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neingeist 10 years ago
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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))
%
% =========================================================================
end

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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 ..];
%
%
% =========================================================================
end

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> Anyone knows how much it costs to host a web portal ?
>
Well, it depends on how many visitors you're expecting.
This can be anywhere from less than 10 bucks a month to a couple of $100.
You should checkout http://www.rackspace.com/ or perhaps Amazon EC2
if youre running something big..
To unsubscribe yourself from this mailing list, send an email to:
groupname-unsubscribe@egroups.com

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Folks,
my first time posting - have a bit of Unix experience, but am new to Linux.
Just got a new PC at home - Dell box with Windows XP. Added a second hard disk
for Linux. Partitioned the disk and have installed Suse 7.2 from CD, which went
fine except it didn't pick up my monitor.
I have a Dell branded E151FPp 15" LCD flat panel monitor and a nVidia GeForce4
Ti4200 video card, both of which are probably too new to feature in Suse's default
set. I downloaded a driver from the nVidia website and installed it using RPM.
Then I ran Sax2 (as was recommended in some postings I found on the net), but
it still doesn't feature my video card in the available list. What next?
Another problem. I have a Dell branded keyboard and if I hit Caps-Lock twice,
the whole machine crashes (in Linux, not Windows) - even the on/off switch is
inactive, leaving me to reach for the power cable instead.
If anyone can help me in any way with these probs., I'd be really grateful -
I've searched the 'net but have run out of ideas.
Or should I be going for a different version of Linux such as RedHat? Opinions
welcome.
Thanks a lot,
Peter
--
Irish Linux Users' Group: ilug@linux.ie
http://www.linux.ie/mailman/listinfo/ilug for (un)subscription information.
List maintainer: listmaster@linux.ie

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%% 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;

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%% Machine Learning Online Class
% Exercise 6 | Spam Classification with SVMs
%
% 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: Email Preprocessing ====================
% To use an SVM to classify emails into Spam v.s. Non-Spam, you first need
% to convert each email into a vector of features. In this part, you will
% implement the preprocessing steps for each email. You should
% complete the code in processEmail.m to produce a word indices vector
% for a given email.
fprintf('\nPreprocessing sample email (emailSample1.txt)\n');
% Extract Features
file_contents = readFile('emailSample1.txt');
word_indices = processEmail(file_contents);
% Print Stats
fprintf('Word Indices: \n');
fprintf(' %d', word_indices);
fprintf('\n\n');
fprintf('Program paused. Press enter to continue.\n');
pause;
%% ==================== Part 2: Feature Extraction ====================
% Now, you will convert each email into a vector of features in R^n.
% You should complete the code in emailFeatures.m to produce a feature
% vector for a given email.
fprintf('\nExtracting features from sample email (emailSample1.txt)\n');
% Extract Features
file_contents = readFile('emailSample1.txt');
word_indices = processEmail(file_contents);
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));
fprintf('Program paused. Press enter to continue.\n');
pause;
%% =========== Part 3: Train Linear SVM for Spam Classification ========
% In this section, you will train a linear classifier to determine if an
% email is Spam or Not-Spam.
% Load the Spam Email dataset
% You will have X, y in your environment
load('spamTrain.mat');
fprintf('\nTraining Linear SVM (Spam Classification)\n')
fprintf('(this may take 1 to 2 minutes) ...\n')
C = 0.1;
model = svmTrain(X, y, C, @linearKernel);
p = svmPredict(model, X);
fprintf('Training Accuracy: %f\n', mean(double(p == y)) * 100);
%% =================== Part 4: Test Spam Classification ================
% After training the classifier, we can evaluate it on a test set. We have
% included a test set in spamTest.mat
% Load the test dataset
% You will have Xtest, ytest in your environment
load('spamTest.mat');
fprintf('\nEvaluating the trained Linear SVM on a test set ...\n')
p = svmPredict(model, Xtest);
fprintf('Test Accuracy: %f\n', mean(double(p == ytest)) * 100);
pause;
%% ================= Part 5: Top Predictors of Spam ====================
% Since the model we are training is a linear SVM, we can inspect the
% weights learned by the model to understand better how it is determining
% whether an email is spam or not. The following code finds the words with
% the highest weights in the classifier. Informally, the classifier
% 'thinks' that these words are the most likely indicators of spam.
%
% Sort the weights and obtin the vocabulary list
[weight, idx] = sort(model.w, 'descend');
vocabList = getVocabList();
fprintf('\nTop predictors of spam: \n');
for i = 1:15
fprintf(' %-15s (%f) \n', vocabList{idx(i)}, weight(i));
end
fprintf('\n\n');
fprintf('\nProgram paused. Press enter to continue.\n');
pause;
%% =================== Part 6: Try Your Own Emails =====================
% Now that you've trained the spam classifier, you can use it on your own
% emails! In the starter code, we have included spamSample1.txt,
% spamSample2.txt, emailSample1.txt and emailSample2.txt as examples.
% The following code reads in one of these emails and then uses your
% learned SVM classifier to determine whether the email is Spam or
% Not Spam
% Set the file to be read in (change this to spamSample2.txt,
% emailSample1.txt or emailSample2.txt to see different predictions on
% different emails types). Try your own emails as well!
filename = 'spamSample1.txt';
% Read and predict
file_contents = readFile(filename);
word_indices = processEmail(file_contents);
x = emailFeatures(word_indices);
p = svmPredict(model, x);
fprintf('\nProcessed %s\n\nSpam Classification: %d\n', filename, p);
fprintf('(1 indicates spam, 0 indicates not spam)\n\n');

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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
%
%
% =============================================================
end

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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

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function sim = linearKernel(x1, x2)
%LINEARKERNEL returns a linear kernel between x1 and x2
% sim = linearKernel(x1, x2) returns a linear kernel between x1 and x2
% and returns the value in sim
% Ensure that x1 and x2 are column vectors
x1 = x1(:); x2 = x2(:);
% Compute the kernel
sim = x1' * x2; % dot product
end

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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

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function stem = porterStemmer(inString)
% Applies the Porter Stemming algorithm as presented in the following
% paper:
% Porter, 1980, An algorithm for suffix stripping, Program, Vol. 14,
% no. 3, pp 130-137
% Original code modeled after the C version provided at:
% http://www.tartarus.org/~martin/PorterStemmer/c.txt
% The main part of the stemming algorithm starts here. b is an array of
% characters, holding the word to be stemmed. The letters are in b[k0],
% b[k0+1] ending at b[k]. In fact k0 = 1 in this demo program (since
% matlab begins indexing by 1 instead of 0). k is readjusted downwards as
% the stemming progresses. Zero termination is not in fact used in the
% algorithm.
% To call this function, use the string to be stemmed as the input
% argument. This function returns the stemmed word as a string.
% Lower-case string
inString = lower(inString);
global j;
b = inString;
k = length(b);
k0 = 1;
j = k;
% With this if statement, strings of length 1 or 2 don't go through the
% stemming process. Remove this conditional to match the published
% algorithm.
stem = b;
if k > 2
% Output displays per step are commented out.
%disp(sprintf('Word to stem: %s', b));
x = step1ab(b, k, k0);
%disp(sprintf('Steps 1A and B yield: %s', x{1}));
x = step1c(x{1}, x{2}, k0);
%disp(sprintf('Step 1C yields: %s', x{1}));
x = step2(x{1}, x{2}, k0);
%disp(sprintf('Step 2 yields: %s', x{1}));
x = step3(x{1}, x{2}, k0);
%disp(sprintf('Step 3 yields: %s', x{1}));
x = step4(x{1}, x{2}, k0);
%disp(sprintf('Step 4 yields: %s', x{1}));
x = step5(x{1}, x{2}, k0);
%disp(sprintf('Step 5 yields: %s', x{1}));
stem = x{1};
end
% cons(j) is TRUE <=> b[j] is a consonant.
function c = cons(i, b, k0)
c = true;
switch(b(i))
case {'a', 'e', 'i', 'o', 'u'}
c = false;
case 'y'
if i == k0
c = true;
else
c = ~cons(i - 1, b, k0);
end
end
% mseq() measures the number of consonant sequences between k0 and j. If
% c is a consonant sequence and v a vowel sequence, and <..> indicates
% arbitrary presence,
% <c><v> gives 0
% <c>vc<v> gives 1
% <c>vcvc<v> gives 2
% <c>vcvcvc<v> gives 3
% ....
function n = measure(b, k0)
global j;
n = 0;
i = k0;
while true
if i > j
return
end
if ~cons(i, b, k0)
break;
end
i = i + 1;
end
i = i + 1;
while true
while true
if i > j
return
end
if cons(i, b, k0)
break;
end
i = i + 1;
end
i = i + 1;
n = n + 1;
while true
if i > j
return
end
if ~cons(i, b, k0)
break;
end
i = i + 1;
end
i = i + 1;
end
% vowelinstem() is TRUE <=> k0,...j contains a vowel
function vis = vowelinstem(b, k0)
global j;
for i = k0:j,
if ~cons(i, b, k0)
vis = true;
return
end
end
vis = false;
%doublec(i) is TRUE <=> i,(i-1) contain a double consonant.
function dc = doublec(i, b, k0)
if i < k0+1
dc = false;
return
end
if b(i) ~= b(i-1)
dc = false;
return
end
dc = cons(i, b, k0);
% cvc(j) is TRUE <=> j-2,j-1,j has the form consonant - vowel - consonant
% and also if the second c is not w,x or y. this is used when trying to
% restore an e at the end of a short word. e.g.
%
% cav(e), lov(e), hop(e), crim(e), but
% snow, box, tray.
function c1 = cvc(i, b, k0)
if ((i < (k0+2)) || ~cons(i, b, k0) || cons(i-1, b, k0) || ~cons(i-2, b, k0))
c1 = false;
else
if (b(i) == 'w' || b(i) == 'x' || b(i) == 'y')
c1 = false;
return
end
c1 = true;
end
% ends(s) is TRUE <=> k0,...k ends with the string s.
function s = ends(str, b, k)
global j;
if (str(length(str)) ~= b(k))
s = false;
return
end % tiny speed-up
if (length(str) > k)
s = false;
return
end
if strcmp(b(k-length(str)+1:k), str)
s = true;
j = k - length(str);
return
else
s = false;
end
% setto(s) sets (j+1),...k to the characters in the string s, readjusting
% k accordingly.
function so = setto(s, b, k)
global j;
for i = j+1:(j+length(s))
b(i) = s(i-j);
end
if k > j+length(s)
b((j+length(s)+1):k) = '';
end
k = length(b);
so = {b, k};
% rs(s) is used further down.
% [Note: possible null/value for r if rs is called]
function r = rs(str, b, k, k0)
r = {b, k};
if measure(b, k0) > 0
r = setto(str, b, k);
end
% step1ab() gets rid of plurals and -ed or -ing. e.g.
% caresses -> caress
% ponies -> poni
% ties -> ti
% caress -> caress
% cats -> cat
% feed -> feed
% agreed -> agree
% disabled -> disable
% matting -> mat
% mating -> mate
% meeting -> meet
% milling -> mill
% messing -> mess
% meetings -> meet
function s1ab = step1ab(b, k, k0)
global j;
if b(k) == 's'
if ends('sses', b, k)
k = k-2;
elseif ends('ies', b, k)
retVal = setto('i', b, k);
b = retVal{1};
k = retVal{2};
elseif (b(k-1) ~= 's')
k = k-1;
end
end
if ends('eed', b, k)
if measure(b, k0) > 0;
k = k-1;
end
elseif (ends('ed', b, k) || ends('ing', b, k)) && vowelinstem(b, k0)
k = j;
retVal = {b, k};
if ends('at', b, k)
retVal = setto('ate', b(k0:k), k);
elseif ends('bl', b, k)
retVal = setto('ble', b(k0:k), k);
elseif ends('iz', b, k)
retVal = setto('ize', b(k0:k), k);
elseif doublec(k, b, k0)
retVal = {b, k-1};
if b(retVal{2}) == 'l' || b(retVal{2}) == 's' || ...
b(retVal{2}) == 'z'
retVal = {retVal{1}, retVal{2}+1};
end
elseif measure(b, k0) == 1 && cvc(k, b, k0)
retVal = setto('e', b(k0:k), k);
end
k = retVal{2};
b = retVal{1}(k0:k);
end
j = k;
s1ab = {b(k0:k), k};
% step1c() turns terminal y to i when there is another vowel in the stem.
function s1c = step1c(b, k, k0)
global j;
if ends('y', b, k) && vowelinstem(b, k0)
b(k) = 'i';
end
j = k;
s1c = {b, k};
% step2() maps double suffices to single ones. so -ization ( = -ize plus
% -ation) maps to -ize etc. note that the string before the suffix must give
% m() > 0.
function s2 = step2(b, k, k0)
global j;
s2 = {b, k};
switch b(k-1)
case {'a'}
if ends('ational', b, k) s2 = rs('ate', b, k, k0);
elseif ends('tional', b, k) s2 = rs('tion', b, k, k0); end;
case {'c'}
if ends('enci', b, k) s2 = rs('ence', b, k, k0);
elseif ends('anci', b, k) s2 = rs('ance', b, k, k0); end;
case {'e'}
if ends('izer', b, k) s2 = rs('ize', b, k, k0); end;
case {'l'}
if ends('bli', b, k) s2 = rs('ble', b, k, k0);
elseif ends('alli', b, k) s2 = rs('al', b, k, k0);
elseif ends('entli', b, k) s2 = rs('ent', b, k, k0);
elseif ends('eli', b, k) s2 = rs('e', b, k, k0);
elseif ends('ousli', b, k) s2 = rs('ous', b, k, k0); end;
case {'o'}
if ends('ization', b, k) s2 = rs('ize', b, k, k0);
elseif ends('ation', b, k) s2 = rs('ate', b, k, k0);
elseif ends('ator', b, k) s2 = rs('ate', b, k, k0); end;
case {'s'}
if ends('alism', b, k) s2 = rs('al', b, k, k0);
elseif ends('iveness', b, k) s2 = rs('ive', b, k, k0);
elseif ends('fulness', b, k) s2 = rs('ful', b, k, k0);
elseif ends('ousness', b, k) s2 = rs('ous', b, k, k0); end;
case {'t'}
if ends('aliti', b, k) s2 = rs('al', b, k, k0);
elseif ends('iviti', b, k) s2 = rs('ive', b, k, k0);
elseif ends('biliti', b, k) s2 = rs('ble', b, k, k0); end;
case {'g'}
if ends('logi', b, k) s2 = rs('log', b, k, k0); end;
end
j = s2{2};
% step3() deals with -ic-, -full, -ness etc. similar strategy to step2.
function s3 = step3(b, k, k0)
global j;
s3 = {b, k};
switch b(k)
case {'e'}
if ends('icate', b, k) s3 = rs('ic', b, k, k0);
elseif ends('ative', b, k) s3 = rs('', b, k, k0);
elseif ends('alize', b, k) s3 = rs('al', b, k, k0); end;
case {'i'}
if ends('iciti', b, k) s3 = rs('ic', b, k, k0); end;
case {'l'}
if ends('ical', b, k) s3 = rs('ic', b, k, k0);
elseif ends('ful', b, k) s3 = rs('', b, k, k0); end;
case {'s'}
if ends('ness', b, k) s3 = rs('', b, k, k0); end;
end
j = s3{2};
% step4() takes off -ant, -ence etc., in context <c>vcvc<v>.
function s4 = step4(b, k, k0)
global j;
switch b(k-1)
case {'a'}
if ends('al', b, k) end;
case {'c'}
if ends('ance', b, k)
elseif ends('ence', b, k) end;
case {'e'}
if ends('er', b, k) end;
case {'i'}
if ends('ic', b, k) end;
case {'l'}
if ends('able', b, k)
elseif ends('ible', b, k) end;
case {'n'}
if ends('ant', b, k)
elseif ends('ement', b, k)
elseif ends('ment', b, k)
elseif ends('ent', b, k) end;
case {'o'}
if ends('ion', b, k)
if j == 0
elseif ~(strcmp(b(j),'s') || strcmp(b(j),'t'))
j = k;
end
elseif ends('ou', b, k) end;
case {'s'}
if ends('ism', b, k) end;
case {'t'}
if ends('ate', b, k)
elseif ends('iti', b, k) end;
case {'u'}
if ends('ous', b, k) end;
case {'v'}
if ends('ive', b, k) end;
case {'z'}
if ends('ize', b, k) end;
end
if measure(b, k0) > 1
s4 = {b(k0:j), j};
else
s4 = {b(k0:k), k};
end
% step5() removes a final -e if m() > 1, and changes -ll to -l if m() > 1.
function s5 = step5(b, k, k0)
global j;
j = k;
if b(k) == 'e'
a = measure(b, k0);
if (a > 1) || ((a == 1) && ~cvc(k-1, b, k0))
k = k-1;
end
end
if (b(k) == 'l') && doublec(k, b, k0) && (measure(b, k0) > 1)
k = k-1;
end
s5 = {b(k0:k), k};

@ -0,0 +1,125 @@
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.
%
% =============================================================
% 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

@ -0,0 +1,18 @@
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

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function submit(partId, webSubmit)
%SUBMIT Submit your code and output to the ml-class servers
% SUBMIT() will connect to the ml-class server and submit your solution
fprintf('==\n== [ml-class] Submitting Solutions | Programming Exercise %s\n==\n', ...
homework_id());
if ~exist('partId', 'var') || isempty(partId)
partId = promptPart();
end
if ~exist('webSubmit', 'var') || isempty(webSubmit)
webSubmit = 0; % submit directly by default
end
% Check valid partId
partNames = validParts();
if ~isValidPartId(partId)
fprintf('!! Invalid homework part selected.\n');
fprintf('!! Expected an integer from 1 to %d.\n', numel(partNames) + 1);
fprintf('!! Submission Cancelled\n');
return
end
if ~exist('ml_login_data.mat','file')
[login password] = loginPrompt();
save('ml_login_data.mat','login','password');
else
load('ml_login_data.mat');
[login password] = quickLogin(login, password);
save('ml_login_data.mat','login','password');
end
if isempty(login)
fprintf('!! Submission Cancelled\n');
return
end
fprintf('\n== Connecting to ml-class ... ');
if exist('OCTAVE_VERSION')
fflush(stdout);
end
% Setup submit list
if partId == numel(partNames) + 1
submitParts = 1:numel(partNames);
else
submitParts = [partId];
end
for s = 1:numel(submitParts)
thisPartId = submitParts(s);
if (~webSubmit) % submit directly to server
[login, ch, signature, auxstring] = getChallenge(login, thisPartId);
if isempty(login) || isempty(ch) || isempty(signature)
% Some error occured, error string in first return element.
fprintf('\n!! Error: %s\n\n', login);
return
end
% Attempt Submission with Challenge
ch_resp = challengeResponse(login, password, ch);
[result, str] = submitSolution(login, ch_resp, thisPartId, ...
output(thisPartId, auxstring), source(thisPartId), signature);
partName = partNames{thisPartId};
fprintf('\n== [ml-class] Submitted Assignment %s - Part %d - %s\n', ...
homework_id(), thisPartId, partName);
fprintf('== %s\n', strtrim(str));
if exist('OCTAVE_VERSION')
fflush(stdout);
end
else
[result] = submitSolutionWeb(login, thisPartId, output(thisPartId), ...
source(thisPartId));
result = base64encode(result);
fprintf('\nSave as submission file [submit_ex%s_part%d.txt (enter to accept default)]:', ...
homework_id(), thisPartId);
saveAsFile = input('', 's');
if (isempty(saveAsFile))
saveAsFile = sprintf('submit_ex%s_part%d.txt', homework_id(), thisPartId);
end
fid = fopen(saveAsFile, 'w');
if (fid)
fwrite(fid, result);
fclose(fid);
fprintf('\nSaved your solutions to %s.\n\n', saveAsFile);
fprintf(['You can now submit your solutions through the web \n' ...
'form in the programming exercises. Select the corresponding \n' ...
'programming exercise to access the form.\n']);
else
fprintf('Unable to save to %s\n\n', saveAsFile);
fprintf(['You can create a submission file by saving the \n' ...
'following text in a file: (press enter to continue)\n\n']);
pause;
fprintf(result);
end
end
end
end
% ================== CONFIGURABLES FOR EACH HOMEWORK ==================
function id = homework_id()
id = '6';
end
function [partNames] = validParts()
partNames = { 'Gaussian Kernel', ...
'Parameters (C, sigma) for Dataset 3', ...
'Email Preprocessing' ...
'Email Feature Extraction' ...
};
end
function srcs = sources()
% Separated by part
srcs = { { 'gaussianKernel.m' }, ...
{ 'dataset3Params.m' }, ...
{ 'processEmail.m' }, ...
{ 'emailFeatures.m' } };
end
function out = output(partId, auxstring)
% Random Test Cases
x1 = sin(1:10)';
x2 = cos(1:10)';
ec = 'the quick brown fox jumped over the lazy dog';
wi = 1 + abs(round(x1 * 1863));
wi = [wi ; wi];
if partId == 1
sim = gaussianKernel(x1, x2, 2);
out = sprintf('%0.5f ', sim);
elseif partId == 2
load('ex6data3.mat');
[C, sigma] = dataset3Params(X, y, Xval, yval);
out = sprintf('%0.5f ', C);
out = [out sprintf('%0.5f ', sigma)];
elseif partId == 3
word_indices = processEmail(ec);
out = sprintf('%d ', word_indices);
elseif partId == 4
x = emailFeatures(wi);
out = sprintf('%d ', x);
end
end
% ====================== SERVER CONFIGURATION ===========================
% ***************** REMOVE -staging WHEN YOU DEPLOY *********************
function url = site_url()
url = 'http://class.coursera.org/ml-007';
end
function url = challenge_url()
url = [site_url() '/assignment/challenge'];
end
function url = submit_url()
url = [site_url() '/assignment/submit'];
end
% ========================= CHALLENGE HELPERS =========================
function src = source(partId)
src = '';
src_files = sources();
if partId <= numel(src_files)
flist = src_files{partId};
for i = 1:numel(flist)
fid = fopen(flist{i});
if (fid == -1)
error('Error opening %s (is it missing?)', flist{i});
end
line = fgets(fid);
while ischar(line)
src = [src line];
line = fgets(fid);
end
fclose(fid);
src = [src '||||||||'];
end
end
end
function ret = isValidPartId(partId)
partNames = validParts();
ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames) + 1);
end
function partId = promptPart()
fprintf('== Select which part(s) to submit:\n');
partNames = validParts();
srcFiles = sources();
for i = 1:numel(partNames)
fprintf('== %d) %s [', i, partNames{i});
fprintf(' %s ', srcFiles{i}{:});
fprintf(']\n');
end
fprintf('== %d) All of the above \n==\nEnter your choice [1-%d]: ', ...
numel(partNames) + 1, numel(partNames) + 1);
selPart = input('', 's');
partId = str2num(selPart);
if ~isValidPartId(partId)
partId = -1;
end
end
function [email,ch,signature,auxstring] = getChallenge(email, part)
str = urlread(challenge_url(), 'post', {'email_address', email, 'assignment_part_sid', [homework_id() '-' num2str(part)], 'response_encoding', 'delim'});
str = strtrim(str);
r = struct;
while(numel(str) > 0)
[f, str] = strtok (str, '|');
[v, str] = strtok (str, '|');
r = setfield(r, f, v);
end
email = getfield(r, 'email_address');
ch = getfield(r, 'challenge_key');
signature = getfield(r, 'state');
auxstring = getfield(r, 'challenge_aux_data');
end
function [result, str] = submitSolutionWeb(email, part, output, source)
result = ['{"assignment_part_sid":"' base64encode([homework_id() '-' num2str(part)], '') '",' ...
'"email_address":"' base64encode(email, '') '",' ...
'"submission":"' base64encode(output, '') '",' ...
'"submission_aux":"' base64encode(source, '') '"' ...
'}'];
str = 'Web-submission';
end
function [result, str] = submitSolution(email, ch_resp, part, output, ...
source, signature)
params = {'assignment_part_sid', [homework_id() '-' num2str(part)], ...
'email_address', email, ...
'submission', base64encode(output, ''), ...
'submission_aux', base64encode(source, ''), ...
'challenge_response', ch_resp, ...
'state', signature};
str = urlread(submit_url(), 'post', params);
% Parse str to read for success / failure
result = 0;
end
% =========================== LOGIN HELPERS ===========================
function [login password] = loginPrompt()
% Prompt for password
[login password] = basicPrompt();
if isempty(login) || isempty(password)
login = []; password = [];
end
end
function [login password] = basicPrompt()
login = input('Login (Email address): ', 's');
password = input('Password: ', 's');
end
function [login password] = quickLogin(login,password)
disp(['You are currently logged in as ' login '.']);
cont_token = input('Is this you? (y/n - type n to reenter password)','s');
if(isempty(cont_token) || cont_token(1)=='Y'||cont_token(1)=='y')
return;
else
[login password] = loginPrompt();
end
end
function [str] = challengeResponse(email, passwd, challenge)
str = sha1([challenge passwd]);
end
% =============================== SHA-1 ================================
function hash = sha1(str)
% Initialize variables
h0 = uint32(1732584193);
h1 = uint32(4023233417);
h2 = uint32(2562383102);
h3 = uint32(271733878);
h4 = uint32(3285377520);
% Convert to word array
strlen = numel(str);
% Break string into chars and append the bit 1 to the message
mC = [double(str) 128];
mC = [mC zeros(1, 4-mod(numel(mC), 4), 'uint8')];
numB = strlen * 8;
if exist('idivide')
numC = idivide(uint32(numB + 65), 512, 'ceil');
else
numC = ceil(double(numB + 65)/512);
end
numW = numC * 16;
mW = zeros(numW, 1, 'uint32');
idx = 1;
for i = 1:4:strlen + 1
mW(idx) = bitor(bitor(bitor( ...
bitshift(uint32(mC(i)), 24), ...
bitshift(uint32(mC(i+1)), 16)), ...
bitshift(uint32(mC(i+2)), 8)), ...
uint32(mC(i+3)));
idx = idx + 1;
end
% Append length of message
mW(numW - 1) = uint32(bitshift(uint64(numB), -32));
mW(numW) = uint32(bitshift(bitshift(uint64(numB), 32), -32));
% Process the message in successive 512-bit chs
for cId = 1 : double(numC)
cSt = (cId - 1) * 16 + 1;
cEnd = cId * 16;
ch = mW(cSt : cEnd);
% Extend the sixteen 32-bit words into eighty 32-bit words
for j = 17 : 80
ch(j) = ch(j - 3);
ch(j) = bitxor(ch(j), ch(j - 8));
ch(j) = bitxor(ch(j), ch(j - 14));
ch(j) = bitxor(ch(j), ch(j - 16));
ch(j) = bitrotate(ch(j), 1);
end
% Initialize hash value for this ch
a = h0;
b = h1;
c = h2;
d = h3;
e = h4;
% Main loop
for i = 1 : 80
if(i >= 1 && i <= 20)
f = bitor(bitand(b, c), bitand(bitcmp(b), d));
k = uint32(1518500249);
elseif(i >= 21 && i <= 40)
f = bitxor(bitxor(b, c), d);
k = uint32(1859775393);
elseif(i >= 41 && i <= 60)
f = bitor(bitor(bitand(b, c), bitand(b, d)), bitand(c, d));
k = uint32(2400959708);
elseif(i >= 61 && i <= 80)
f = bitxor(bitxor(b, c), d);
k = uint32(3395469782);
end
t = bitrotate(a, 5);
t = bitadd(t, f);
t = bitadd(t, e);
t = bitadd(t, k);
t = bitadd(t, ch(i));
e = d;
d = c;
c = bitrotate(b, 30);
b = a;
a = t;
end
h0 = bitadd(h0, a);
h1 = bitadd(h1, b);
h2 = bitadd(h2, c);
h3 = bitadd(h3, d);
h4 = bitadd(h4, e);
end
hash = reshape(dec2hex(double([h0 h1 h2 h3 h4]), 8)', [1 40]);
hash = lower(hash);
end
function ret = bitadd(iA, iB)
ret = double(iA) + double(iB);
ret = bitset(ret, 33, 0);
ret = uint32(ret);
end
function ret = bitrotate(iA, places)
t = bitshift(iA, places - 32);
ret = bitshift(iA, places);
ret = bitor(ret, t);
end
% =========================== Base64 Encoder ============================
% Thanks to Peter John Acklam
%
function y = base64encode(x, eol)
%BASE64ENCODE Perform base64 encoding on a string.
%
% BASE64ENCODE(STR, EOL) encode the given string STR. EOL is the line ending
% sequence to use; it is optional and defaults to '\n' (ASCII decimal 10).
% The returned encoded string is broken into lines of no more than 76
% characters each, and each line will end with EOL unless it is empty. Let
% EOL be empty if you do not want the encoded string broken into lines.
%
% STR and EOL don't have to be strings (i.e., char arrays). The only
% requirement is that they are vectors containing values in the range 0-255.
%
% This function may be used to encode strings into the Base64 encoding
% specified in RFC 2045 - MIME (Multipurpose Internet Mail Extensions). The
% Base64 encoding is designed to represent arbitrary sequences of octets in a
% form that need not be humanly readable. A 65-character subset
% ([A-Za-z0-9+/=]) of US-ASCII is used, enabling 6 bits to be represented per
% printable character.
%
% Examples
% --------
%
% If you want to encode a large file, you should encode it in chunks that are
% a multiple of 57 bytes. This ensures that the base64 lines line up and
% that you do not end up with padding in the middle. 57 bytes of data fills
% one complete base64 line (76 == 57*4/3):
%
% If ifid and ofid are two file identifiers opened for reading and writing,
% respectively, then you can base64 encode the data with
%
% while ~feof(ifid)
% fwrite(ofid, base64encode(fread(ifid, 60*57)));
% end
%
% or, if you have enough memory,
%
% fwrite(ofid, base64encode(fread(ifid)));
%
% See also BASE64DECODE.
% Author: Peter John Acklam
% Time-stamp: 2004-02-03 21:36:56 +0100
% E-mail: pjacklam@online.no
% URL: http://home.online.no/~pjacklam
if isnumeric(x)
x = num2str(x);
end
% make sure we have the EOL value
if nargin < 2
eol = sprintf('\n');
else
if sum(size(eol) > 1) > 1
error('EOL must be a vector.');
end
if any(eol(:) > 255)
error('EOL can not contain values larger than 255.');
end
end
if sum(size(x) > 1) > 1
error('STR must be a vector.');
end
x = uint8(x);
eol = uint8(eol);
ndbytes = length(x); % number of decoded bytes
nchunks = ceil(ndbytes / 3); % number of chunks/groups
nebytes = 4 * nchunks; % number of encoded bytes
% add padding if necessary, to make the length of x a multiple of 3
if rem(ndbytes, 3)
x(end+1 : 3*nchunks) = 0;
end
x = reshape(x, [3, nchunks]); % reshape the data
y = repmat(uint8(0), 4, nchunks); % for the encoded data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Split up every 3 bytes into 4 pieces
%
% aaaaaabb bbbbcccc ccdddddd
%
% to form
%
% 00aaaaaa 00bbbbbb 00cccccc 00dddddd
%
y(1,:) = bitshift(x(1,:), -2); % 6 highest bits of x(1,:)
y(2,:) = bitshift(bitand(x(1,:), 3), 4); % 2 lowest bits of x(1,:)
y(2,:) = bitor(y(2,:), bitshift(x(2,:), -4)); % 4 highest bits of x(2,:)
y(3,:) = bitshift(bitand(x(2,:), 15), 2); % 4 lowest bits of x(2,:)
y(3,:) = bitor(y(3,:), bitshift(x(3,:), -6)); % 2 highest bits of x(3,:)
y(4,:) = bitand(x(3,:), 63); % 6 lowest bits of x(3,:)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Now perform the following mapping
%
% 0 - 25 -> A-Z
% 26 - 51 -> a-z
% 52 - 61 -> 0-9
% 62 -> +
% 63 -> /
%
% We could use a mapping vector like
%
% ['A':'Z', 'a':'z', '0':'9', '+/']
%
% but that would require an index vector of class double.
%
z = repmat(uint8(0), size(y));
i = y <= 25; z(i) = 'A' + double(y(i));
i = 26 <= y & y <= 51; z(i) = 'a' - 26 + double(y(i));
i = 52 <= y & y <= 61; z(i) = '0' - 52 + double(y(i));
i = y == 62; z(i) = '+';
i = y == 63; z(i) = '/';
y = z;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Add padding if necessary.
%
npbytes = 3 * nchunks - ndbytes; % number of padding bytes
if npbytes
y(end-npbytes+1 : end) = '='; % '=' is used for padding
end
if isempty(eol)
% reshape to a row vector
y = reshape(y, [1, nebytes]);
else
nlines = ceil(nebytes / 76); % number of lines
neolbytes = length(eol); % number of bytes in eol string
% pad data so it becomes a multiple of 76 elements
y = [y(:) ; zeros(76 * nlines - numel(y), 1)];
y(nebytes + 1 : 76 * nlines) = 0;
y = reshape(y, 76, nlines);
% insert eol strings
eol = eol(:);
y(end + 1 : end + neolbytes, :) = eol(:, ones(1, nlines));
% remove padding, but keep the last eol string
m = nebytes + neolbytes * (nlines - 1);
n = (76+neolbytes)*nlines - neolbytes;
y(m+1 : n) = '';
% extract and reshape to row vector
y = reshape(y, 1, m+neolbytes);
end
% output is a character array
y = char(y);
end

@ -0,0 +1,20 @@
% submitWeb Creates files from your code and output for web submission.
%
% If the submit function does not work for you, use the web-submission mechanism.
% Call this function to produce a file for the part you wish to submit. Then,
% submit the file to the class servers using the "Web Submission" button on the
% Programming Exercises page on the course website.
%
% You should call this function without arguments (submitWeb), to receive
% an interactive prompt for submission; optionally you can call it with the partID
% if you so wish. Make sure your working directory is set to the directory
% containing the submitWeb.m file and your assignment files.
function submitWeb(partId)
if ~exist('partId', 'var') || isempty(partId)
partId = [];
end
submit(partId, 1);
end

@ -0,0 +1,54 @@
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

@ -0,0 +1,192 @@
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

@ -0,0 +1,24 @@
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 0], 'Color', 'b');
hold off;
end

@ -0,0 +1,16 @@
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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