Description of slmeans

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slmeans

PURPOSE

SLMEANS Compute the mean vectors

SYNOPSIS

function varargout = slmeans(X, w, nums)

DESCRIPTION

SLMEANS Compute the mean vectors

 $ Syntax $
   - v = slmeans(X)
   - v = slmeans(X, w)
   - V = slmeans(X, [], nums)
   - V = slmeans(X, w, nums)
   - [V, v] = slmeans(X, [], nums)
   - [V, v] = slmeans(X, w, nums)

 $ Arguments $
   - X:            the sample matrix with each column representing a sample
   - w:            the sample weights
   - nums:         the number of samples in each group
   - v:            the overall mean vector
   - V:            the matrix of mean vectors for each group

 $ Description $
   - v = slmeans(X) computes the mean vector of X

   - v = slmeans(X, w) computes the weighted mean vector of X, with weights
     specified by w.

   - V = slmeans(X, [], nums) computes the mean vectors for groups, 
     each group of vectors are gathered together, and the number
     of vectors in each collection is specified in nums

   - V = slmeans(X, w, nums) computes the weighted mean vectors for 
     groups of vectors.

   - [V, v] = slmeans(X, w, nums) computes the mean vectors for groups
     of vectors and the overall mean vector v.

   - [V, v] = slmeans(X, w, nums) computes the weighted mean vectors for
     groups of vectors and the overall weighted mean vector v.

 $ Remarks $
   - If there are n samples in d-dimensional space, then X should be a 
     d x n matrix, w should be a 1 x n row vector. If the vectors are
     grouped in k groups, then nums should be a 1 x k row vector.
     Then v would be a d x 1 vector, V would be a d x k matrix.

 $ History $
   - Created by Dahua Lin on Dec 18th, 2005
   - Modified by Dahua Lin on Apr 22nd, 2005
       - extract the function computing mean of a group to an external
         function.
       - modify some comments

CROSS-REFERENCE INFORMATION

This function calls:

• slmean SLMEAN Compute the mean vector of samples
• slnums2bounds SLNUMS2BOUNDS Compute the index-boundaries from section sizes

This function is called by:

• sldlda SLDLDA Performs Direct Linear Discriminant Analysis
• slfld SLFLD Performs Fisher Linear Discriminant Analysis
• slnlda SLNLDA Performs Nullspace-based Linear Discriminant Analysis
• slscatter SLSCATTER Compute the scatter matrix

SOURCE CODE

0001 function varargout = slmeans(X, w, nums)
0002 %SLMEANS Compute the mean vectors
0003 %
0004 % $ Syntax $
0005 %   - v = slmeans(X)
0006 %   - v = slmeans(X, w)
0007 %   - V = slmeans(X, [], nums)
0008 %   - V = slmeans(X, w, nums)
0009 %   - [V, v] = slmeans(X, [], nums)
0010 %   - [V, v] = slmeans(X, w, nums)
0011 %
0012 % $ Arguments $
0013 %   - X:            the sample matrix with each column representing a sample
0014 %   - w:            the sample weights
0015 %   - nums:         the number of samples in each group
0016 %   - v:            the overall mean vector
0017 %   - V:            the matrix of mean vectors for each group
0018 %
0019 % $ Description $
0020 %   - v = slmeans(X) computes the mean vector of X
0021 %
0022 %   - v = slmeans(X, w) computes the weighted mean vector of X, with weights
0023 %     specified by w.
0024 %
0025 %   - V = slmeans(X, [], nums) computes the mean vectors for groups,
0026 %     each group of vectors are gathered together, and the number
0027 %     of vectors in each collection is specified in nums
0028 %
0029 %   - V = slmeans(X, w, nums) computes the weighted mean vectors for
0030 %     groups of vectors.
0031 %
0032 %   - [V, v] = slmeans(X, w, nums) computes the mean vectors for groups
0033 %     of vectors and the overall mean vector v.
0034 %
0035 %   - [V, v] = slmeans(X, w, nums) computes the weighted mean vectors for
0036 %     groups of vectors and the overall weighted mean vector v.
0037 %
0038 % $ Remarks $
0039 %   - If there are n samples in d-dimensional space, then X should be a
0040 %     d x n matrix, w should be a 1 x n row vector. If the vectors are
0041 %     grouped in k groups, then nums should be a 1 x k row vector.
0042 %     Then v would be a d x 1 vector, V would be a d x k matrix.
0043 %
0044 % $ History $
0045 %   - Created by Dahua Lin on Dec 18th, 2005
0046 %   - Modified by Dahua Lin on Apr 22nd, 2005
0047 %       - extract the function computing mean of a group to an external
0048 %         function.
0049 %       - modify some comments
0050 %
0051 
0052 %% parse and verify input arguments
0053 if ndims(X) ~= 2
0054     error('sltoolbox:invaliddims', 'X should be a 2D matrix');
0055 end
0056 [d, n] = size(X);
0057 
0058 % for weights
0059 if nargin < 2 || isempty(w)
0060     w = [];
0061 else
0062     if ~isequal(size(w), [1, n])
0063         error('sltoolbox:sizmismatch', ...
0064             'the weight vector should be a 1 x n row vector');
0065     end
0066 end
0067 
0068 % for groupping
0069 if nargin < 3 || isempty(nums)
0070     isgrouped = false;
0071 else
0072     isgrouped = true;
0073     if size(nums, 1) ~= 1
0074         error('sltoolbox:invalidarg', ...
0075             'the nums vector should be a row vector');
0076     end
0077     if sum(nums) ~= n
0078         error('sltoolbox:sizmismatch', ...
0079             'the nums vector does not match the total number of vectors');
0080     end
0081     [sp, ep] = slnums2bounds(nums);  % group index boundary
0082     k = length(nums);  % number of groups
0083 end
0084 
0085 %% compute
0086 if ~isgrouped
0087     v = slmean(X, w, true);
0088     varargout = {v};
0089 else
0090     V = zeros(d, k);       
0091     
0092     % compute group-wise mean
0093     if isempty(w)
0094         for i = 1 : k
0095             V(:, i) = slmean(X(:, sp(i):ep(i)), [], true);
0096         end
0097     else
0098         for i = 1 : k
0099             V(:, i) = slmean(X(:, sp(i):ep(i)), w(sp(i):ep(i)), true);
0100         end
0101     end
0102     
0103     if nargout <= 1
0104         varargout = {V};
0105     else
0106         % compute group weights
0107         if isempty(w)
0108             gw = nums;
0109         else
0110             gw = zeros(1, k);
0111             for i = 1 : k
0112                 gw(i) = sum(w(sp(i):ep(i)));
0113             end
0114         end
0115         
0116         % compute overall mean
0117         v = slmean(V, gw, true);
0118         
0119         varargout = {V, v};
0120     end
0121 end
0122 
0123 
0124

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