【吴恩达】机器学习第13章下以及ex6编程作业

1.核函数

这里的核函数的定义是高斯核函数。度量的是x与l值之间的欧式距离。

对于高斯核函数来说，L一般被称为标记点，一般直接选取样本中的X，比如

那么我们如何计算f呢：

对于每一个来说，我们选定x,然后使用不同的来计算：

比如

因此，m是样本个数。

note1:核函数不仅是高斯核函数一种，还有很多其他种类。比如多项式核函数等。高斯核函数应用在逻辑回归问题上会使问题的求解变慢，但是在SVM问题上就有很好的效果。

note2:使用高斯核函数需要进行特征缩放。比如房子大小、卧室数目这些特征之间的差值比较大，在进行相似度函数（核函数）计算时，由于卧室数目这一项的值比较小，所以就会导致几乎忽略。那么对于整体结果而言，会有很大的不良影响。

note3:的选择。C（svm表达式中）.目前的办法是手动调参，设置不同的值进行误差计算。选择误差最小的。

2.什么时候用逻辑回归？什么时候用SVM：

1.当数据集特征数n大，样本数m小的时候，用逻辑回归。

2.当数据集特征数n小，样本数m适中，用svm(with 核函数）

3.当数据集特征数小，但是样本数大,添加更多的特征，两个都试试，看谁效果好。

当样本数m过大的时候，用SVM进行计算，计算量很大。因为m大，也就是说我们要计算m个参数。

3.SVM多分类问题：

同逻辑回归一样，那个种类对应的最大，选哪个类i。其中对应第i类。

4.编程答案

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(-sum((x1-x2).^2)/2/(sigma^2))

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 = 0.1;


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(vocabList{i},str)==1,
		    word_indices = [word_indices;i];
	
	end	   

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


    % Print to screen, ensuring that the output lines are not too long
    if (l + length(str) + 1) > 78
        fprintf('\n');
        l = 0;
    end
    fprintf('%s ', str);
    l = l + length(str) + 1;

end

% Print footer
fprintf('\n\n=========================\n');

end



function x = emailFeatures(word_indices)
%EMAILFEATURES takes in a word_indices vector and produces a feature vector
%from the word indices
%   x = EMAILFEATURES(word_indices) takes in a word_indices vector and 
%   produces a feature vector from the word indices. 

% Total number of words in the dictionary
n = 1899;

% You need to return the following variables correctly.
x = zeros(n, 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Fill in this function to return a feature vector for the
%               given email (word_indices). To help make it easier to 
%               process the emails, we have have already pre-processed each
%               email and converted each word in the email into an index in
%               a fixed dictionary (of 1899 words). The variable
%               word_indices contains the list of indices of the words
%               which occur in one email.
% 
%               Concretely, if an email has the text:
%
%                  The quick brown fox jumped over the lazy dog.
%
%               Then, the word_indices vector for this text might look 
%               like:
%               
%                   60  100   33   44   10     53  60  58   5
%
%               where, we have mapped each word onto a number, for example:
%
%                   the   -- 60
%                   quick -- 100
%                   ...
%
%              (note: the above numbers are just an example and are not the
%               actual mappings).
%
%              Your task is take one such word_indices vector and construct
%              a binary feature vector that indicates whether a particular
%              word occurs in the email. That is, x(i) = 1 when word i
%              is present in the email. Concretely, if the word 'the' (say,
%              index 60) appears in the email, then x(60) = 1. The feature
%              vector should look like:
%
%              x = [ 0 0 0 0 1 0 0 0 ... 0 0 0 0 1 ... 0 0 0 1 0 ..];
%              
%

               for i=1:size(word_indices),
			        x(word_indices(i))=1;
			   
% =========================================================================
    

end