Machine learning吳恩達第二周coding作業（選做）

1.Feature Normalization：

歸一化的處理

function [X_norm, mu, sigma] = featureNormalize(X)
%FEATURENORMALIZE Normalizes the features in X 
%   FEATURENORMALIZE(X) returns a normalized version of X where
%   the mean value of each feature is 0 and the standard deviation
%   is 1. This is often a good preprocessing step to do when
%   working with learning algorithms.

% You need to set these values correctly
X_norm = X;
mu = zeros(1, size(X, 2));
sigma = zeros(1, size(X, 2));

% ====================== YOUR CODE HERE ======================
% Instructions: First, for each feature dimension, compute the mean
%               of the feature and subtract it from the dataset,
%               storing the mean value in mu. Next, compute the 
%               standard deviation of each feature and divide
%               each feature by it's standard deviation, storing
%               the standard deviation in sigma. 
%
%               Note that X is a matrix where each column is a 
%               feature and each row is an example. You need 
%               to perform the normalization separately for 
%               each feature. 
%
% Hint: You might find the 'mean' and 'std' functions useful.
%       

for i=1:size(X,2),
  mu(i)=mean(X(:,i));
  sigma(i)=std(X(:,i));
  X_norm(:,i)=(X_norm(:,i)-mu(i))/sigma(i);
end;








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

end      

 2. Computing Cost (for Multiple Variables) && Gradient Descent (for Multiple Variables)

由于我們單變量的時候就是用矩陣形式處理的，是以代碼與單變量相同；

3.Normal Equations

function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression 
%   NORMALEQN(X,y) computes the closed-form solution to linear 
%   regression using the normal equations.

theta = zeros(size(X, 2), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%

% ---------------------- Sample Solution ----------------------

theta=inv(X'*X)*X'*y;


% -------------------------------------------------------------


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

end