compute_mapping.m

数据降维工具箱

function [mappedA, mapping] = compute_mapping(A, type, no_dims, varargin)
%COMPUTE_MAPPING Performs dimensionality reduction on a dataset A
%
%   mappedA = compute_mapping(A, type)
%   mappedA = compute_mapping(A, type, no_dims)
%
% Performs a technique for dimensionality reduction on the data specified 
% in A, reducing data with a lower dimensionality in mappedA.
% The data on which dimensionality reduction is performed is given in A
% (rows correspond to observations, columns to dimensions). A may also be a
% (labeled or unlabeled) PRTools dataset.
% The type of dimensionality reduction used is specified by type. Possible
% values are 'PCA', 'SPCA', 'LDA', 'ICA', 'MDS', 'Isomap', 'LandmarkIsomap',
% 'LLE', 'Laplacian', 'HessianLLE', 'LTSA', 'DiffusionMaps', 'KernelPCA', 
% 'GDA', 'SNE', 'SPE', 'AutoEncoder', and 'AutoEncoderEA'. 
% The function returns the low-dimensional representation of the data in the 
% matrix mappedA. If A was a PRTools dataset, then mappedA is a PRTools 
% dataset as well. For some techniques, information on the mapping is 
% returned in the struct mapping.
% The variable no_dims specifies the number of dimensions in the embedded
% space (default = 2). For 'LDA' and 'GDA', the labels of the instances 
% should be specified in the first column of A. 
%
%   mappedA = compute_mapping(A, type, no_dims, parameters)
%   mappedA = compute_mapping(A, type, no_dims, parameters, eig_impl)
%
% Free parameters of the techniques can be defined as well (on the place of
% the dots). These parameters differ per technique, and are listed below.
% For techniques that perform spectral analysis of a sparse matrix, one can 
% also specify in eig_impl the eigenanalysis implementation that is used. 
% Possible values are 'Matlab' and 'JDQR' (default = 'Matlab'). We advice
% to use the 'Matlab' for datasets of with 10,000 or less datapoints; 
% for larger problems the 'JDQR' might prove to be more fruitful. 
% The free parameters for the techniques are listed below (the parameters 
% should be provided in this order):
%
%   PCA:            - none
%   LDA:            - none
%   MDS:            - none
%   Isomap:         - <int> k -> default = 12
%   LandmarkIsomap: - <int> k -> default = 12
%                   - <double> percentage -> default = 0.2
%   LLE:            - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   Laplacian:      - <int> k -> default = 12
%                   - <double> sigma -> default = 1.0
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   HessianLLE:     - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   LTSA:           - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   MVU:            - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   CCA:            - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   FastMVU:        - <int> k -> default = 12
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   DiffusionMaps:  - <double> sigma -> default = 1.0
%   KernelPCA:      - <char[]> kernel -> {'linear', 'poly', ['gauss']} 
%                   - kernel parameters: type HELP GRAM for info
%   GDA:            - <char[]> kernel -> {'linear', 'poly', ['gauss']} 
%                   - kernel parameters: type HELP GRAM for info
%   SNE:            - <double> sigma -> default = 1.0
%   LPP:            - <int> k -> default = 12
%   NPE:            - <int> k -> default = 12
%   LLTSA:          - <int> k -> default = 12
%   SPE:            - <char[]> type -> {['Global'], 'Local'}
%                   - if 'Local': <int> k -> default = 12
%   SimplePCA       - none
%   ProbPCA:        - <int> max_iterations -> default = 200
%   AutoEncoderRBM: - none
%   AutoEncoderEA:  - none
%   LLC:            - <int> k -> default = 12
%                   - <int> no_analyzers -> default = 20
%                   - <int> max_iterations -> default = 200
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   ManifoldChart:  - <int> no_analyzers -> default = 40
%                   - <int> max_iterations -> default = 200
%                   - <char[]> eig_impl -> {['Matlab'], 'JDQR'}
%   CFA:            - <int> no_analyzers -> default = 40
%                   - <int> max_iterations -> default = 200
%
%
% In the parameter list above, {.., ..} indicates a list of options, and []
% indicates the default setting. The variable k indicates the number of 
% nearest neighbors in a neighborhood graph. Alternatively, k may also have 
% the value 'adaptive', indicating the use of adaptive neighborhood selection
% in the construction of the neighborhood graph. Note that in LTSA and
% HessianLLE, the setting 'adaptive' might cause singularities. Using the
% JDQR-solver or a fixed setting of k might resolve this problem. SPE does
% not yet support adaptive neighborhood selection.
% 
% The variable sigma indicates the variance of a Gaussian kernel. The 
% parameters no_analyzers and max_iterations indicate repectively the number
% of factor analyzers that is used in an MFA model and the number of 
% iterations that is used in an EM algorithm. The parameter type in SPE 
% indicates whether a local or a global stress function is minimized.
%

% This file is part of the Matlab Toolbox for Dimensionality Reduction v0.3b.
% The toolbox can be obtained from http://www.cs.unimaas.nl/l.vandermaaten
% You are free to use, change, or redistribute this code in any way you
% want for non-commercial purposes. However, it is appreciated if you 
% maintain the name of the original author.
%
% (C) Laurens van der Maaten
% Maastricht University, 2007

    welcome;
    
    % Check inputs
    if nargin < 2
        error('Function requires at least two inputs.');
    end
    if ~exist('no_dims', 'var')
        no_dims = 2;
    end
    if ~isempty(varargin) && strcmp(varargin{length(varargin)}, 'JDQR')
        eig_impl = 'JDQR';
        varargin(length(varargin)) = [];
    elseif ~isempty(varargin) && strcmp(varargin{length(varargin)}, 'Matlab')
        eig_impl = 'Matlab';
        varargin(length(varargin)) = [];
    else
        eig_impl = 'Matlab';
    end
    mapping = struct;
    
    % Handle PRTools dataset
    if strcmp(class(A), 'dataset')
        prtools = 1;
        AA = A;
        if ~strcmp(type, {'LDA', 'FDA', 'GDA', 'KernelLDA', 'KernelFDA'})
            A = A.data;
        else
            A = [double(A.labels) A.data];
        end
    else 
        prtools = 0;
    end
    
    % Make sure we are working with doubles
    A = double(A);
    
    % Check whether value of no_dims is correct
    if no_dims < 1 || no_dims > size(A, 2) || round(no_dims) ~= no_dims
        error('Value of no_dims should be a positive integer smaller than the original data dimensionality.');
    end
    
    % Switch case
    switch type
        case 'Isomap'         
            % Compute Isomap mapping
			if isempty(varargin), [mappedA, mapping] = isomap(A, no_dims, 12);
            else [mappedA, mapping] = isomap(A, no_dims, varargin{1}); end
            mapping.name = 'Isomap';
			
		case 'LandmarkIsomap'
			% Compute Landmark Isomap mapping
            if isempty(varargin), [mappedA, mapping] = landmark_isomap(A, no_dims, 12, 0.2);
			elseif length(varargin) == 1, [mappedA, mapping] = landmark_isomap(A, no_dims, varargin{1}, 0.2);
            elseif length(varargin) >  1, [mappedA, mapping] = landmark_isomap(A, no_dims, varargin{1}, varargin{2}); end
            mapping.name = 'LandmarkIsomap';
            
        case {'Laplacian', 'LaplacianEig', 'LaplacianEigen' 'LaplacianEigenmaps'}
            % Compute Laplacian Eigenmaps-based mapping
            if isempty(varargin), [mappedA, mapping] = laplacian_eigen(A, no_dims, 12, 1, eig_impl);
			elseif length(varargin) == 1, [mappedA, mapping] = laplacian_eigen(A, no_dims, varargin{1}, 1, eig_impl);
            elseif length(varargin) > 1,  [mappedA, mapping] = laplacian_eigen(A, no_dims, varargin{1}, varargin{2}, eig_impl); end