## Thursday, June 18, 2015

### Support Vector Machines - Machine Learning

My solutions to Week 7 Exercises:

Part 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
%
%

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

% =============================================================

end```

Part 2 : Parameters (C, sigma) for Dataset 3

Helpful : Training Sets, Validation Sets, Test Sets - Explanation

```function [C, sigma] = dataset3Params(X, y, Xval, yval)
%EX6PARAMS 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] = EX6PARAMS(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))
%

cvals = [0.01 0.03 0.1 0.3 1 3 10 30]
sigmavals = cvals;
errorMin = 10^8;

for i=1:8
cval = cvals(i);
for j=1:8
sigmaval = sigmavals(j);
model = svmTrain(X, y, cval, @(x, l)gaussianKernel(x, l, sigmaval));
predictions = svmPredict(model, Xval);
error = mean(double(predictions ~= yval));
if error<errorMin C = cval; sigma = sigmaval; errorMin = error;end
end
end

% =========================================================================

end```

Part 3 : Email Preprocessing

```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.
%
for i = 1:length(vocabList)
if strcmp(vocabList{i}, str)==1; word_indices = [word_indices; i]; break; end
end

% =============================================================

% 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```

Part 4 : Email Feature Extraction

```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 ..];
%
%

for i = 1:size(word_indices, 1)
x(word_indices(i)) = 1;
end

% =========================================================================

end```