## Recent Posts ▸ Support vector machines (SVMs) to build a spam classifier.

I have recently completed the Machine Learning course from Coursera by Andrew NG.

While doing the course we have to go through various quiz and assignments.

Here, I am sharing my solutions for the weekly assignments throughout the course.

These solutions are for reference only.

It is recommended that you should solve the assignments by yourself honestly then only it makes sense to complete the course.
But, In case you stuck in between, feel free to refer to the solutions provided by me.

#### NOTE:

Don't just copy paste the code for the sake of completion.
Even if you copy the code, make sure you understand the code first.

Click here to check out week-6 assignment solutions, Scroll down for the solutions for week-7 assignment.

In this exercise, you will be using support vector machines (SVMs) to build a spam classifier. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.

It consist of the following files:
• ex6.m - Octave/MATLAB script for the first half of the exercise
• ex6data1.mat - Example Dataset 1
• ex6data2.mat - Example Dataset 2
• ex6data3.mat - Example Dataset 3
• svmTrain.m - SVM training function
• svmPredict.m - SVM prediction function
• plotData.m - Plot 2D data
• visualizeBoundaryLinear.m - Plot linear boundary
• visualizeBoundary.m - Plot non-linear boundary
• linearKernel.m - Linear kernel for SVM
• Gaussian kernel for SVM
• Parameters to use for Dataset 3
• ex6 spam.m - Octave/MATLAB script for the second half of the exercise
• spamTrain.mat - Spam training set
• spamTest.mat - Spam test set
• emailSample1.txt - Sample email 1
• emailSample2.txt - Sample email 2
• spamSample1.txt - Sample spam 1
• spamSample2.txt - Sample spam 2
• vocab.txt - Vocabulary list
• getVocabList.m - Load vocabulary list
• porterStemmer.m - Stemming function
• submit.m - Submission script that sends your solutions to our servers
• Email preprocessing
• [*] emailFeatures.m - Feature extraction from emails
• YouTube videos featuring Free IOT/ML tutorials
* indicates files you will need to complete

### 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
%
%

sim = exp(-1*sum(abs(x1-x2).^2)/(2*sigma^2));

% =============================================================
end```

### dataset3Params.m :

```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```

### processEmail.m :

```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.
%

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

% 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, ...

% Look for strings with @ in the middle

% 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```

### 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).
%
%              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```

I tried to provide optimized solutions like vectorized implementation for each assignment. If you think that more optimization can be done, then put suggest the corrections / improvements.

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Feel free to ask doubts in the comment section. I will try my best to solve it.
If you find this helpful by any mean like, comment and share the post.
This is the simplest way to encourage me to keep doing such work.

Thanks and Regards,
-Akshay P. Daga