gaussmix.m

matlab的一个第三方语音信号处理工具箱

        ii=1:jx;
        kk=repmat(ii,k,1);
        km=repmat(1:k,1,jx);
        py=reshape(sum((xs(kk(:),:)-m(km(:),:)).^2.*vi(km(:),:),2),k,jx)+lvm(:,wnj);
        mx=max(py,[],1);                % find normalizing factor for each data point to prevent underflow when using exp()
        px=exp(py-mx(wk,:));            % find normalized probability of each mixture for each datapoint
        ps=sum(px,1);                   % total normalized likelihood of each data point
        px=px./ps(wk,:);                % relative mixture probabilities for each data point (columns sum to 1)
        lpx(ii)=log(ps)+mx;
        pk=sum(px,2);                   % effective number of data points for each mixture (could be zero due to underflow)
        sx=px*xs(ii,:);
        sx2=px*xs2(ii,:);

        for il=2:nl
            ix=jx+1;
            jx=jx+nb;                    % increment upper limit
            ii=ix:jx;
            kk=repmat(ii,k,1);
            py=reshape(sum((xs(kk(:),:)-m(im,:)).^2.*vi(im,:),2),k,nb)+lvm(:,wnb);
            mx=max(py,[],1);                % find normalizing factor for each data point to prevent underflow when using exp()
            px=exp(py-mx(wk,:));            % find normalized probability of each mixture for each datapoint
            ps=sum(px,1);                   % total normalized likelihood of each data point
            px=px./ps(wk,:);                % relative mixture probabilities for each data point (columns sum to 1)
            lpx(ii)=log(ps)+mx;
            pk=pk+sum(px,2);                   % effective number of data points for each mixture (could be zero due to underflow)
            sx=sx+px*xs(ii,:);
            sx2=sx2+px*xs2(ii,:);
        end
        g=sum(lpx);                    % total log probability summed over all data points
        gg(j)=g;
        w=pk/n;                         % normalize to get the weights
        if pk                       % if all elements of pk are non-zero
            m=sx./pk(:,wp);
            v=sx2./pk(:,wp);
        else
            wm=pk==0;                       % mask indicating mixtures with zero weights
            [vv,mk]=sort(lpx);             % find the lowest probability data points
            m=zeros(k,p);                   % initialize means and variances to zero (variances are floored later)
            v=m;
            m(wm,:)=xs(mk(1:sum(wm)),:);                % set zero-weight mixture means to worst-fitted data points
            wm=~wm;                         % mask for non-zero weights
            m(wm,:)=sx(wm,:)./pk(wm,wp);  % recalculate means and variances for mixtures with a non-zero weight
            v(wm,:)=sx2(wm,:)./pk(wm,wp);
        end
        v=max(v-m.^2,c);                % apply floor to variances

        if g-g1<=th && j>1
            if ~ss, break; end  %  stop
            ss=ss-1;       % stop next time
        end

    end
    if sd && ~fv  % we need to calculate the final probabilities
        pp=lpx'-0.5*p*log(2*pi)-lsx;   % log of total probability of each data point
        gg=gg(1:j)/n-0.5*p*log(2*pi)-lsx;    % average log prob at each iteration
        g=gg(end);
        %     gg' % *** DEBUG ***
        m=m1;       % back up to previous iteration
        v=v1;
        w=w1;
        mm=sum(m,1)/k;
        f=(m(:)'*m(:)-k*mm(:)'*mm(:))/sum(v(:));
    end
    if ~fv
        m=m.*sx0(ones(k,1),:)+mx0(ones(k,1),:);  % unscale means
        v=v.*repmat(sx0.^2,k,1);                % and variances
    else
        v1=v;
        v=zeros(p,p,k);
        mk=eye(p)==1;                                    % mask for diagonal elements
        v(repmat(mk,[1 1 k]))=v1';            % set from v1
    end
end
if fv              % check if full covariance matrices were requested
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    % Full Covariance matrices  %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    pl=p*(p+1)/2;
    lix=1:p^2;
    cix=repmat(1:p,p,1);
    rix=cix';
    lix(cix>rix)=[];                                        % index of lower triangular elements
    cix=cix(lix);                                           % index of lower triangular columns
    rix=rix(lix);                                           % index of lower triangular rows
    dix=find(rix==cix);
    lixi=zeros(p,p);
    lixi(lix)=1:pl;
    lixi=lixi';
    lixi(lix)=1:pl;                                        % reverse index to build full matrices
    v=reshape(v,p^2,k);
    v=v(lix,:)';                                            % lower triangular in rows

    % If data size is large then do calculations in chunks

    nb=min(n,max(1,floor(memsize/(24*p*k))));    % chunk size for testing data points
    nl=ceil(n/nb);                  % number of chunks
    jx0=n-(nl-1)*nb;                % size of first chunk
    %
    th=(l-floor(l))*n;
    sd=(nargout > 3*(l~=0)); % = 1 if we are outputting log likelihood values
    l=floor(l)+sd;   % extra loop needed to calculate final G value
    %
    lpx=zeros(1,n);             % log probability of each data point
    wk=ones(k,1);
    wp=ones(1,p);

    wpl=ones(1,pl);       % 1 index for lower triangular matrix
    wnb=ones(1,nb);
    wnj=ones(1,jx0);

    % EM loop

    g=0;                           % dummy initial value for comparison
    gg=zeros(l+1,1);
    ss=sd;                       % initialize stopping count (0 or 1)
    vi=zeros(p*k,p);                    % stack of k inverse cov matrices each size p*p
    vim=zeros(p*k,1);                   % stack of k vectors of the form inv(v)*m
    mtk=vim;                             % stack of k vectors of the form m
    lvm=zeros(k,1);
    wpk=repmat((1:p)',k,1);
    for j=1:l
        g1=g;                    % save previous log likelihood (2*pi factor omitted)
        m1=m;                       % save previous means, variances and weights
        v1=v;
        w1=w;

        for ik=1:k

            % these lines added for debugging only
            %             vk=reshape(v(k,lixi),p,p);
            %             condk(ik)=cond(vk);
            %%%%%%%%%%%%%%%%%%%%
            [uvk,dvk]=eig(reshape(v(ik,lixi),p,p));      % convert lower triangular to full and find eigenvalues
            dvk=max(diag(dvk),c);                           % apply variance floor to eigenvalues
            vik=-0.5*uvk*diag(dvk.^(-1))*uvk';   % calculate inverse
            vi((ik-1)*p+(1:p),:)=vik;           % vi contains all mixture inverses stacked on top of each other
            vim((ik-1)*p+(1:p))=vik*m(ik,:)';   % vim contains vi*m for all mixtures stacked on top of each other
            mtk((ik-1)*p+(1:p))=m(ik,:)';       % mtk contains all mixture means stacked on top of each other
            lvm(ik)=log(w(ik))-0.5*sum(log(dvk));       % vm contains the weighted sqrt of det(vi) for each mixture
        end
        %
        %         % first do partial chunk
        %
        jx=jx0;
        ii=1:jx;
        xii=xs(ii,:).';
        py=reshape(sum(reshape((vi*xii-vim(:,wnj)).*(xii(wpk,:)-mtk(:,wnj)),p,jx*k),1),k,jx)+lvm(:,wnj);
        mx=max(py,[],1);                % find normalizing factor for each data point to prevent underflow when using exp()
        px=exp(py-mx(wk,:));  % find normalized probability of each mixture for each datapoint
        ps=sum(px,1);                   % total normalized likelihood of each data point
        px=px./ps(wk,:);                % relative mixture probabilities for each data point (columns sum to 1)
        lpx(ii)=log(ps)+mx;
        pk=sum(px,2);                   % effective number of data points for each mixture (could be zero due to underflow)
        sx=px*xs(ii,:);
        sx2=px*(xs(ii,rix).*xs(ii,cix));            % accumulator for variance calculation (lower tri cov matrix as a row)

        for il=2:nl
            ix=jx+1;
            jx=jx+nb;        % increment upper limit
            ii=ix:jx;
            xii=xs(ii,:).';
            py=reshape(sum(reshape((vi*xii-vim(:,wnb)).*(xii(wpk,:)-mtk(:,wnb)),p,nb*k),1),k,nb)+lvm(:,wnb);
            mx=max(py,[],1);                % find normalizing factor for each data point to prevent underflow when using exp()
            px=exp(py-mx(wk,:));  % find normalized probability of each mixture for each datapoint
            ps=sum(px,1);                   % total normalized likelihood of each data point
            px=px./ps(wk,:);                % relative mixture probabilities for each data point (columns sum to 1)
            lpx(ii)=log(ps)+mx;
            pk=pk+sum(px,2);                % effective number of data points for each mixture (could be zero due to underflow)
            sx=sx+px*xs(ii,:);               % accumulator for mean calculation
            sx2=sx2+px*(xs(ii,rix).*xs(ii,cix));            % accumulator for variance calculation
        end
        g=sum(lpx);                    % total log probability summed over all data points
        gg(j)=g;                        % save convergence history
        w=pk/n;                         % normalize to get the column of weights
        if pk                       % if all elements of pk are non-zero
            m=sx./pk(:,wp);         % find mean and mean square
            v=sx2./pk(:,wpl);
        else
            wm=pk==0;                       % mask indicating mixtures with zero weights
            [vv,mk]=sort(lpx);             % find the lowest probability data points
            m=zeros(k,p);                   % initialize means and variances to zero (variances are floored later)
            v=zeros(k,pl);
            m(wm,:)=xs(mk(1:sum(wm)),:);                % set zero-weight mixture means to worst-fitted data points
            wm=~wm;                         % mask for non-zero weights
            m(wm,:)=sx(wm,:)./pk(wm,wp);  % recalculate means and variances for mixtures with a non-zero weight
            v(wm,:)=sx2(wm,:)./pk(wm,wpl);
        end
        v=v-m(:,cix).*m(:,rix);                 % subtract off mean squared
        if g-g1<=th && j>1
            if ~ss, break; end  %  stop
            ss=ss-1;       % stop next time
        end
    end
    if sd  % we need to calculate the final probabilities       
        pp=lpx'-0.5*p*log(2*pi)-lsx;   % log of total probability of each data point
        gg=gg(1:j)/n-0.5*p*log(2*pi)-lsx;    % average log prob at each iteration
        g=gg(end);
        %             gg' % *** DEBUG ONLY ***
        m=m1;       % back up to previous iteration
        v=zeros(p,p,k);
        trv=0;      % sum of variance matrix traces
        for ik=1:k
            [uvk,dvk]=eig(reshape(v1(ik,lixi),p,p));      % convert lower triangular to full and find eigenvectors
            dvk=max(diag(dvk),c);                       % apply variance floor
            v(:,:,ik)=uvk*diag(dvk)*uvk';          % reconstitute full matrix
            trv=trv+sum(dvk);
        end
        w=w1;
        mm=sum(m,1)/k;
        f=(m(:)'*m(:)-k*mm(:)'*mm(:))/trv;
    else
        v1=v;               % lower triangular form
        v=zeros(p,p,k);
        for ik=1:k
            [uvk,dvk,]=eig(reshape(v1(k,lixi),p,p));      % convert lower triangular to full and find eigenvectors
            dvk=max(diag(dvk),c);                       % apply variance floor
            v(:,:,ik)=uvk*diag(dvk)*uvk';          % reconstitute full matrix
        end
    end
    m=m.*sx0(ones(k,1),:)+mx0(ones(k,1),:);  % unscale means
    v=v.*repmat(sx0'*sx0,[1 1 k]);
end
if l==0         % suppress the first three output arguments if l==0
    m=g;
    v=f;
    w=pp;
end