feature normalization

以你之姓@ 2022-03-07 14:40 162阅读 0赞

I was doing Coursera—machine learning(Andrew Ng)第二周编程作业  
reading this  
[线性回归--Octave实现][--Octave]  
[Coursera机器学习-Week 2-编程作业:Linear Regression][--Octave]  
[Coursera—machine learning(Andrew Ng)第二周编程作业][Coursera_machine learning_Andrew Ng]

I don't really get this

sigma = std(X, 1, 1);

despite it says ...still don't get it  
well my friends say it's 样本方差是n-1  
统计学

>> help std
    'std' is a function from the file E:\Octave\Octave-4.4.1\share\octave\4.4.1\m\statistics\std.m
    
     -- std (X)
     -- std (X, OPT)
     -- std (X, OPT, DIM)
         Compute the standard deviation of the elements of the vector X.
    
         The standard deviation is defined as
    
              std (X) = sqrt ( 1/(N-1) SUM_i (X(i) - mean(X))^2 )
    
         where N is the number of elements of the X vector.
    
         If X is a matrix, compute the standard deviation for each column
         and return them in a row vector.
    
         The argument OPT determines the type of normalization to use.
         Valid values are
    
         0:
              normalize with N-1, provides the square root of the best
              unbiased estimator of the variance [default]
    
         1:
              normalize with N, this provides the square root of the second
              moment around the mean
    
         If the optional argument DIM is given, operate along this
         dimension.
    
         See also: var, bounds, mad, range, iqr, mean, median.
    
    Additional help for built-in functions and operators is
    available in the online version of the manual.  Use the command
    'doc <topic>' to search the manual index.

But it seems the code can be simple like this..  
I don't know whether I am right here though..

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.
    %       
    mu = mean(X);
    sigma = std(X);
    disp('mu'),disp(mu);
    disp('sigma'),disp(sigma);
    
    sigma= std(X);
    X_norm = (X-mu) ./ sigma;
      
    disp('X_norm'),disp(X_norm);
    
    
    
    % ============================================================
    
    end

There are two ways to write a cost function  
1.

J = 1/(2*m)*((X*theta)-y)'*((X*theta)-y);

h= zeros(m,1);
    h = X*theta;
    J = (1/(2*m))*sum((h-y).^2);

[--Octave]: https://blog.csdn.net/f_zyj/article/details/78935379
[Coursera_machine learning_Andrew Ng]: https://blog.csdn.net/ccblogger/article/details/78415881