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Highlights from
Recognizing Far-Near Relations of Clusters by GDEM, Visualization by Line-Pearl Pattern

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from Recognizing Far-Near Relations of Clusters by GDEM, Visualization by Line-Pearl Pattern by Kaijun Wang
measure far-near degrees (distances) between clusters & dense degrees of border regions of clusters

test_regionsize.m 
function [traA1,layA1,traB1,layB1,A1,B1] = test_regionsize(data,type,Dist,A1,A2,A1h,A2h,B1,B2,B1h,B2h)
% computing propagation distances in region A1 & B1
% testing dense or sparse with t-test & Mann-Whitney test

alpha1 = 0.05;
alpha2 = 0.05;
tail1 = 'left';  % alternative hypotheses: x<y
tail2 = 'right'; % alternative hypotheses: x>y
k = 5;

% prepare data
[traA1, Ra1] = propag_intra(Dist,A1,A1(1));
[layA1, Ra2] = propag_center(data,Dist,A1,B1,type);

if ~isempty(A2)
[traA2, Rb1] = propag_intra(Dist,A2,A2(1));
[layA2, Rb2] = propag_center(data,Dist,A2,A1,type);
X = [Ra1 Ra2];
Y = [Rb1 Rb2];

% test if x>y
[h1,stats] = bitest(X,Y,alpha1,alpha1,tail2);

if h1
  if ~isempty(A1h)
    A1f = setdiff(A1,A1h);
    Q = border_points(Dist,A1f,B1,1);
    [traA3, Rc1] = propag_intra(Dist,A1f,Q);
    [layA3, Rc2] = propag_center(data,Dist,A1f,B1,type);
    X = [Rc1 Rc2];
    [traA4, Rd1] = propag_intra(Dist,A1h,A1h(1));
    [layA4, Rd2] = propag_center(data,Dist,A1h,B1,type);
    Y = [Rd1 Rd2];
    
    % test if x<y
    [h1,stats] = bitest(X,Y,alpha1,alpha1,tail1);
    if h1      % reduce A1
        A1 = A1h; traA1 = traA4; layA1 = layA4;
    end
  end
else
    % test if kx<y. A tighter condition for enlargement
    [h1,stats] = bitest(k*X,Y,alpha1,alpha2,tail1);
    if h1      % enlarge A1
        if isempty(A2h)
            A1 = [A1; A2];
        else
            A1 = [A1; A2h];
        end
        [traA1, Ra1] = propag_intra(Dist,A1,A1(1));
        [layA1, Ra2] = propag_center(data,Dist,A1,B1,type);
    end
end

end


% prepare data
[traB1, Ra1] = propag_intra(Dist,B1,B1(1));
[layB1, Ra2] = propag_center(data,Dist,B1,A1,type);
if isempty(B2)
    return
end
[traB2, Rb1] = propag_intra(Dist,B2,B2(1));
[layB2, Rb2] = propag_center(data,Dist,B2,B1,type);
X = [Ra1 Ra2];
Y = [Rb1 Rb2];

% test if x>y
[h2,stats] = bitest(X,Y,alpha1,alpha1,tail2);

if h2
  if ~isempty(B1h)
    B1f = setdiff(B1,B1h);
    Q = border_points(Dist,B1f,A1,1);
    [traB3, Rc1] = propag_intra(Dist,B1f,Q);
    [layB3, Rc2] = propag_center(data,Dist,B1f,A1,type);
    X = [Rc1 Rc2];
    [traB4, Rd1] = propag_intra(Dist,B1h,B1h(1));
    [layB4, Rd2] = propag_center(data,Dist,B1h,A1,type);
    Y = [Rd1 Rd2];
    
    % test if x<y
    [h2,stats] = bitest(X,Y,alpha1,alpha1,tail1);
    if h2      % reduce B1
        B1 = B1h; traB1 = traB4; layB1 = layB4;
    end
  end
else
    % test if kx<y. A tighter condition for enlargement
    [h2,stats] = bitest(k*X,Y,alpha1,alpha2,tail1);
    if h2      % enlarge B1
        if isempty(B2h)
            B1 = [B1; B2];
        else
            B1 = [B1; B2h];
        end
        [traB1, Ra1] = propag_intra(Dist,B1,B1(1));
        [layB1, Ra2] = propag_center(data,Dist,B1,A1,type);
    end
end

function [h,stats] = bitest(X,Y,alpha1,alpha2,tail)
% H=1, reject hypothesis that X has a normal distribution at alpha1 level
[h1,p] = lillietest(X,alpha1); % Lilliefors test
h2 = 1;
if h1 == 0
    [h2,p] = lillietest(Y,alpha1);
end

if h1 == 0 && h2 == 0
% Assuming: two samples come from normal distr. with unknown unequal variances
% It uses Satterthwaite's approximation for the degrees of freedom.
    [h,p,ci,stats] = ttest2(X,Y,alpha2,tail,'unequal');
    stats.p=p;
    stats.ci=ci;
else
    [h, stats] = mannwtest(X,Y,alpha2,tail);
end

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