Description of slmean

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slmean

PURPOSE

SLMEAN Compute the mean vector of samples

SYNOPSIS

function v = slmean(M, w, hasbeenchecked)

DESCRIPTION

SLMEAN Compute the mean vector of samples

 $ Syntax $
   - v = slmean(M)
   - v = slmean(M, w)
   - v = slmean(M, w, true)

 $ Arguments $
   - M:        the matrix of sample vectors stored as columns
   - w:        the weights of the vectors
   - v:        the computed mean vector

 $ Description $
   - v = slmean(M) computes the mean vector of column vectors in M.
   
   - v = slmean(M, w) computes the weighted mean vector of column vectors
     in M. w is the weights of the samples. if w is empty, the normal
     mean vector would be computed. 

   - v = slmean(M, w, true) indicates that the size consistency has been
     checked by invoker. Then in this function, it will not be checked
     again. This syntax is designed for the sake of efficiency.

 $ Remarks $
   - M should be a 2D matrix (d x n), then w should be a 1 x n row vector,
     v would be a d x 1 column vector.

 $ History $
   - Created by Dahua Lin on Apr 22nd, 2006
   - Modified by Dahua Lin on Sep 10th, 2006
       - replace slmul by slmulvec to increase efficiency

CROSS-REFERENCE INFORMATION

This function calls:

• slmulvec SLMULVEC multiplies a vector to columns or rows of a matrix

This function is called by:

• slkmeans SLKMEANS Performs K-Means Clustering on samples
• sldistmean SLDISTMEAN Uses fast method to compute means of pairwise distances
• sllocaltanspace SLLOCALTANSPACE Solves the local tangent spaces
• slcov SLCOV Compute the covariance matrix
• slcovlarge SLCOVLARGE Computes large covariance matrix using memory-efficient way
• slgaussest SLGAUSSEST Estimates the Gaussian models from samples
• slmeans SLMEANS Compute the mean vectors
• slcopca SLCOPCA Performs Coupled PCA Learning
• slpca SLPCA Learns a PCA model from training samples
• slscatter SLSCATTER Compute the scatter matrix

SOURCE CODE

0001 function v = slmean(M, w, hasbeenchecked)
0002 %SLMEAN Compute the mean vector of samples
0003 %
0004 % $ Syntax $
0005 %   - v = slmean(M)
0006 %   - v = slmean(M, w)
0007 %   - v = slmean(M, w, true)
0008 %
0009 % $ Arguments $
0010 %   - M:        the matrix of sample vectors stored as columns
0011 %   - w:        the weights of the vectors
0012 %   - v:        the computed mean vector
0013 %
0014 % $ Description $
0015 %   - v = slmean(M) computes the mean vector of column vectors in M.
0016 %
0017 %   - v = slmean(M, w) computes the weighted mean vector of column vectors
0018 %     in M. w is the weights of the samples. if w is empty, the normal
0019 %     mean vector would be computed.
0020 %
0021 %   - v = slmean(M, w, true) indicates that the size consistency has been
0022 %     checked by invoker. Then in this function, it will not be checked
0023 %     again. This syntax is designed for the sake of efficiency.
0024 %
0025 % $ Remarks $
0026 %   - M should be a 2D matrix (d x n), then w should be a 1 x n row vector,
0027 %     v would be a d x 1 column vector.
0028 %
0029 % $ History $
0030 %   - Created by Dahua Lin on Apr 22nd, 2006
0031 %   - Modified by Dahua Lin on Sep 10th, 2006
0032 %       - replace slmul by slmulvec to increase efficiency
0033 %
0034 
0035 %% parse and verify input arguments
0036 
0037 if nargin < 3 || ~hasbeenchecked
0038 
0039     if ndims(M) ~= 2
0040         error('sltoolbox:invaliddims', 'M should be a 2D matrix');
0041     end
0042 
0043     n = size(M, 2); % number of samples
0044     if nargin < 2 || isempty(w)
0045         is_weighted = false;
0046     else
0047         is_weighted = true;
0048 
0049         % check size consistency
0050         [wd1, wd2] = size(w);
0051         if ndims(w) ~= 2 || wd1 ~= 1 || wd2 ~= n;
0052             error('sltoolbox:sizmismatch', ...
0053                 'w is not a valid row vector consistent with M');
0054         end    
0055     end
0056     
0057 else  
0058     n = size(M, 2); % number of samples
0059     is_weighted = ~isempty(w);
0060 end
0061 
0062 
0063 %% compute
0064 
0065 if ~is_weighted    
0066     v = sum(M, 2) / n;    
0067 else
0068     
0069     % normalize the weights
0070     w = w / sum(w);    
0071     v = sum(slmulvec(M, w, 2), 2);    
0072 end
0073

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