# Coursera: Machine Learning (Week 7) [Assignment Solution] - Andrew NG

▸ 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.

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.

I tried to provide optimized solutions like

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**[*] gaussianKernel.m -**Gaussian kernel for SVM**[*] dataset3Params.m -**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**readFile.m -**Reads a file into a character string**submit.m -**Submission script that sends your solutions to our servers**[*] processEmail.m -**Email preprocessing**[*] emailFeatures.m -**Feature extraction from emails**Video -**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.
%
% 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
```

**Check-out our free tutorials on IOT (Internet of Things):**

**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 ..];
%
%
%% 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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**-Akshay P. Daga**

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