Description of sllle

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sllle

PURPOSE

SLLLE Performs Locally Linear Embedding

SYNOPSIS

function [Y, spectrum, WG] = sllle(X, G, d, rwparams)

DESCRIPTION

SLLLE Performs Locally Linear Embedding

 $ Syntax $
   - Y = sllle(X, G, d)
   - Y = sllle(X, G, d, rwparams)
   - [Y, spectrum, WG] = sllle(X, G, d)

 $ Arguments $
   - X:        The sample matrix (d x n)
   - G:        The neighborhood graph or the cell array of parameters to 
               generate the neighborhood graph. 
               For a graph, G should have n nodes, where n is the number
               of samples in X. The non-zero of the entry (i,j) means 
               the i-th sample is the neighbor of the j-th sample.
               If it is a set of parameters, it is in the form of 
               {method, ...}, which will be input to slfindnn to 
               construct a neighborhood graph. 
   - d:        The dimension of the embeded space. 
   - rwparams: The cell array parameters for solving reconstruction weights
               default = {}
   - Y:        The coordinates of samples in the embeded space
   - WG:       The weight graph computed

 $ Description $
   - Y = sllle(X, G, d) solves the locally linear embedding of X in a 
     d-dimensional linear space. 

   - Y = sllle(X, G, d, rwparams) uses special set of parameters to 
     control the solving of reconstruction parameters.

   - [Y, spectrum, WG] = sllle(X, G, d) additionally returns the spectrum
     and the local construction weight graph.

 $ Remarks $
   - It integrates the functions: 
       - slfindnn and slnngraph: for graph construction
       - slreconweights: for local reconstruction weight solving
       - sllle_wg: solves LLE from constructed weight graph
   - Only the zero/non-zero of G takes effects, it will not make use
     of the values in G.

 $ History $
   - Created by Dahua Lin, on Sep 11st, 2006

CROSS-REFERENCE INFORMATION

This function calls:

• sladjmat SLADJMAT Constructs the adjacency matrix representation of a graph
• slgraphinfo SLGRAPHINFO Extracts basic information of a given graph representation
• slnngraph SLNNGRAPH Constructs a nearest neighborhood based graph
• sllle_wg SLLLE_WG Solves the Locally Linear Embedding from weight graph
• slnbreconweights SLNBRECONWEIGHTS Solve the optimal reconstruction weights on given neighbors
• raise_lackinput RAISE_LACKINPUT Raises an error indicating lack of input argument

This function is called by:

SOURCE CODE

0001 function [Y, spectrum, WG] = sllle(X, G, d, rwparams)
0002 %SLLLE Performs Locally Linear Embedding
0003 %
0004 % $ Syntax $
0005 %   - Y = sllle(X, G, d)
0006 %   - Y = sllle(X, G, d, rwparams)
0007 %   - [Y, spectrum, WG] = sllle(X, G, d)
0008 %
0009 % $ Arguments $
0010 %   - X:        The sample matrix (d x n)
0011 %   - G:        The neighborhood graph or the cell array of parameters to
0012 %               generate the neighborhood graph.
0013 %               For a graph, G should have n nodes, where n is the number
0014 %               of samples in X. The non-zero of the entry (i,j) means
0015 %               the i-th sample is the neighbor of the j-th sample.
0016 %               If it is a set of parameters, it is in the form of
0017 %               {method, ...}, which will be input to slfindnn to
0018 %               construct a neighborhood graph.
0019 %   - d:        The dimension of the embeded space.
0020 %   - rwparams: The cell array parameters for solving reconstruction weights
0021 %               default = {}
0022 %   - Y:        The coordinates of samples in the embeded space
0023 %   - WG:       The weight graph computed
0024 %
0025 % $ Description $
0026 %   - Y = sllle(X, G, d) solves the locally linear embedding of X in a
0027 %     d-dimensional linear space.
0028 %
0029 %   - Y = sllle(X, G, d, rwparams) uses special set of parameters to
0030 %     control the solving of reconstruction parameters.
0031 %
0032 %   - [Y, spectrum, WG] = sllle(X, G, d) additionally returns the spectrum
0033 %     and the local construction weight graph.
0034 %
0035 % $ Remarks $
0036 %   - It integrates the functions:
0037 %       - slfindnn and slnngraph: for graph construction
0038 %       - slreconweights: for local reconstruction weight solving
0039 %       - sllle_wg: solves LLE from constructed weight graph
0040 %   - Only the zero/non-zero of G takes effects, it will not make use
0041 %     of the values in G.
0042 %
0043 % $ History $
0044 %   - Created by Dahua Lin, on Sep 11st, 2006
0045 %
0046 
0047 %% parse and verify input arguments
0048 
0049 if nargin < 3
0050     raise_lackinput('sllle', 3);
0051 end
0052 
0053 if ~isnumeric(X) || ndims(X) ~= 2
0054     error('sltoolbox:invalidarg', ...
0055         'X should be a 2D numeric matrix');
0056 end
0057 n = size(X, 2);
0058 
0059 if d >= n
0060     error('sltoolbox:invalidarg', ...
0061         'd should be strictly less than n');
0062 end
0063 
0064 if nargin < 4
0065     rwparams = {};
0066 end
0067 
0068 
0069 %% process the graph
0070 
0071 if iscell(G)
0072     G = slnngraph(X, [], G, 'valtype', 'logical', 'sparse', true);
0073 end
0074 
0075 gi = slgraphinfo(G, {'square'});
0076 if ~strcmp(gi.form, 'adjmat')
0077     G = sladjmat(G, 'valtype', 'logical', 'sparse', true);
0078 end
0079 
0080 %% solve reconstruction weights
0081 
0082 WG = slnbreconweights(X, [], G, rwparams{:});
0083 clear G;
0084 
0085 %% solve the embedding
0086 
0087 [Y, spectrum] = sllle_wg(WG, d);
0088     
0089 
0090     
0091     
0092     
0093     
0094 
0095 
0096 
0097

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