svr.m

SVR程序,直接用就可以了,没有错误,其中还有一些变量需再编程序算,如:MSE

function [nsv, beta, bias] = svr(X,Y,ker,kerOptions,C,loss,e)
%SVR Support Vector Regression
%
%  Usage: [nsv beta bias] = svr(X,Y,ker,kerOptions,C,loss,e)
%
%  Parameters: X          - Training inputs
%              Y          - Training targets
%              ker        - kernel function
%              kerOptions - kernel function
%              C          - upper bound (non-separable case)
%              loss       - loss function
%              e          - insensitivity
%              nsv        - number of support vectors
%              beta       - Difference of Lagrange Multipliers
%              bias       - bias term
%
%  Author: Steve Gunn ([e-mail])


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% check correct number of arguments
if (nargin < 3 | nargin > 7)
    help svr
    return
end

% fprintf('Support Vector Regressing ....\n')
% fprintf('______________________________\n')
n = size(X,1);
if (nargin<6)
    e = 0.0;
end

if (nargin<5)
    loss='eInsensitive';
end

if (nargin<4)
    C = Inf;
end

if (nargin<3)
    ker='linear';
end

% tolerance for support vector detection
epsilon = svtol(C);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% construct the kernel matrix

% fprintf('Constructing ...\n');
H = zeros(n,n);
for i=1:n
    for j=1:n
        H(i,j) = svkernel(ker,kerOptions,X(i,:),X(j,:));
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% set up the parameters for the optimization problem
switch lower(loss)
    case 'einsensitive',
        Hb = [H -H; -H H];
        c  = [ (e*ones(n,1) - Y) ;
            (e*ones(n,1) + Y) ];

        vlb = zeros(2*n,1);  % set the bounds: alphas >= 0
        vub = C*ones(2*n,1); %                 alphas <= C
        x0  = zeros(2*n,1);  % the starting point is [0 0 0 ... 0]
        
        neqcstr = nobias(ker); % set the number of equality constraints (1 or 0)
        if neqcstr
            A = [ones(1,n) -ones(1,n)];
            b = 0; % set the constraint Ax = b
        else
            A = [];
            b = [];
        end
        
    case 'quadratic',
        Hb = H + eye(n)/(2*C);
        c  = -Y;
        
        vlb = -1e30*ones(n,1);
        vub = 1e30*ones(n,1);
        x0  = zeros(n,1); % the starting point is [0 0 0   0]
        
        neqcstr = nobias(ker); % set the number of equality constraints (1 or 0)
        if neqcstr
            A = ones(1,n);
            b = 0; % set the constraint Ax = b
        else
            A = [];
            b = [];
        end
        
    otherwise
        disp('Error: Unknown Loss Function\n');
        
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Add small amount of zero order regularisation to avoid problems when Hessian
% is badly conditioned. Rank is always less than or equal to n. Note that adding
% to much reg will peturb solution

Hb = Hb + 1e-10*eye(size(Hb));

% solve the optimisation problem

% fprintf('Optimizing ...\n');
st = cputime;

[alpha lambda how] = gunnqp(Hb, c, A, b, vlb, vub, x0, neqcstr);

% fprintf('Execution time : %4.1f seconds\n',cputime - st);
% fprintf('Status : %s\n',how);

switch lower(loss)
    case 'einsensitive',
        beta =  alpha(1:n) - alpha(n+1:2*n);
        
    case 'quadratic',
        beta = alpha;
end

% fprintf('|w0|^2    : %f\n',beta'*H*beta);
% fprintf('Sum beta : %f\n',sum(beta));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute the number of support vectors
svi = find( abs(beta) > epsilon );
nsv = length( svi );

% fprintf('Support Vectors : %d (%3.1f%%)\n',nsv,100*nsv/n);

% implicit bias, b0
bias = 0;

% Explicit bias, b0
if nobias(ker) ~= 0
    
    switch lower(loss)
        case 'einsensitive',
            % find bias from average of support vectors with interpolation
            % error. SVs with interpolation error e have alphas: 0 < alpha < C
            svii = find( abs(beta) > epsilon & abs(beta) < (C - epsilon));
            
            if length(svii) > 0
                bias = (1/length(svii))*sum(Y(svii) - e*sign(beta(svii)) - H(svii,svi)*beta(svi));
            else
                fprintf('No support vectors with interpolation error e - cannot compute bias.\n');
                bias = (max(Y)+min(Y))/2;
            end
            
        case 'quadratic',
            bias = mean(Y - H*beta);
    end
    
end