % Sorting prediction_error in ascending order
  sorted_result = sortrows(result, 1);
  % C and sigma corresponding to min(prediction_error)
  C = sorted_result(1,2);
  sigma = sorted_result(1,3);
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % =========================================================================
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.
    %
    %% %%%%% WORKING: SOLUTION %%%%%%%%%%
    % find index of the word in vocabList (if Exist)
    index = find(strcmp(str,vocabList),1);
    % Add the index in the vector word_indices
    word_indices = [word_indices; index];
    %% =============================================================
    % 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 ..];
  %
  %
  %% WORKING: SOLUTION 1 %%%%%%
  % for i = 1:length(word_indices)
  %     x1 = ([1:n] == word_indices(i));
  %     x = x | x1';
  % end
  %% WORKING: SOLUTION 2 %%%%%%
  for i = 1:length(word_indices)
      x(word_indices(i)) = 1;
  end
  % =========================================================================
end