Description of slkfd

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slkfd

PURPOSE

SLKFD Perform Kernelized Fisher Discriminant Analysis

SYNOPSIS

function A = slkfd(K, nums, varargin)

DESCRIPTION

SLKFD Perform Kernelized Fisher Discriminant Analysis

 $ Syntax $
   - A = slkfd(K, nums, ...)

 $ Arguments $
   - K:        the kernel gram matrix of the training samples
   - nums:     the numbers of samples in all classes
   - A:        the projection coefficient matrix 
 
 $ Description $
   - A = slkfd(K, nums, ...) performs Kernerlized Fisher discriminant 
     analysis on the samples X according to the specified properties. 
     \*
     \t   Table 1.  The properties of Fisher Discriminant Analysis   \\
     \h     name     &     description                                \\
           'sol'     &  The cell containing the arguments for solving
                        the generalized eigen-problem by slsymgeig.  
                        default = {}.                                 \\
           'dimset'  &  The cell containing the arguments for determining
                        the output feature dimension. default = {}.
                        (refer to sldim_by_eigval).                   \\
           'Sb'      &  The pre-computed kernelized between-class 
                        scattering matrix or the cell containing 
                        the arguments for computing the kernelized 
                        scatter matrix in the form {type, ...}, 
                        which is input to slkernelscatter.     \\
           'Sw'      &  The pre-computed kernelized within-class 
                        scattering matrix or the cell containing 
                        the arguments for computing the scatter 
                        matrix in the form {type, ...}, which is 
                        input to slkernelscatter.     \\
         'weights'   &  The sample weights. default = [].   \\
     \*  

 $ History $
   - Created by Dahua Lin on May 03, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• slsymgeig SLSYMGEIG Solve the generalized eigen decomposition for symmetric matrices
• sldim_by_eigval SLDIM_BY_EIGVAL Determines the dimension of principal subspace by eigenvalues
• slscatter SLSCATTER Compute the scatter matrix
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument
• slparseprops SLPARSEPROPS Parses input parameters

This function is called by:

SOURCE CODE

0001 function A = slkfd(K, nums, varargin)
0002 %SLKFD Perform Kernelized Fisher Discriminant Analysis
0003 %
0004 % $ Syntax $
0005 %   - A = slkfd(K, nums, ...)
0006 %
0007 % $ Arguments $
0008 %   - K:        the kernel gram matrix of the training samples
0009 %   - nums:     the numbers of samples in all classes
0010 %   - A:        the projection coefficient matrix
0011 %
0012 % $ Description $
0013 %   - A = slkfd(K, nums, ...) performs Kernerlized Fisher discriminant
0014 %     analysis on the samples X according to the specified properties.
0015 %     \*
0016 %     \t   Table 1.  The properties of Fisher Discriminant Analysis   \\
0017 %     \h     name     &     description                                \\
0018 %           'sol'     &  The cell containing the arguments for solving
0019 %                        the generalized eigen-problem by slsymgeig.
0020 %                        default = {}.                                 \\
0021 %           'dimset'  &  The cell containing the arguments for determining
0022 %                        the output feature dimension. default = {}.
0023 %                        (refer to sldim_by_eigval).                   \\
0024 %           'Sb'      &  The pre-computed kernelized between-class
0025 %                        scattering matrix or the cell containing
0026 %                        the arguments for computing the kernelized
0027 %                        scatter matrix in the form {type, ...},
0028 %                        which is input to slkernelscatter.     \\
0029 %           'Sw'      &  The pre-computed kernelized within-class
0030 %                        scattering matrix or the cell containing
0031 %                        the arguments for computing the scatter
0032 %                        matrix in the form {type, ...}, which is
0033 %                        input to slkernelscatter.     \\
0034 %         'weights'   &  The sample weights. default = [].   \\
0035 %     \*
0036 %
0037 % $ History $
0038 %   - Created by Dahua Lin on May 03, 2006
0039 %
0040 
0041 %% parse and verify input arguments
0042 
0043 if nargin < 2
0044     raise_lackinput('slkfd', 2);
0045 end
0046 
0047 % for K
0048 n = size(K, 1);
0049 if ~isequal(size(K), [n, n])
0050     error('sltoolbox:invaliddims', ...
0051         'K should be a square matrix');
0052 end
0053 
0054 % for nums
0055 nc = length(nums);
0056 if ~isequal(size(nums), [1 nc])
0057     error('sltoolbox:sizmismatch', ...
0058         'nums should be a 1 x nc row vector');
0059 end
0060 
0061 % for options
0062 
0063 opts.sol = {};
0064 opts.dimset = {};
0065 opts.Sb = {'Sb'};
0066 opts.Sw = {'Sw'};
0067 opts.weights = [];
0068 opts = slparseprops(opts, varargin{:});
0069 
0070 has_Sb = ~isempty(opts.Sb) && isnumeric(opts.Sb);
0071 has_Sw = ~isempty(opts.Sw) && isnumeric(opts.Sw);
0072 if has_Sb
0073     Sb = opts.Sb;
0074     if ~isequal(size(Sb), [n n])
0075         error('sltoolbox:sizmismatch', ...
0076             'Sb should be a n x n matrix');
0077     end
0078 end
0079 if has_Sw
0080     Sw = opts.Sw;
0081     if ~isequal(size(Sw), [n n])
0082         error('sltoolbox:sizmismatch', ...
0083             'Sw should be a n x n matrix');
0084     end
0085 end
0086 
0087 if ~isempty(opts.weights)
0088     w = opts.weights;
0089     if ~isequal(size(w), [1 n])
0090         error('sltoolbox:sizmismatch', ...
0091             'The weights should be a 1 x n row vector');
0092     end
0093 else
0094     w = [];
0095 end
0096 
0097 
0098 %% Compute
0099 
0100 %% Step 1: Construct the eigen-problem
0101 
0102 if ~has_Sb
0103     Sb = slscatter(K, opts.Sb{:}, 'sweights', w, 'nums', nums);
0104 end
0105 
0106 if ~has_Sw
0107     Sw = slscatter(K, opts.Sw{:}, 'sweights', w, 'nums', nums);
0108 end
0109 
0110 
0111 %% Step 2: Resolve the eigen-problem
0112 
0113 [evs, A] = slsymgeig(Sb, Sw, opts.sol{:});
0114 
0115 rk = sldim_by_eigval(evs, opts.dimset{:});
0116 A = A(:, 1:rk);
0117 
0118

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