Added solution to assignments

machine-learning-ex6/ex6/dataset3Params.m

+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))
+%
+temp_error = 10000;
+for C_i = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30]
+    for sigma_i = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30]
+        model= svmTrain(X, y, C_i, @(x1, x2) gaussianKernel(x1, x2, sigma_i));
+        predictions = svmPredict(model, Xval);
+        error = mean(double(predictions ~= yval));  
+        if error < temp_error
+            temp_error = error;
+            C = C_i;
+            sigma = sigma_i;
+        end
+    end
+end
+% =========================================================================
+
+end

machine-learning-ex6/ex6/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. 
+n = 1899;
+x = zeros(n, 1);
+for i = word_indices
+    x(i) = 1;
+end
+end

machine-learning-ex6/ex6/emailSample1.txt

+> 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
+

machine-learning-ex6/ex6/emailSample2.txt

+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
+
+

machine-learning-ex6/ex6/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 = %f :' ...
+         '\n\t%f\n(for sigma = 2, this value should be about 0.324652)\n'], sigma, 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;
+

machine-learning-ex6/ex6/ex6_spam.m

+clear ; close all; clc
+file_contents = readFile('emailSample1.txt');
+word_indices  = processEmail(file_contents);
+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));
+
+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);
+
+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;
+
+
+
+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');
+

machine-learning-ex6/ex6/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;
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Fill in this function to return the similarity between x1
+%               and x2 computed using a Gaussian kernel with bandwidth
+%               sigma
+%
+%
+sim = exp(-1*(sum((x1-x2).^2))/(2*sigma^2));
+% =============================================================
+    
+end

machine-learning-ex6/ex6/getVocabList.m

+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

machine-learning-ex6/ex6/lib/jsonlab/AUTHORS.txt

+The author of "jsonlab" toolbox is Qianqian Fang. Qianqian
+is currently an Assistant Professor at Massachusetts General Hospital, 
+Harvard Medical School.
+
+Address: Martinos Center for Biomedical Imaging, 
+         Massachusetts General Hospital, 
+         Harvard Medical School
+         Bldg 149, 13th St, Charlestown, MA 02129, USA
+URL: http://nmr.mgh.harvard.edu/~fangq/
+Email: <fangq at nmr.mgh.harvard.edu> or <fangqq at gmail.com>
+
+
+The script loadjson.m was built upon previous works by
+
+- Nedialko Krouchev: http://www.mathworks.com/matlabcentral/fileexchange/25713
+       date: 2009/11/02
+- François Glineur: http://www.mathworks.com/matlabcentral/fileexchange/23393
+       date: 2009/03/22
+- Joel Feenstra: http://www.mathworks.com/matlabcentral/fileexchange/20565
+       date: 2008/07/03
+
+
+This toolbox contains patches submitted by the following contributors:
+
+- Blake Johnson <bjohnso at bbn.com>
+  part of revision 341
+
+- Niclas Borlin <Niclas.Borlin at cs.umu.se>
+  various fixes in revision 394, including
+  - loadjson crashes for all-zero sparse matrix.
+  - loadjson crashes for empty sparse matrix.
+  - Non-zero size of 0-by-N and N-by-0 empty matrices is lost after savejson/loadjson.
+  - loadjson crashes for sparse real column vector.
+  - loadjson crashes for sparse complex column vector.
+  - Data is corrupted by savejson for sparse real row vector.
+  - savejson crashes for sparse complex row vector. 
+
+- Yul Kang <yul.kang.on at gmail.com>
+  patches for svn revision 415.
+  - savejson saves an empty cell array as [] instead of null
+  - loadjson differentiates an empty struct from an empty array

machine-learning-ex6/ex6/lib/jsonlab/ChangeLog.txt

+============================================================================
+
+   JSONlab - a toolbox to encode/decode JSON/UBJSON files in MATLAB/Octave
+
+----------------------------------------------------------------------------
+
+JSONlab ChangeLog (key features marked by *):
+
+== JSONlab 1.0 (codename: Optimus - Final), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2015/01/02 polish help info for all major functions, update examples, finalize 1.0
+ 2014/12/19 fix a bug to strictly respect NoRowBracket in savejson
+
+== JSONlab 1.0.0-RC2 (codename: Optimus - RC2), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/11/22 show progress bar in loadjson ('ShowProgress') 
+ 2014/11/17 add Compact option in savejson to output compact JSON format ('Compact')
+ 2014/11/17 add FastArrayParser in loadjson to specify fast parser applicable levels
+ 2014/09/18 start official github mirror: https://github.com/fangq/jsonlab
+
+== JSONlab 1.0.0-RC1 (codename: Optimus - RC1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/09/17  fix several compatibility issues when running on octave versions 3.2-3.8
+ 2014/09/17  support 2D cell and struct arrays in both savejson and saveubjson
+ 2014/08/04  escape special characters in a JSON string
+ 2014/02/16  fix a bug when saving ubjson files
+
+== JSONlab 0.9.9 (codename: Optimus - beta), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2014/01/22  use binary read and write in saveubjson and loadubjson
+
+== JSONlab 0.9.8-1 (codename: Optimus - alpha update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2013/10/07 better round-trip conservation for empty arrays and structs (patch submitted by Yul Kang)
+
+== JSONlab 0.9.8 (codename: Optimus - alpha), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+ 2013/08/23 *universal Binary JSON (UBJSON) support, including both saveubjson and loadubjson
+
+== JSONlab 0.9.1 (codename: Rodimus, update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+ 2012/12/18 *handling of various empty and sparse matrices (fixes submitted by Niclas Borlin)
+
+== JSONlab 0.9.0 (codename: Rodimus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/06/17 *new format for an invalid leading char, unpacking hex code in savejson
+ 2012/06/01  support JSONP in savejson
+ 2012/05/25  fix the empty cell bug (reported by Cyril Davin)
+ 2012/04/05  savejson can save to a file (suggested by Patrick Rapin)
+
+== JSONlab 0.8.1 (codename: Sentiel, Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/02/28  loadjson quotation mark escape bug, see http://bit.ly/yyk1nS
+ 2012/01/25  patch to handle root-less objects, contributed by Blake Johnson
+
+== JSONlab 0.8.0 (codename: Sentiel), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2012/01/13 *speed up loadjson by 20 fold when parsing large data arrays in matlab
+ 2012/01/11  remove row bracket if an array has 1 element, suggested by Mykel Kochenderfer
+ 2011/12/22 *accept sequence of 'param',value input in savejson and loadjson
+ 2011/11/18  fix struct array bug reported by Mykel Kochenderfer
+
+== JSONlab 0.5.1 (codename: Nexus Update 1), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2011/10/21  fix a bug in loadjson, previous code does not use any of the acceleration
+ 2011/10/20  loadjson supports JSON collections - concatenated JSON objects
+
+== JSONlab 0.5.0 (codename: Nexus), FangQ <fangq (at) nmr.mgh.harvard.edu> ==
+
+ 2011/10/16  package and release jsonlab 0.5.0
+ 2011/10/15 *add json demo and regression test, support cpx numbers, fix double quote bug
+ 2011/10/11 *speed up readjson dramatically, interpret _Array* tags, show data in root level
+ 2011/10/10  create jsonlab project, start jsonlab website, add online documentation
+ 2011/10/07 *speed up savejson by 25x using sprintf instead of mat2str, add options support
+ 2011/10/06 *savejson works for structs, cells and arrays
+ 2011/09/09  derive loadjson from JSON parser from MATLAB Central, draft savejson.m

machine-learning-ex6/ex6/lib/jsonlab/LICENSE_BSD.txt

+Copyright 2011-2015 Qianqian Fang <fangq at nmr.mgh.harvard.edu>. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification, are
+permitted provided that the following conditions are met:
+
+   1. Redistributions of source code must retain the above copyright notice, this list of
+      conditions and the following disclaimer.
+
+   2. Redistributions in binary form must reproduce the above copyright notice, this list
+      of conditions and the following disclaimer in the documentation and/or other materials
+      provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY EXPRESS OR IMPLIED
+WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS 
+OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+The views and conclusions contained in the software and documentation are those of the
+authors and should not be interpreted as representing official policies, either expressed
+or implied, of the copyright holders.

machine-learning-ex6/ex6/lib/jsonlab/jsonopt.m

+function val=jsonopt(key,default,varargin)
+%
+% val=jsonopt(key,default,optstruct)
+%
+% setting options based on a struct. The struct can be produced
+% by varargin2struct from a list of 'param','value' pairs
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+%
+% $Id: loadjson.m 371 2012-06-20 12:43:06Z fangq $
+%
+% input:
+%      key: a string with which one look up a value from a struct
+%      default: if the key does not exist, return default
+%      optstruct: a struct where each sub-field is a key 
+%
+% output:
+%      val: if key exists, val=optstruct.key; otherwise val=default
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+% 
+
+val=default;
+if(nargin<=2) return; end
+opt=varargin{1};
+if(isstruct(opt) && isfield(opt,key))
+    val=getfield(opt,key);
+end
+

machine-learning-ex6/ex6/lib/jsonlab/mergestruct.m

+function s=mergestruct(s1,s2)
+%
+% s=mergestruct(s1,s2)
+%
+% merge two struct objects into one
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+% date: 2012/12/22
+%
+% input:
+%      s1,s2: a struct object, s1 and s2 can not be arrays
+%
+% output:
+%      s: the merged struct object. fields in s1 and s2 will be combined in s.
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details 
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+%
+
+if(~isstruct(s1) || ~isstruct(s2))
+    error('input parameters contain non-struct');
+end
+if(length(s1)>1 || length(s2)>1)
+    error('can not merge struct arrays');
+end
+fn=fieldnames(s2);
+s=s1;
+for i=1:length(fn)              
+    s=setfield(s,fn{i},getfield(s2,fn{i}));
+end
+

machine-learning-ex6/ex6/lib/jsonlab/varargin2struct.m

+function opt=varargin2struct(varargin)
+%
+% opt=varargin2struct('param1',value1,'param2',value2,...)
+%   or
+% opt=varargin2struct(...,optstruct,...)
+%
+% convert a series of input parameters into a structure
+%
+% authors:Qianqian Fang (fangq<at> nmr.mgh.harvard.edu)
+% date: 2012/12/22
+%
+% input:
+%      'param', value: the input parameters should be pairs of a string and a value
+%       optstruct: if a parameter is a struct, the fields will be merged to the output struct
+%
+% output:
+%      opt: a struct where opt.param1=value1, opt.param2=value2 ...
+%
+% license:
+%     BSD, see LICENSE_BSD.txt files for details 
+%
+% -- this function is part of jsonlab toolbox (http://iso2mesh.sf.net/cgi-bin/index.cgi?jsonlab)
+%
+
+len=length(varargin);
+opt=struct;
+if(len==0) return; end
+i=1;
+while(i<=len)
+    if(isstruct(varargin{i}))
+        opt=mergestruct(opt,varargin{i});
+    elseif(ischar(varargin{i}) && i<len)
+        opt=setfield(opt,varargin{i},varargin{i+1});
+        i=i+1;
+    else
+        error('input must be in the form of ...,''name'',value,... pairs or structs');
+    end
+    i=i+1;
+end
+

machine-learning-ex6/ex6/lib/makeValidFieldName.m

+function str = makeValidFieldName(str)
+% From MATLAB doc: field names must begin with a letter, which may be
+% followed by any combination of letters, digits, and underscores.
+% Invalid characters will be converted to underscores, and the prefix
+% "x0x[Hex code]_" will be added if the first character is not a letter.
+    isoct=exist('OCTAVE_VERSION','builtin');
+    pos=regexp(str,'^[^A-Za-z]','once');
+    if(~isempty(pos))
+        if(~isoct)
+            str=regexprep(str,'^([^A-Za-z])','x0x${sprintf(''%X'',unicode2native($1))}_','once');
+        else
+            str=sprintf('x0x%X_%s',char(str(1)),str(2:end));
+        end
+    end
+    if(isempty(regexp(str,'[^0-9A-Za-z_]', 'once' ))) return;  end
+    if(~isoct)
+        str=regexprep(str,'([^0-9A-Za-z_])','_0x${sprintf(''%X'',unicode2native($1))}_');
+    else
+        pos=regexp(str,'[^0-9A-Za-z_]');
+        if(isempty(pos)) return; end
+        str0=str;
+        pos0=[0 pos(:)' length(str)];
+        str='';
+        for i=1:length(pos)
+            str=[str str0(pos0(i)+1:pos(i)-1) sprintf('_0x%X_',str0(pos(i)))];
+        end
+        if(pos(end)~=length(str))
+            str=[str str0(pos0(end-1)+1:pos0(end))];
+        end
+    end

machine-learning-ex6/ex6/lib/submitWithConfiguration.m

+function submitWithConfiguration(conf)
+  addpath('./lib/jsonlab');
+
+  parts = parts(conf);
+
+  fprintf('== Submitting solutions | %s...\n', conf.itemName);
+
+  tokenFile = 'token.mat';
+  if exist(tokenFile, 'file')
+    load(tokenFile);
+    [email token] = promptToken(email, token, tokenFile);
+  else
+    [email token] = promptToken('', '', tokenFile);
+  end
+
+  if isempty(token)
+    fprintf('!! Submission Cancelled\n');
+    return
+  end
+
+  try
+    response = submitParts(conf, email, token, parts);
+  catch
+    e = lasterror();
+    fprintf('\n!! Submission failed: %s\n', e.message);
+    fprintf('\n\nFunction: %s\nFileName: %s\nLineNumber: %d\n', ...
+      e.stack(1,1).name, e.stack(1,1).file, e.stack(1,1).line);
+    fprintf('\nPlease correct your code and resubmit.\n');
+    return
+  end
+
+  if isfield(response, 'errorMessage')
+    fprintf('!! Submission failed: %s\n', response.errorMessage);
+  elseif isfield(response, 'errorCode')
+    fprintf('!! Submission failed: %s\n', response.message);
+  else
+    showFeedback(parts, response);
+    save(tokenFile, 'email', 'token');
+  end
+end
+
+function [email token] = promptToken(email, existingToken, tokenFile)
+  if (~isempty(email) && ~isempty(existingToken))
+    prompt = sprintf( ...
+      'Use token from last successful submission (%s)? (Y/n): ', ...
+      email);
+    reenter = input(prompt, 's');
+
+    if (isempty(reenter) || reenter(1) == 'Y' || reenter(1) == 'y')
+      token = existingToken;
+      return;
+    else
+      delete(tokenFile);
+    end
+  end
+  email = input('Login (email address): ', 's');
+  token = input('Token: ', 's');
+end
+
+function isValid = isValidPartOptionIndex(partOptions, i)
+  isValid = (~isempty(i)) && (1 <= i) && (i <= numel(partOptions));
+end
+
+function response = submitParts(conf, email, token, parts)
+  body = makePostBody(conf, email, token, parts);
+  submissionUrl = submissionUrl();
+
+  responseBody = getResponse(submissionUrl, body);
+  jsonResponse = validateResponse(responseBody);
+  response = loadjson(jsonResponse);
+end
+
+function body = makePostBody(conf, email, token, parts)
+  bodyStruct.assignmentSlug = conf.assignmentSlug;
+  bodyStruct.submitterEmail = email;
+  bodyStruct.secret = token;
+  bodyStruct.parts = makePartsStruct(conf, parts);
+
+  opt.Compact = 1;
+  body = savejson('', bodyStruct, opt);
+end
+
+function partsStruct = makePartsStruct(conf, parts)
+  for part = parts
+    partId = part{:}.id;
+    fieldName = makeValidFieldName(partId);
+    outputStruct.output = conf.output(partId);
+    partsStruct.(fieldName) = outputStruct;
+  end
+end
+
+function [parts] = parts(conf)
+  parts = {};
+  for partArray = conf.partArrays
+    part.id = partArray{:}{1};
+    part.sourceFiles = partArray{:}{2};
+    part.name = partArray{:}{3};
+    parts{end + 1} = part;
+  end
+end
+
+function showFeedback(parts, response)
+  fprintf('== \n');
+  fprintf('== %43s | %9s | %-s\n', 'Part Name', 'Score', 'Feedback');
+  fprintf('== %43s | %9s | %-s\n', '---------', '-----', '--------');
+  for part = parts
+    score = '';
+    partFeedback = '';
+    partFeedback = response.partFeedbacks.(makeValidFieldName(part{:}.id));
+    partEvaluation = response.partEvaluations.(makeValidFieldName(part{:}.id));
+    score = sprintf('%d / %3d', partEvaluation.score, partEvaluation.maxScore);
+    fprintf('== %43s | %9s | %-s\n', part{:}.name, score, partFeedback);
+  end
+  evaluation = response.evaluation;
+  totalScore = sprintf('%d / %d', evaluation.score, evaluation.maxScore);
+  fprintf('==                                   --------------------------------\n');
+  fprintf('== %43s | %9s | %-s\n', '', totalScore, '');
+  fprintf('== \n');
+end
+
+% use urlread or curl to send submit results to the grader and get a response
+function response = getResponse(url, body)
+% try using urlread() and a secure connection
+  params = {'jsonBody', body};
+  [response, success] = urlread(url, 'post', params);
+
+  if (success == 0)
+    % urlread didn't work, try curl & the peer certificate patch
+    if ispc
+      % testing note: use 'jsonBody =' for a test case
+      json_command = sprintf('echo jsonBody=%s | curl -k -X POST -d @- %s', body, url);
+    else
+      % it's linux/OS X, so use the other form
+      json_command = sprintf('echo ''jsonBody=%s'' | curl -k -X POST -d @- %s', body, url);
+    end
+    % get the response body for the peer certificate patch method
+    [code, response] = system(json_command);
+    % test the success code
+    if (code ~= 0)
+      fprintf('[error] submission with curl() was not successful\n');
+    end
+  end
+end
+
+% validate the grader's response
+function response = validateResponse(resp)
+  % test if the response is json or an HTML page
+  isJson = length(resp) > 0 && resp(1) == '{';
+  isHtml = findstr(lower(resp), '<html');
+
+  if (isJson)
+    response = resp;
+  elseif (isHtml)
+    % the response is html, so it's probably an error message
+    printHTMLContents(resp);
+    error('Grader response is an HTML message');
+  else
+    error('Grader sent no response');
+  end
+end
+
+% parse a HTML response and print it's contents
+function printHTMLContents(response)
+  strippedResponse = regexprep(response, '<[^>]+>', ' ');
+  strippedResponse = regexprep(strippedResponse, '[\t ]+', ' ');
+  fprintf(strippedResponse);
+end
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% Service configuration
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function submissionUrl = submissionUrl()
+  submissionUrl = 'https://www-origin.coursera.org/api/onDemandProgrammingImmediateFormSubmissions.v1';
+end

machine-learning-ex6/ex6/linearKernel.m

+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
\ No newline at end of file

machine-learning-ex6/ex6/plotData.m

+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

machine-learning-ex6/ex6/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.
+    %
+    for i = 1:length(vocabList)
+        if strcmp(str, vocabList{i}) == 1
+            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

machine-learning-ex6/ex6/readFile.m

+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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machine-learning-ex6/ex6/submit.m

+function submit()
+  addpath('./lib');
+
+  conf.assignmentSlug = 'support-vector-machines';
+  conf.itemName = 'Support Vector Machines';
+  conf.partArrays = { ...
+    { ...
+      '1', ...
+      { 'gaussianKernel.m' }, ...
+      'Gaussian Kernel', ...
+    }, ...
+    { ...
+      '2', ...
+      { 'dataset3Params.m' }, ...
+      'Parameters (C, sigma) for Dataset 3', ...
+    }, ...
+    { ...
+      '3', ...
+      { 'processEmail.m' }, ...
+      'Email Preprocessing', ...
+    }, ...
+    { ...
+      '4', ...
+      { 'emailFeatures.m' }, ...
+      'Email Feature Extraction', ...
+    }, ...
+  };
+  conf.output = @output;
+
+  submitWithConfiguration(conf);
+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

machine-learning-ex6/ex6/svmPredict.m

+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
+

machine-learning-ex6/ex6/svmTrain.m

+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

machine-learning-ex6/ex6/token.txt

+tmgyxd2gMeptEbRU
\ No newline at end of file

machine-learning-ex6/ex6/visualizeBoundary.m

+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

machine-learning-ex6/ex6/visualizeBoundaryLinear.m

+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