一、ex6.m
%% Machine Learning Online Class
% Exercise 6 | Support Vector Machines
%
% Instructions
% ------------
%
% This file contains code that helps you get started on the
% exercise. You will need to complete the following functions:
%
% gaussianKernel.m
% dataset3Params.m
% processEmail.m
% emailFeatures.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%
%% Initialization
clear ; close all; clc
%% =============== Part 1: Loading and Visualizing Data ================
% We start the exercise by first loading and visualizing the dataset.
% The following code will load the dataset into your environment and plot
% the data.
%
fprintf('Loading and Visualizing Data ...\n')
% Load from ex6data1:
% You will have X, y in your environment
load('ex6data1.mat');
% Plot training data
plotData(X, y);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ==================== Part 2: Training Linear SVM ====================
% The following code will train a linear SVM on the dataset and plot the
% decision boundary learned.
%
% Load from ex6data1:
% You will have X, y in your environment
load('ex6data1.mat');
fprintf('\nTraining Linear SVM ...\n')
% You should try to change the C value below and see how the decision
% boundary varies (e.g., try C = 1000)
C = 1;
model = svmTrain(X, y, C, @linearKernel, 1e-3, 20);
visualizeBoundaryLinear(X, y, model);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% =============== Part 3: Implementing Gaussian Kernel ===============
% You will now implement the Gaussian kernel to use
% with the SVM. You should complete the code in gaussianKernel.m
%
fprintf('\nEvaluating the Gaussian Kernel ...\n')
x1 = [1 2 1]; x2 = [0 4 -1]; sigma = 2;
sim = gaussianKernel(x1, x2, sigma);
fprintf(['Gaussian Kernel between x1 = [1; 2; 1], x2 = [0; 4; -1], sigma = 0.5 :' ...
'\n\t%f\n(this value should be about 0.324652)\n'], sim);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% =============== Part 4: Visualizing Dataset 2 ================
% The following code will load the next dataset into your environment and
% plot the data.
%
fprintf('Loading and Visualizing Data ...\n')
% Load from ex6data2:
% You will have X, y in your environment
load('ex6data2.mat');
% Plot training data
plotData(X, y);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ========== Part 5: Training SVM with RBF Kernel (Dataset 2) ==========
% After you have implemented the kernel, we can now use it to train the
% SVM classifier.
%
fprintf('\nTraining SVM with RBF Kernel (this may take 1 to 2 minutes) ...\n');
% Load from ex6data2:
% You will have X, y in your environment
load('ex6data2.mat');
% SVM Parameters
C = 1; sigma = 0.1;
% We set the tolerance and max_passes lower here so that the code will run
% faster. However, in practice, you will want to run the training to
% convergence.
model= svmTrain(X, y, C, @(x1, x2) gaussianKernel(x1, x2, sigma));
visualizeBoundary(X, y, model);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% =============== Part 6: Visualizing Dataset 3 ================
% The following code will load the next dataset into your environment and
% plot the data.
%
fprintf('Loading and Visualizing Data ...\n')
% Load from ex6data3:
% You will have X, y in your environment
load('ex6data3.mat');
% Plot training data
plotData(X, y);
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ========== Part 7: Training SVM with RBF Kernel (Dataset 3) ==========
% This is a different dataset that you can use to experiment with. Try
% different values of C and sigma here.
%
% Load from ex6data3:
% You will have X, y in your environment
load('ex6data3.mat');
% Try different SVM Parameters here
[C, sigma] = dataset3Params(X, y, Xval, yval);
% Train the SVM
model= svmTrain(X, y, C, @(x1, x2) gaussianKernel(x1, x2, sigma));
visualizeBoundary(X, y, model);
fprintf('Program paused. Press enter to continue.\n');
pause;
二、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; % 1*1
% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return the similarity between x1
% and x2 computed using a Gaussian kernel with bandwidth
% sigma
%
%
square_diff = sum((x1 - x2) .^ 2);
sim = exp(-square_diff / 2 /(sigma^2));
% =============================================================
end
三、dataset3Params.m
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; % 1*1
sigma = 0.3; % 1*1
% ====================== 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))
%
set_values = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30];
results = [];
long = numel(set_values);
for i = 1:long
for j = 1:long
C_temp = set_values(i);
sigma_temp = set_values(j);
model = svmTrain(X, y, C_temp, @(x1, x2) gaussianKernel(x1, x2, sigma_temp));
predictions = svmPredict(model, Xval);
pre_error = mean(double(predictions ~= yval));
results = [results; C_temp, sigma_temp, pre_error];
end
end
[smallest_error, idx] = min(results(:, 3));
C = results(idx, 1);
sigma = results(idx, 2);
% =========================================================================
end
四、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.
%
%%%%%%%%%%%%%%%%%%%%% NOT CORRECT %%%%%%%%%%%%%%%%%%%%%
%str2 = str(:);
%long_dic = numel(vocabList2);
%long_email = numel(str2);
%for i = 1:long_email
%for j = 1:long_dic
%if 1 == strcmp(str2(i), vocabList2(j))
%word_indices = [word_indices ; j];
%break;
%end % if-end
%end
%end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%CORRECT
word_indices = [word_indices, find(ismember(vocabList, str))];
% =============================================================
% 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
五、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); % 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 ..];
%
%
x([word_indices]) = 1;
% =========================================================================
end
六、submit results
