svcm_train.m

svm_increasement Matlab Program

        f = find(isnan(g));
        if any(f)
           fprintf('svcm_train error: g(%g) = %g\n', [f, g(f)]')
        end
        f = find(a>C);
        if any(f)
           fprintf('svcm_train error: a(%g) = %g > C\n', [f, a(f)]')
        end
        f = find(a<0);
        if any(f)
           fprintf('svcm_train error: a(%g) = %g < 0\n', [f, a(f)]')
        end
        f = inde(find(a(inde)>C|a(inde)<C));
        if any(f)
                fprintf('svcm_train error: a(%g) = %g ~= C\n', [f, a(f)]')
        end
        if abs(y'*a)>tol
                fprintf('svcm_train error: y''*a = %g ~= 0 (tol=%g)\n', y'*a, tol);
        end
        Rdiv = max(max(abs(Qss*R-diag(ones(ls+1,1)))));
        if Rdiv>tol
            if flag==2|flag==4    % support vector added
                fprintf('svcm_train error: divergence %g in R expansion (tol=%g; pivot=%g)\n',...
                         Rdiv, tol, pivot);
            elseif flag==3        % support vector removed
                fprintf('svcm_train error: divergence %g in R contraction (tol=%g)\n', Rdiv, tol);
            else                  % no support vector added or removed; strange...
                fprintf('svcm_train error: divergence %g in R ?  (tol=%g)\n', Rdiv, tol);
            end
        end
        if keepe&keepr            % only check g when Qe and Qr are readily available
            greal = Qs'*[b;a(inds)]-(1+eps);
            if le>0
                greal = greal+Qe'*a(inde);
            end
            if lr>0
                greal = greal+Qr'*a(indr);
            end
            if max(abs(greal-g))>tol
                fprintf('svcm_train error: tolerance (tol=%g) exceeded in computation of g\n', tol);
            end
        end
        f = inds(find(abs(g(inds))>tol));
        if any(f)
            fprintf('svcm_train error: g(%g) = %g ~= 0 (tol=%g)\n', [f, g(f), f*0+tol]');
        end
        f = inde(find(g(inde)>tol));
        if any(f)
            fprintf('svcm_train error: g(%g) = %g > 0 (tol=%g)\n', [f, g(f), f*0+tol]');
        end
        Wreal = 0.5*sum((g-b*y-1-eps).*a);        % energy
        if abs(Wreal-W)>tol*abs(W)
            fprintf('svcm_train error: energy W = %g ~= %g (tol=%g)\n', W, Wreal, tol);
        end
        inda = sort([indo;inds;inde]);
        if any(inda~=(1:L)')
            fprintf('svcm_train error: union [indo;inds;inde] does not equate entire set\n');
        end
        if ls~=length(inds)
            fprintf('svcm_train error: miscount in number of support vectors\n');
        end
        if le~=length(inde)
            fprintf('svcm_train error: miscount in number of error vectors\n');
        end
        if lo~=length(indo)
            fprintf('svcm_train error: miscount in number of other vectors\n');
        end
    end

    memcount = max(memcount,ls+keepe*le+keepr*lr+~(keepe&keepr));        % kernel storage

    if verbose
        fprintf('    c: %g (#%g)', y(indc)>0, indc)
        if leaveoneout
            fprintf(', margin: %6.3g, gamma: %6.3g', g(indc)+1, gammac)
        end
        fprintf(' | s: ')
        fprintf('%g', y(inds)>0)
        if ls<6
            fprintf(' (')
            fprintf('#%g', inds)
            fprintf(')')
        end
        fprintf(' | e: 0:%g, 1:%g\n', sum(y(inde)<0), sum(y(inde)>0))
    end

    if converged                        % indc finished; report
        if ~training & ~leaveoneout     % retraining or tracing back; uninteresting
            % nothing
        elseif ~terse & ~leaveoneout
            fprintf('  iteration %3g: %3g support vectors; %3g error vectors;  energy %g\n', ...
                iter, ls, le, W)
        elseif ~terse % & leaveoneout
            fprintf('  iteration %3g: %3g leave-one-out errors', iter, lw)
            fprintf(' (# %g: margin %g)\n', indc, g(indc)+1)
        elseif ~leaveoneout % & terse
            if ls+le>la
                fprintf('+')
            elseif ls+le<la
                fprintf('-')
            else
                fprintf('=')
            end
        else % leaveoneout & terse
            if g(indc)<-1
                fprintf('x')
            else
                fprintf('o')
            end
        end
    la = ls+le;
    end

    % prepare for next iteration, if any
    indoc = indo(find(indo~=indco));       % indo other than indco (leave-one-out index, if active)
    free = a(indoc)>0|g(indoc)<0;          % candidate support/error vectors in indoc
    if any(free)
        left = indoc(free);                % candidates left, keep (re-)training
        leaveoneout = 0;                   % interrupt leave-one-out, if active
    else % ~any(free)                      % done; finish up and (re-)initiate leave-one-out
        if training                        % first time around (not re-training)
            % print out results of svm training
            if terse
                fprintf('\n\n  %g support vectors; %g error vectors; energy %g\n\n', ...
                                 ls, le, W)
            else
                fprintf('\n%4g epoch kernel evaluations (%3g%% of run-time)\n',...
                        kernelcount, round(kernelcount/(ls+le)*100))
                fprintf(  '%4g epoch vectors in memory  (%3g%% of data)\n\n',...
                        memcount, round(memcount/(N+1)*100))
            end
            if visualize

                % plot a trajectory
                figure(2)  
                h=image(atraj/C*length(gray));
                h2=get(h,'Parent');
                set(h2,'YDir','normal')     % 'image' normally reverts the y axis
                colormap(1-gray)
                xlabel('Iteration')
                ylabel('Coefficients \alpha_{\it{i}}')
                print -deps atraj.eps

                % plot g trajectory
                figure(3)
                gmax = max(max(abs(gtraj)));
                h=image((gtraj/gmax+1)/2*length(gray));
                h2=get(h,'Parent');
                set(h2,'YDir','normal')     % 'image' normally reverts the y axis
                grey = gray;                            
                redblue = min(grey,1-grey);             
                redblue(:,1) = redblue(:,1)+1-grey(:,1);
                redblue(:,2) = 2*redblue(:,2);          
                redblue(:,3) = redblue(:,3)+grey(:,3);  
                colormap(redblue)
                xlabel('Iteration')
                ylabel('Coefficients {\it{g}_{\it{i}}}')
                print -deps gtraj.eps

                save traj atraj gtraj ctraj
            end
            if debug                        % store final result to compare with retraining later
                afinal = a;
                gfinal = g;
                Wfinal = W;
            end

            % initiate first leave-one-out
            leaveoneout = 1;
            indl = [inds;inde];             % support and error vectors (others already correct)
            indw = indl(g(indl)<-1);        % leave-one-out errors so far (g<-1) ...
            lw = length(indw);              % ... their number
            indl = indl(g(indl)>=-1);       % remove errors so far from leave-one-out stack
            indco = indl(length(indl));     % pick first leave-one-out index; top of stack ...
            left = indco;                   % ... and let indc=indco (untrain; upc=0)

            training = 0;                   % don't ever visit again!
        elseif ~leaveoneout                 % retrained or traced back
            if debug&~any(find(indo==indco))
                % traced back; compare with previously trained results
                if max(abs(a-afinal))>tol
                        fprintf('svcm_train error: final coeffs. a exceed tolerance (tol=%g)\n', tol);
                end
                if max(abs(g-gfinal))>tol
                        fprintf('svcm_train error: final derivatives g exceed tolerance (tol=%g)\n', tol);
                end
                if abs(W-Wfinal)>tol*abs(W)
                        fprintf('svcm_train error: final energy W = %g ~= %g (tol=%g)\n', Wfinal, W, tol);
                end
            end
            if any(indl)
                indco = indl(length(indl)); % leave-one-out index; top of stack
                left = indco;
                leaveoneout = 1;
            else % ~any(indl)               % finished all leave-one-outs; summarize, and done!
                continued = 0;
                ltw = sum(g<-1);            % number of training errors
                if terse
                    fprintf('\n\n  %g leave-one-out errors;', lw)
                    fprintf(' %g training errors\n\n', ltw)
                else % ~terse
                    fprintf('\n%4g training points\n', L)
                    fprintf(  '%4g support/error vectors (%g/%g)\n', la, ls, le)
                    fprintf(  '%4g leave-one-out errors  (%3.1f%%)\n', lw, lw/L*100)
                    fprintf(  '%4g training errors       (%3.1f%%)\n', ltw, ltw/L*100)
                    fprintf('\n%4g epoch kernel evaluations (%3g%% of run-time)\n',...
                        kernelcount, round(kernelcount/(ls+le)*100))
                    fprintf(  '%4g epoch vectors in memory  (%3g%% of data)\n\n',...
                        memcount, round(memcount/(N+1)*100))
                end
                if visualize                % plot g trajectory
                    figure(1)
                    hold off
                    xlabel('\alpha_{\it{c}}')
                    ylabel('\it{g_c}')
                    axis([-0.1*C, 1.1*C, -1.2, 0.2])
                    h=line([0,0,C,C],[-1,0,0,-1]);
                    set(h,'Color',[0 0 0])
                    set(h,'LineStyle',':')
                    set(h,'LineWidth',[0.2])
                    h=line([0,C],[-1,-1]);
                    set(h,'Color',[0 0 0])
                    set(h,'LineStyle','--')
                    set(h,'LineWidth',[1.0])
                    print -deps gctraj.eps
                end
            end
            else % leaveoneout              % leave-one-out procedure
            if flag==1                      % finished leave-one-out, now trace back
                % note: already decremented indl and updated indw/lw above
                leaveoneout = 0;
                indco = 0;
            else                            % not done yet with leave-one-out ...
                left = indco;               % ... continue with indc=indco
            end
        end
    end
end