function result=mona(x,banner)
%MONA returns clusters according to mona (monothetic
%clustering)
%
%The algorithm is fully described in:
% Kaufman, L. and Rousseeuw, P.J. (1990),
% "Finding groups in data: An introduction to cluster analysis",
% Wiley-Interscience: New York (Series in Applied Probability and
% Statistics), ISBN 0-471-87876-6.
%
% Required input argument:
% x : Data matrix (rows = observations, columns = variables)
% containing only binary values.
% The missing values are indicated by the value 2
%
% Optional input argument:
% banner : draws picture
% Possible values are 0 : do not create a banner
% 1 : create a banner
% (in case banner is not given, banner = 0)
% I/O:
% result=mona(x,1)
%
% Example (subtracted from the referenced book)
% load animal.mat
% result=mona(animal,1);
%
% The output of MONA is a structure containing
% result.matrix : revised matrix xx (contains only 0 and 1 and missing
% values are estimated)
% result.number : number of observations
% result.var : number of variables
% result.ner : order of objects
% result.lava : variable used for separation
% result.nban : seperation step
% (The value on the ith index is the stepnumber from
% the seperation of the elements with index 1 to i
% from the elements with index i+1 to result.number)
% If it equals zero, then there was no separation
%
% And MONA will create the plot banner if banner equals 1.
%
% This function is part of LIBRA: the Matlab Library for Robust Analysis,
% available at:
% http://wis.kuleuven.be/stat/robust.html
%
% Written by Wai Yan Kong (May 2006)
resl=[];
% Check whether the number of input is correct
if (nargin<1)
error('One input argument required (datamatrix)')
elseif (nargin<2)
banner=0;
elseif (nargin>2)
error('Too many input arguments')
end
% Define number of observations and variables
S=size(x);
S1=S(1);
S2=S(2);
resl.number=S(1);
resl.var=S(2);
% Check whether x is a matrix containing only binary values
% and whether x has missing values
% We make a revised matrix xx
missing=zeros(1,S2);
for j = 1:S2
for i= 1:S1
if (x(i,j)==0 | x(i,j)==1)
missing(j)=missing(j);
xx(i,j)=x(i,j);
elseif (x(i,j)==2)
missing(j)=missing(j)+1;
for k=1:S2
a=0;
b=0;
c=0;
d=0;
if k~=j
if x(i,k) ~= 2
for t=1:S1
if (x(t,j)==1 & x(t,k)==1)
a=a+1;
elseif (x(t,j)==1 & x(t,k)==0)
b=b+1;
elseif (x(t,j)==0 & x(t,k)==1)
c=c+1;
elseif (x(t,j)==0 & x(t,k)==0)
d=d+1;
end
end
end
end
association(k)=abs(a*d-b*c);
resinbetween(k)=a*d-b*c;
[C,I]=max(association);
if resinbetween(I)>0
xx(i,j)=x(i,I);
elseif resinbetween(I)<0
xx(i,j)=1-x(i,I);
end
end
else
error('inputmatrix must have binary values or value 2 for missing values')
end
end
end
TotalMissing=sum(missing);
fprintf(1,'This inputmatrix has %d missing values\n',TotalMissing)
% Check situations where Mona is not applicable
One=0;
for j=1:S2
if missing(j)>=1
One=One+1;
end
end
if One==S2
error('each variable has at least one missing value')
end
for j=1:S2
if (missing(j)>= (S1/2))
fprintf(1,'Variable %d has %d missing values\n',j,missing(j))
error('The number of missing values for some variable equals or is more than half of the number of objects')
end
gelijk=0;
for s=1:S1-1
if xx(s,j)==xx(s+1,j)
gelijk=gelijk+1;
end
end
if gelijk==S1-1
fprintf(1,'Variable %d has identical values\n',j)
error('all values are identical for some variable')
end
end
% We make the rowvector kx by reading the revised matrix xx
% row by row
Lengte=S1*S2;
kx=zeros(1,Lengte);
for i = 1:S1
for j= 1:S2
kx((i-1)*S2+j) = xx(i,j);
end
end
% Actual calculations
[ner,lava,nban]=monac(resl.number,resl.var,kx);
% We want lava and nban to be vectors of length S1-1
lava2=zeros(1,S1-1);
nban2=zeros(1,S1-1);
for i = 1:S1-1
lava2(i) = lava(i+1);
nban2(i) = nban(i+1);
end
% Create a banner
if (banner==1)
whitebg([1 1 1]);
stepmax=max(nban2)+1;
Y=nban2;
Y(find(Y==0))=stepmax;
Y1=fliplr(Y);
barh(Y1,1)
title 'Banner of Mona'
xlabel('Separation Step')
XT=0:stepmax;
set(gca,'XTick',XT);
set(gca,'XTickLabel',XT);
axis([0,stepmax,0.5,S1-0.5])
ylabel('Objects')
La1=num2str(lava2);
La2=fliplr(La1);
for k=1:S1-1
La3(k)=La2(k+((k-1)*2));
end
for i=1:S1-1
if(Y1(i)<stepmax)
text(Y1(i)+0.3,i,La3(i))
end
end
YT=0.5:S1;
set(gca,'YTick',YT);
set(gca,'YTickLabel',fliplr(ner));
elseif ((banner~=0) & (banner~=1) & (nargin==2))
error('banner must equals 0 or 1')
end
% Putting things together
result = struct('Matrix',xx,'Observations',S1,'Variables',S2,...
'Objectorder',ner,'UsedVariable',lava2,'SeperationStep',nban2);