# octave2python: ex6

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### Gaussian Kernel

• Octave
``````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
%
%

magnitude = sum((x2-x1).^2)
sim = e^(-magnitude/(2 * sigma^2))

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

end
``````
• python
``````def gaussianKernel(x1, x2, sigma):
"""
Returns a radial basis function kernel between x1 and x2.

Parameters
----------
x1 :  numpy ndarray
A vector of size (n, ), representing the first datapoint.

x2 : numpy ndarray
A vector of size (n, ), representing the second datapoint.

sigma : float
The bandwidth parameter for the Gaussian kernel.

Returns
-------
sim : float
The computed RBF between the two provided data points.

Instructions
------------
Fill in this function to return the similarity between `x1` and `x2`
computed using a Gaussian kernel with bandwidth `sigma`.
"""
sim = 0
# ====================== YOUR CODE HERE ======================
magnitude = np.sum((x1 - x2)**2)
sim = np.exp(-magnitude/ (2 * (sigma**2)))

# =============================================================
return sim
``````

### Parameters (C, Sigma) for dataset 3

• Octave
``````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))
%

values = [0.01 0.03 0.1 0.3 1 3 10 30];

error_min = inf;

fprintf('chill hommie i am looking for C and sigma, yo values\n');
for C = values
for sigma = values
fprintf('.');
model = svmTrain(X, y, C, @(x1, x2) gaussianKernel(x1, x2, sigma));
err = mean(double(svmPredict(model, Xval) ~= yval));
if (err <= error_min )
C_final     = C;
sigma_final = sigma;
error_min   = err;
fprintf('new min found C, sigma = %f, %f with error = %f', C_final, sigma_final, error_min)
end
end
end
C     = C_final;
sigma = sigma_final;

fprintf('Best value C, sigma = [%f %f] with prediction error = %f\n', C, sigma, error_min);

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

end
``````
• python
``````
``````

### 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(str, vocabList{i}))
word_indices = [ word_indices; i];
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
``````
• python

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