FindSubNetwork.m

function [XNext, YNext,Obj]= FindSubNetwork_bi1(beta,SPMatrix)
    [n1,n2]=size(SPMatrix);
    IterMax=1000;
    Epsilon=0.0001;
    Threshold=1e-8;
    p=50000;
    Iter=1;        %The number of the iterative
    %X0=ones(n,1)*(1/n);
    for i=1:1
    X0=sparse(rand(1,n1));
    Y0=sparse(rand(1,n2));
    alpha= X0*SPMatrix*Y0'/beta;       % Langrange mulitiplier
    XPre= ( X0.*(Y0*SPMatrix')/(beta*alpha) ).^(1/beta);
    YPre= ( Y0.*(XPre*SPMatrix)/(beta*alpha) ).^(1/beta);
    Error=max(norm(XPre-X0,'fro')+norm(YPre-Y0,'fro'),10*Epsilon);
    YNext=YPre;
    while (Iter < IterMax ) && (Error > Epsilon)  
        alpha= XPre*SPMatrix*YPre'/beta;
        XNext= ( XPre.*(YPre*SPMatrix')/(beta*alpha) ).^(1/beta);
        YNext= ( YPre.*(XPre*SPMatrix)/(beta*alpha) ).^(1/beta);
        Error=norm(XNext-XPre,'fro')+norm(YNext-YPre,'fro');
        Iter=Iter+1;
        XPre=XNext;
        YPre=YNext;
        Obj=trace(XPre*SPMatrix*YPre');
    end 
    ObjValue(i,1)=Obj;
    XNextPool{1,i}=XNext;
    YNextPool{1,i}=YNext;
    end
    [d f]=max(ObjValue);
    XNext=XNextPool{1,f};
    YNext=YNextPool{1,f};