function [AlphaY, SVs, Bias, Parameters, nSV, nLabel] = mexSVMTrain(Samples, Labels, Parameters, Weight, Verbose)
% Usages:
% [AlphaY, SVs, Bias, Parameters, nSV, nLabel] = mexSVMTrain(Samples, Labels)
% [AlphaY, SVs, Bias, Parameters, nSV, nLabel] = mexSVMTrain(Samples, Labels, Parameters)
% [AlphaY, SVs, Bias, Parameters, nSV, nLabel] = mexSVMTrain(Samples, Labels, Parameters, Weight)
% [AlphaY, SVs, Bias, Parameters, nSV, nLabel] = mexSVMTrain(Samples, Labels, Parameters, Weight, Verbose)
%
% Construct a SVM, either classifier or regressioner, based on Dr. Chih-Jen's LIBSVM algorithm (version 2.33).
% It is able to deal with both 2-class and multi-class problem when used in classification.
% When it is used to deal with multiclass problem, 1-1, or pairwise, multi-class
% scheme is used to reduce the multiclass problem to L(L-1)/2 2-class problems, where L is number of
% classes involved.
%
%  please refer to http://www.csie.ntu.edu.tw/~cjlin/libsvm for more information
%
% Inputs:
%    Samples    - training samples, MxN, (a row of column vectors);
%    Labels     - labels of training samples, 1xN, (a row vector);
%    Parameters - the paramters required by the training algorithm (a <=11-element row vector);
%     +------------------------------------------------------------------
%     |Kernel Type| Degree | Gamma | Coefficient | C |Cache size|epsilon| 
%     +------------------------------------------------------------------
%       ----------------------------------------------+
%       | SVM type | nu | loss toleration | shrinking |
%       ----------------------------------------------+
%            where Kernel Type: (default: 2) 
%                     0 --- Linear
%                     1 --- Polynomial: (Gamma*<X(:,i),X(:,j)>+Coefficient)^Degree
%                     2 --- RBF: (exp(-Gamma*|X(:,i)-X(:,j)|^2)) 
%                     3 --- Sigmoid: tanh(Gamma*<X(:,i),X(:,j)>+Coefficient)
%                  Degree: default 3
%                  Gamma: If the input value is zero, Gamma will be set defautly as
%                         1/(max_pattern_dimension) in the function. If the input
%                         value is non-zero, Gamma will remain unchanged in the 
%                         function. (default: 1)
%                  Coefficient: default 0
%                  C: Cost of constrain violation for C-SVC, epsilon-SVR, and nu-SVR (default 1)
%                  Cache Size: Space to hold the elements of K(<X(:,i),X(:,j)>) matrix (default 40MB)
%                  epsilon: tolerance of termination criterion (default: 0.001)
%                  SVM Type: (default: 0)
%                     0 --- c-SVC 
%                     1 --- nu-SVC
%                     2 --- one-class SVM
%                     3 --- epsilon-SVR 
%                     4 --- nu-SVR
%                  nu: nu of nu-SVC, one-class SVM, and nu-SVR (default: 0.5)
%                  loss tolerance: epsilon in loss function of epsilon-SVR (default: 0.1)
%                  shrinking: whether to use the shrinking heuristics, 0 or 1 (default: 1)
%    Weight     - a row vector or scalar, C of class i is weight(i)*C in C-SVC (default: all 1's);
%    Verbose    - verbose level (default: 0).
%                    0 --- very silent 
%                    1 --- a little verbose
%
% Outputs:  
%    AlphaY    - Alpha * Y, where Alpha is the non-zero Lagrange Coefficients, and
%                    Y is the corresponding Labels, (L-1) x sum(nSV);
%                All the AlphaYs are organized as follows: (pretty fuzzy !)
%      				classifier between class i and j: coefficients with
%			  	         i are in AlphaY(j-1, start_Pos_of_i:(start_Pos_of_i+1)-1),
%				         j are in AlphaY(i, start_Pos_of_j:(start_Pos_of_j+1)-1)
%    SVs       - Support Vectors. (Sample corresponding the non-zero Alpha), M x sum(nSV),
%                All the SVs are stored in the format as follows:
%                 [SVs from Class 1, SVs from Class 2, ... SVs from Class L];
%    Bias      - Bias of all the 2-class classifier(s), 1 x L*(L-1)/2;
%    Parameters -  Output parameters used in training;
%    nSV       -  numbers of SVs in each class, 1xL;
%    nLabel    -  Labels of each class, 1xL.
%
% By Junshui Ma, and Yi Zhao (02/15/2002)
%