function W = lssvc(A, TYPE, PAR, C)
%LSSVC Least-Squares Support Vector Classifier
%
% W = lssvc(A,TYPE,PAR,C);
%
% INPUT
% A dataset
% TYPE Type of the kernel (optional; default: 'p')
% PAR Kernel parameter (optional; default: 1)
% C Regularization parameter (optional; default: 1)
%
% OUTPUT
% W Mapping: Least-Squares Support Vector Classifier
%
% DESCRIPTION
% Optimizes a least-squares support vector classifier for the dataset A by
% quadratic programming. The classifier can be of one of the types
% as defined by PROXM. Default is linear (TYPE = 'p', PAR = 1). The
% regularization parameter C allows for seeting the level of overfitting.
% A smaller value for C allows for more class overlap. Default C = 10.
%
% NOTE
% This implementation uses the LS-SVMLab toolbox. This toolbox is available
% from http://www.esat.kuleuven.ac.be/sista/lssvmlab/. Make sure the path
% to LS-SVMLab is set in Matlab.
%
% See also MAPPINGS, DATASETS, PROXM
% Copyright: L.J.P. van der Maaten, l.vandermaaten@micc.unimaas.nl
% MICC-IKAT, Maastricht University, Maastricht, The Netherlands
name = 'LSSVC';
% Check whether LS-SVMLab is installed and set in the path
if ~exist('trainlssvm.m', 'file')
error('Could not find LS-SVMLab. Make sure LS-SVMLab is installed and set in the Matlab path.');
end
% Perform LS-SVM training on dataset A
if nargin <= 1 || (nargin >= 2 && ~isa(TYPE, 'prmapping'))
% Set LS-SVM parameters
if ~exist('TYPE', 'var') || ~isstruct(TYPE)
if nargin < 2 || isempty(TYPE), data.kernel = 'p'; else data.kernel = TYPE; end % kernel function
if nargin < 3 || isempty(PAR), data.par = 1; else data.par = PAR; end % kernel parameters
if nargin < 4 || isempty(C), data.gamma = 10; else data.gamma = C; end % regularization parameter
data.par2 = -1;
% LS-SVMLab uses different naming for kernels; correct this
switch lower(data.kernel)
case {'p', 'polynomial'}, data.kernel = 'poly_kernel'; data.par2 = 1;
case {'h', 'homogeneous'}, data.kernel = 'poly_kernel'; data.par2 = 0;
case {'e', 'exponential'}, error('This kernel is not supported by LS-SVMLab.');
case {'r', 'radial_basis'}, data.kernel = 'RBF_kernel'; data.par = data.par^2; % LS-SVMLab uses sigma^2 as input
case {'s', 'sigmoid'}, data.kernel = 'MLP_kernel';
case {'d', 'distance'}, error('This kernel is not supported by LS-SVMLab.');
case {'m', 'minkowski'}, error('This kernel is not supported by LS-SVMLab.');
case {'c', 'city-block'}, error('This kernel is not supported by LS-SVMLab.');
case {'o', 'cosine'}, error('This kernel is not supported by LS-SVMLab.');
otherwise, error('Unknown kernel function.');
end
else
data = TYPE;
end
% Handle the case in which the dataset is empty
if ~exist('A', 'var') || isempty(A)
W = prmapping('lssvc', 'untrained', data);
W = setname(W, name);
return;
end
% Perform some checks on the data
islabtype(A, 'crisp'); % allow crisp labels only
isvaldset(A, 1, 2); % at least one object per class, two objects
if ischar(A.lablist), error('Only numerical labels are allowed in LSSVC.'); end
% Train binary LS-SVM
[m, k, c] = getsize(A); % size of the training set
if length(A.lablist) <= 2
if strcmp(data.kernel, 'poly_kernel')
[alpha, b] = trainlssvm({A.data, A.labels, 'classification', data.gamma, [data.par2; data.par], data.kernel});
else
[alpha, b] = trainlssvm({A.data, A.labels, 'classification', data.gamma, data.par, data.kernel});
end
% Train multi-class LS-SVM
else
[labels_code, codebook, old_codebook] = code(A.labels, 'code_MOC');
if strcmp(data.kernel, 'poly_kernel')
[alpha, b] = trainlssvm({A.data, labels_code, 'classification', data.gamma, [data.par2; data.par], data.kernel});
else
[alpha, b] = trainlssvm({A.data, labels_code, 'classification', data.gamma, data.par, data.kernel});
end
end
% Store results of training in data-struct
data.A = A;
data.alpha = alpha;
data.b = b;
if length(A.lablist) > 2
data.labels_code = labels_code;
data.codebook = codebook;
data.old_codebook = old_codebook;
end
W = prmapping('lssvc', 'trained', data, getlablist(A), k, c);
W = setname(W, name);
% Apply LS-SVM mapping B on dataset A
elseif nargin == 2 && isa(TYPE, 'prmapping')
% Initialize some variables
B = TYPE;
[m, k] = getsize(A); % size of the test set
[k, c] = size(B); % K features with C classes
W = zeros(m, c); % output: C class densities for M objects
% Perform binary classification
if length(B.data.A.lablist) <= 2
if strcmp(B.data.kernel, 'poly_kernel')
C = simlssvm({B.data.A.data, B.data.A.labels, 'classification', B.data.gamma, [B.data.par2; B.data.par], B.data.kernel, 'preprocess'}, ...
{B.data.alpha, B.data.b}, A.data);
else
C = simlssvm({B.data.A.data, B.data.A.labels, 'classification', B.data.gamma, B.data.par, B.data.kernel, 'preprocess'}, ...
{B.data.alpha, B.data.b}, A.data);
end
% Perform multi-class classification (only numerical labels!)
else
if strcmp(B.data.kernel, 'poly_kernel')
C = simlssvm({B.data.A.data, B.data.labels_code, 'classification', B.data.gamma, [B.data.par2; B.data.par], B.data.kernel, 'preprocess'}, ...
{B.data.alpha, B.data.b}, A.data);
else
C = simlssvm({B.data.A.data, B.data.labels_code, 'classification', B.data.gamma, B.data.par, B.data.kernel, 'preprocess'}, ...
{B.data.alpha, B.data.b}, A.data);
end
C = code(C, B.data.old_codebook, [], B.data.codebook, 'codedist_hamming');
end
% Make sure all labels are numbered in the same way as in A
for i=1:length(C)
[tf, loc] = ismember(B.data.A.lablist, C(i));
W(i, find(loc)) = 1;
end
% Return new labeled dataset
W = setdat(A, W, B);
% Should not happen
else
error('Illegal call.');
end