%%Machine learning From Andrew
%%By youknowwho3_3 in 优快云 #GirlsHelpGirls#DOUBANEZU
%%Support Vector Machines(SVMs)
%%In this exercise, you will be using support vector machines (SVMs) to build a spam classifier.
%1. Support Vector Machines
% 1.1 Example dataset 1
% 1.2 SVM with gaussian kernels
% 1.2.1 Gaussian kernel
% 1.2.2 Example dataset 2
% 1.2.3 Example dataset 3 2. Spam Classification
% 2.1 Preprocessing emails
% 2.1.1 Vocabulary list
% 2.2 Extracting features from emails
% 2.3 Training SVM for spam classification
% 2.4 Top predictors for spam
% 2.5 Optional (ungraded) exercise: Try your own emails
% 2.6 Optional (ungraded) exercise: Build your own dataset
%%
% Load from ex6data1:
% You will have X, y in your environment
load('ex6data1.mat');
% Plot training data
plotData(X, y);%provided
C = 1;
%subplot(1,2,1)
%c=1;
model = svmTrain(X, y, C, @linearKernel, 1e-3, 20);
visualizeBoundaryLinear(X, y, model);
%hold on;
%subplot(1,2,2)
%c=100;
%model = svmTrain(X, y, C, @linearKernel, 1e-3, 20);
%visualizeBoundaryLinear(X, y, model);
%%1.2 SVM with gaussian kernels
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 = %f : \n\t%g\n', sigma, sim);
% Load from ex6data2:
% You will have X, y in your environment
load('ex6data2.mat');
% Plot training data
plotData(X, y);
% 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);
% Load from ex6data3:
% You will have X, y in your environment
load('ex6data3.mat');
% Plot training data
plotData(X, y);
% 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);
%%2. Spam Classification
%% Initialization
clear;
% Extract Features
file_contents = readFile('emailSample1.txt');
word_indices = processEmail(file_contents);
% Print Stats
disp(word_indices)
% Extract Features
features = emailFeatures(word_indices);
% Print Stats
fprintf('Length of feature vector: %d\n', length(features));
fprintf('Number of non-zero entries: %d\n', sum(features > 0));
% Load the Spam Email dataset
% You will have X, y in your environment
load('spamTrain.mat');
C = 0.1;
model = svmTrain(X, y, C, @linearKernel);
p = svmPredict(model, X);
fprintf('Training Accuracy: %f\n', mean(double(p == y)) * 100);
% Load the test dataset
% You will have Xtest, ytest in your environment
load('spamTest.mat');
p = svmPredict(model, Xtest);
fprintf('Test Accuracy: %f\n', mean(double(p == ytest)) * 100);
% Sort the weights and obtin the vocabulary list
[weight, idx] = sort(model.w, 'descend');
vocabList = getVocabList();
for i = 1:15
if i == 1
fprintf('Top predictors of spam: \n');
end
fprintf('%-15s (%f) \n', vocabList{idx(i)}, weight(i));
end
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 ..];
%
%
for i=1:size(word_indices)
x(word_indices(i)) = 1;
end
% =========================================================================
end
function vocabList = getVocabList()
%GETVOCABLIST reads the fixed vocabulary list in vocab.txt and returns a
%cell array of the words
% vocabList = GETVOCABLIST() reads the fixed vocabulary list in vocab.txt
% and returns a cell array of the words in vocabList.
%% Read the fixed vocabulary list
fid = fopen('vocab.txt');
% Store all dictionary words in cell array vocab{}
n = 1899; % Total number of words in the dictionary
% For ease of implementation, we use a struct to map the strings => integers
% In practice, you'll want to use some form of hashmap
vocabList = cell(n, 1);
for i = 1:n
% Word Index (can ignore since it will be = i)
fscanf(fid, '%d', 1);
% Actual Word
vocabList{i} = fscanf(fid, '%s', 1);
end
fclose(fid);
end
function file_contents = readFile(filename)
%READFILE reads a file and returns its entire contents
% file_contents = READFILE(filename) reads a file and returns its entire
% contents in file_contents
%
% Load File
fid = fopen(filename);
if fid
file_contents = fscanf(fid, '%c', inf);
fclose(fid);
else
file_contents = '';
fprintf('Unable to open %s\n', filename);
end
end
%function processEmail
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.
%
idx = strmatch(str, vocabList, 'exact');
if ~isempty(idx)
word_indices = [word_indices; idx];
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
%function gaussianKernel
function sim = gaussianKernel(x1, x2, sigma)
x1=x1(:);
x2=x2(:);
%所有元素重新变成一列排列
sim=exp(-sum(x1-x2).^2/(2*sigma^2));
end
%function dataset3Params
function [C, sigma] = dataset3Params(X, y, Xval, yval)
C = 1;
sigma = 0.3;
results = eye(64,3);
errorRow = 0;
for C_test = [0.01 0.03 0.1 0.3 1, 3, 10 30]
for sigma_test = [0.01 0.03 0.1 0.3 1, 3, 10 30]
errorRow = errorRow + 1;
model = svmTrain(X, y, C_test, @(x1, x2) gaussianKernel(x1, x2, sigma_test));
predictions = svmPredict(model, Xval);
prediction_error = mean(double(predictions ~= yval));
results(errorRow,:) = [C_test, sigma_test, prediction_error];
end
end
sorted_results = sortrows(results, 3); % sort matrix by column #3, the error, ascending
C = sorted_results(1,1);
sigma = sorted_results(1,2);
end
function plotData(X, y)
%PLOTDATA Plots the data points X and y into a new figure
% PLOTDATA(x,y) plots the data points with + for the positive examples
% and o for the negative examples. X is assumed to be a Mx2 matrix.
%
% Note: This was slightly modified such that it expects y = 1 or y = 0
% Find Indices of Positive and Negative Examples
pos = find(y == 1); neg = find(y == 0);
% Plot Examples
plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 1, 'MarkerSize', 7)
hold on;
plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y', 'MarkerSize', 7)
hold off;
end
function pred = svmPredict(model, X)
%SVMPREDICT returns a vector of predictions using a trained SVM model
%(svmTrain).
% pred = SVMPREDICT(model, X) returns a vector of predictions using a
% trained SVM model (svmTrain). X is a mxn matrix where there each
% example is a row. model is a svm model returned from svmTrain.
% predictions pred is a m x 1 column of predictions of {0, 1} values.
%
% Check if we are getting a column vector, if so, then assume that we only
% need to do prediction for a single example
if (size(X, 2) == 1)
% Examples should be in rows
X = X';
end
% Dataset
m = size(X, 1);
p = zeros(m, 1);
pred = zeros(m, 1);
if strcmp(func2str(model.kernelFunction), 'linearKernel')
% We can use the weights and bias directly if working with the
% linear kernel
p = X * model.w + model.b;
elseif strfind(func2str(model.kernelFunction), 'gaussianKernel')
% Vectorized RBF Kernel
% This is equivalent to computing the kernel on every pair of examples
X1 = sum(X.^2, 2);
X2 = sum(model.X.^2, 2)';
K = bsxfun(@plus, X1, bsxfun(@plus, X2, - 2 * X * model.X'));
K = model.kernelFunction(1, 0) .^ K;
K = bsxfun(@times, model.y', K);
K = bsxfun(@times, model.alphas', K);
p = sum(K, 2);
else
% Other Non-linear kernel
for i = 1:m
prediction = 0;
for j = 1:size(model.X, 1)
prediction = prediction + ...
model.alphas(j) * model.y(j) * ...
model.kernelFunction(X(i,:)', model.X(j,:)');
end
p(i) = prediction + model.b;
end
end
% Convert predictions into 0 / 1
pred(p >= 0) = 1;
pred(p < 0) = 0;
end
function [model] = svmTrain(X, Y, C, kernelFunction, ...
tol, max_passes)
%SVMTRAIN Trains an SVM classifier using a simplified version of the SMO
%algorithm.
% [model] = SVMTRAIN(X, Y, C, kernelFunction, tol, max_passes) trains an
% SVM classifier and returns trained model. X is the matrix of training
% examples. Each row is a training example, and the jth column holds the
% jth feature. Y is a column matrix containing 1 for positive examples
% and 0 for negative examples. C is the standard SVM regularization
% parameter. tol is a tolerance value used for determining equality of
% floating point numbers. max_passes controls the number of iterations
% over the dataset (without changes to alpha) before the algorithm quits.
%
% Note: This is a simplified version of the SMO algorithm for training
% SVMs. In practice, if you want to train an SVM classifier, we
% recommend using an optimized package such as:
%
% LIBSVM (http://www.csie.ntu.edu.tw/~cjlin/libsvm/)
% SVMLight (http://svmlight.joachims.org/)
%
%
if ~exist('tol', 'var') || isempty(tol)
tol = 1e-3;
end
if ~exist('max_passes', 'var') || isempty(max_passes)
max_passes = 5;
end
% Data parameters
m = size(X, 1);
n = size(X, 2);
% Map 0 to -1
Y(Y==0) = -1;
% Variables
alphas = zeros(m, 1);
b = 0;
E = zeros(m, 1);
passes = 0;
eta = 0;
L = 0;
H = 0;
% Pre-compute the Kernel Matrix since our dataset is small
% (in practice, optimized SVM packages that handle large datasets
% gracefully will _not_ do this)
%
% We have implemented optimized vectorized version of the Kernels here so
% that the svm training will run faster.
if strcmp(func2str(kernelFunction), 'linearKernel')
% Vectorized computation for the Linear Kernel
% This is equivalent to computing the kernel on every pair of examples
K = X*X';
elseif strfind(func2str(kernelFunction), 'gaussianKernel')
% Vectorized RBF Kernel
% This is equivalent to computing the kernel on every pair of examples
X2 = sum(X.^2, 2);
K = bsxfun(@plus, X2, bsxfun(@plus, X2', - 2 * (X * X')));
K = kernelFunction(1, 0) .^ K;
else
% Pre-compute the Kernel Matrix
% The following can be slow due to the lack of vectorization
K = zeros(m);
for i = 1:m
for j = i:m
K(i,j) = kernelFunction(X(i,:)', X(j,:)');
K(j,i) = K(i,j); %the matrix is symmetric
end
end
end
% Train
fprintf('\nTraining ...');
dots = 12;
while passes < max_passes,
num_changed_alphas = 0;
for i = 1:m,
% Calculate Ei = f(x(i)) - y(i) using (2).
% E(i) = b + sum (X(i, :) * (repmat(alphas.*Y,1,n).*X)') - Y(i);
E(i) = b + sum (alphas.*Y.*K(:,i)) - Y(i);
if ((Y(i)*E(i) < -tol && alphas(i) < C) || (Y(i)*E(i) > tol && alphas(i) > 0)),
% In practice, there are many heuristics one can use to select
% the i and j. In this simplified code, we select them randomly.
j = ceil(m * rand());
while j == i, % Make sure i \neq j
j = ceil(m * rand());
end
% Calculate Ej = f(x(j)) - y(j) using (2).
E(j) = b + sum (alphas.*Y.*K(:,j)) - Y(j);
% Save old alphas
alpha_i_old = alphas(i);
alpha_j_old = alphas(j);
% Compute L and H by (10) or (11).
if (Y(i) == Y(j)),
L = max(0, alphas(j) + alphas(i) - C);
H = min(C, alphas(j) + alphas(i));
else
L = max(0, alphas(j) - alphas(i));
H = min(C, C + alphas(j) - alphas(i));
end
if (L == H),
% continue to next i.
continue;
end
% Compute eta by (14).
eta = 2 * K(i,j) - K(i,i) - K(j,j);
if (eta >= 0),
% continue to next i.
continue;
end
% Compute and clip new value for alpha j using (12) and (15).
alphas(j) = alphas(j) - (Y(j) * (E(i) - E(j))) / eta;
% Clip
alphas(j) = min (H, alphas(j));
alphas(j) = max (L, alphas(j));
% Check if change in alpha is significant
if (abs(alphas(j) - alpha_j_old) < tol),
% continue to next i.
% replace anyway
alphas(j) = alpha_j_old;
continue;
end
% Determine value for alpha i using (16).
alphas(i) = alphas(i) + Y(i)*Y(j)*(alpha_j_old - alphas(j));
% Compute b1 and b2 using (17) and (18) respectively.
b1 = b - E(i) ...
- Y(i) * (alphas(i) - alpha_i_old) * K(i,j)' ...
- Y(j) * (alphas(j) - alpha_j_old) * K(i,j)';
b2 = b - E(j) ...
- Y(i) * (alphas(i) - alpha_i_old) * K(i,j)' ...
- Y(j) * (alphas(j) - alpha_j_old) * K(j,j)';
% Compute b by (19).
if (0 < alphas(i) && alphas(i) < C),
b = b1;
elseif (0 < alphas(j) && alphas(j) < C),
b = b2;
else
b = (b1+b2)/2;
end
num_changed_alphas = num_changed_alphas + 1;
end
end
if (num_changed_alphas == 0),
passes = passes + 1;
else
passes = 0;
end
fprintf('.');
dots = dots + 1;
if dots > 78
dots = 0;
fprintf('\n');
end
if exist('OCTAVE_VERSION')
fflush(stdout);
end
end
fprintf(' Done! \n\n');
% Save the model
idx = alphas > 0;
model.X= X(idx,:);
model.y= Y(idx);
model.kernelFunction = kernelFunction;
model.b= b;
model.alphas= alphas(idx);
model.w = ((alphas.*Y)'*X)';
end
function visualizeBoundary(X, y, model, varargin)
%VISUALIZEBOUNDARY plots a non-linear decision boundary learned by the SVM
% VISUALIZEBOUNDARYLINEAR(X, y, model) plots a non-linear decision
% boundary learned by the SVM and overlays the data on it
% Plot the training data on top of the boundary
plotData(X, y)
% Make classification predictions over a grid of values
x1plot = linspace(min(X(:,1)), max(X(:,1)), 100)';
x2plot = linspace(min(X(:,2)), max(X(:,2)), 100)';
[X1, X2] = meshgrid(x1plot, x2plot);
vals = zeros(size(X1));
for i = 1:size(X1, 2)
this_X = [X1(:, i), X2(:, i)];
vals(:, i) = svmPredict(model, this_X);
end
% Plot the SVM boundary
hold on
contour(X1, X2, vals, [0.5 0.5], 'b');
hold off;
end
function visualizeBoundaryLinear(X, y, model)
%VISUALIZEBOUNDARYLINEAR plots a linear decision boundary learned by the
%SVM
% VISUALIZEBOUNDARYLINEAR(X, y, model) plots a linear decision boundary
% learned by the SVM and overlays the data on it
w = model.w;
b = model.b;
xp = linspace(min(X(:,1)), max(X(:,1)), 100);
yp = - (w(1)*xp + b)/w(2);
plotData(X, y);
hold on;
plot(xp, yp, '-b');
hold off
end
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