function?mappedData?=?gda（datatrainDatatrainLabelnDimoptions）

%?GDA?Performs?Generalized?Discriminant?Analysis?a?non-linear?feature
%?dimensionality?reduction?technique.
%?
%?GDA?is?one?of?dimensionality?reduction?techniques?which?projects?a?data?
%?matrix?from?a?high-dimensional?space?into?a?low-dimensional?space?by?
%?maximizing?the?ratio?of?between-class?scatter?to?within-class?scatter.?
%?
%?
%?Inputs:
%???????data:???????????p-dimensional?matrix?containing?the?high-dimensional?data?to?be?projected
%???????????????????????p:??number?of?dimensions?in?high-dimensional?space
%
%???????trainData:??????pxn?matrix?containing?the?high-dimensional?training?data
%???????????????????????n:??number?of?training?samples
%?
%???????trainLabel:?????Row?vector?of?length?n?containing?the?class?labels?for?training?data
%?
%???????nDim:???????????Numer?of?dimensions?to?be?retained?（nDim?%???????????????????????Default:????c-1
%???????????????????????c:??number?of?classes
%?
%???????options:????????Please?see?the?kernel?function?（kernel.m）.
%?????????
%?
%?Output:
%???????mappedData:??????nDim-dimensional?projected?data?matrix
%?
%?
%?Sample?use:
%?trainGda??=??gda（trainDatatrainDatatrainLabel）;?????%?Project?the?training?data?matrix?into?a?low-dimensional?space
%?testGda??=??gda（testDatatrainDatatrainLabel）;???????%?Project?the?test?data?matrix?into?a?low-dimensional?space
%?
%?
%?
%???Details?can?be?found?in?Section?4.3?of:
%???
%???M.?Haghighat?S.?Zonouz?M.?Abdel-Mottaleb?“CloudID:?Trustworthy?
%???cloud-based?and?cross-enterprise?biometric?identification“?
%???Expert?Systems?with?Applications?vol.?42?no.?21?pp.?7905-7916?2015.
%?
%?
%?
%?（C）	Mohammad?Haghighat?University?of?Miami
%???????haghighat@ieee.org
%???????PLEASE?CITE?THE?ABOVE?PAPER?IF?YOU?USE?THIS?CODE.
%?
%?Thanks?to?Dr.?Saeed?Meshgini?for?his?helps.



if（size（data1）?~=?size（trainData1））
???error（‘DATA?and?TRAINDATA?must?be?in?the?same?space?with?equal?dimensions.‘）;
end

if（size（trainData2）?~=?size（trainLabel2））
???error（‘The?length?of?the?TRAINLABEL?must?be?equal?to?the?number?of?columns?in?TRAINDATA.‘）;
end

if?（~exist（‘options‘‘var‘））
???options.KernelType=‘linear‘;
end


%?Separate?samples?of?each?class?in?a?cell?array

c?=?max（trainLabel）;
dataCell?=?cell（1c）;
nSample?=?zeros（1c）;
for?i?=?1:c
????ind?=?find（trainLabel==i）;
????nSample（i）?=?length（ind）;
????dataCell{1i}?=?trainData（:ind）;
end
clear?trainLabel


%?Create?class-specific?kernel?for?the?training?data

kTrainCell?=?cell（cc）;
for?p?=?1:c
????for?q?=?1:c
????????Kpq?=?zeros（nSample（p）nSample（q））;
????????classP?=?dataCell{1p};
????????classQ?=?dataCell{1q};
????????for?i?=?1:nSample（p）
????????????for?j?=?1:nSample（q）
????????????????Kpq（ij）?=?kernel（classP（:i）classQ（:j）options）;
????????????end
????????end
????????kTrainCell{pq}?=?Kpq;
????end
end
kTrain?=?cell2mat（kTrainCell）;
clear?kTrainCell

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2015-08-21?15:55??mhaghighat-Generalized_Discriminant_Analysis-a447238\
?????文件????????1289??2015-08-21?15:55??mhaghighat-Generalized_Discriminant_Analysis-a447238\LICENSE.md
?????文件?????????780??2015-08-21?15:55??mhaghighat-Generalized_Discriminant_Analysis-a447238\README.md
?????文件????????5784??2015-08-21?15:55??mhaghighat-Generalized_Discriminant_Analysis-a447238\gda.m
?????文件????????6038??2015-08-21?15:55??mhaghighat-Generalized_Discriminant_Analysis-a447238\kernel.m