%?>?-------------------------
%?>?Support?Vector?Clustring??
%>?滕曉云2008.10
%?>?-------------------------
%?>?A?non-parametric?clustring?algorithm?based?on?support?vector?
%?>?approach.
%?>
%?>?Reference:?
%?>?A.Ben-HurD.HornH.T.Siegelmann?and?V.Vapnik.
%?>?Support?Vector?Clustring.
%?>
%?>?Parameters:
%?>?
%?>?example?-?integer?number?coding?the?wanted?Sample?set.
%?>?C?-?Defines?the?fraction?of?points?which?are?allowed
%?>?to?become?outliers.
%?>?（p?=?1/CN?where?N?is?the?the?total?sampels?number）.
%?>?q...each?q?value?is?a?different?width?of?the?gaussian?kernel.

clc;
clear;


%>?自己設置的參數?
example_set=5;
C=1;
q=1;
%?tem?=?rand（110）;
%?
%?Samples?=?[2+tem2+tem12+tem12+tem;2+tem12+tem2+tem12+tem];
%?
%?%?>?Plot
%?
%?
%?nof_samples?=?size（Samples2）;
%?classification?=?zeros（nof_samples1）;

%??Samples?from?a?given?example?set:?
tem?=?rand（15）;
Samples?=?[2+tem2+tem2+tem2+tem6+tem6+tem6+tem6+tem10+tem10+tem10+tem10+tem14+tem14+tem14+tem14+tem;2+tem6+tem10+tem14+tem2+tem6+tem10+tem14+tem2+tem6+tem10+tem14+tem2+tem6+tem10+tem14+tem];
nof_samples?=?size（Samples2）;
[attrN]?=?size（Samples）;
%??Preforms?Support?Vector?Clustering?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
%?>?Calculates?the?Kernel?Matrix?here?use?Gaussian?kernel
K?=?zeros（N）;

for?i?=?1:N
for?j?=?1:N
%?>?Calculate?the?Gaussian?Kernel?for?each?data?points‘?pair.
K（ij）?=?exp（-q?*?（Samples（:i）-Samples（:j））‘?*?（Samples（:i）-Samples（:j）））;
end
end

%?>?Finds?the?Lagrangian?multipliers?for?the?given??constrains%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A?=?ones（1N）;?
b?=?1;
low_bound?=?zeros（N1）;
up_bound?=?ones（N1）?*?C;
beta?=?quadprog（2*K?-diag（K）[][]?A?b?low_bound?up_bound）;?

%??>?Finds?the?support?vectors?and?outliers%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

BSV?=?zeros（attrN）;
SV?=?zeros（attrN）;
nof_BSV?=?0;
nof_SV?=?0;

for?i?=?1:N?

%?>?BSV?-?outliers?（?only?when?beta?equlas?C?-?the?upper?bound）
if?beta（i）?==?C;
nof_BSV?=?nof_BSV?+?1;?
BSV（:?nof_BSV）?=?Samples（:i）;

%?>?SV?-?beta?is?between?0?and?C
elseif?beta（i）?>?1e-6?
%?????>?epsilon
nof_SV?=?nof_SV?+?1;
SV（:nof_SV）?=?Samples（:i）;
end

end

%?>?Corrects?the?matrics?sizes
BSV?=?BSV（:?1:nof_BSV）;
SV?=?SV（:1:nof_SV）;

%?>?Calcultes?the?radius?of?the?sphere?and?the?quadratic?part?of?the?distance?equation?from?the?sphere‘s?center.?
distance?=?zeros（nof_SV1）;?
quad?=?0;
for?i?=?1:N
for?j?=?1:N
quad?=?quad?+?beta（i）?*?beta（j）?*?K（ij）;
end
end

for?i?=?1:nof_SV
????
k?=?zeros（N1）;
for?j?=?1:N
k（j）?=?exp（-q?*?（Samples（:j）-SV（:i））‘?*?（Samples（:j）-SV（:i）））;
end

kdiag?=?1;???%%%%%其實都是exp（-q?*?（SV（:i）-SV（:i））‘?*?（SV（:i）-SV（:i）））;
distance（i）?=?kdiag?-?2*beta‘*k?+?quad;

end?

R?=?max（distance）;
%?Finds?the?clusters?assignments%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
adjacent?=?