%?eigenface

clear?all
close?all
clc

%step?1:Get?some?data
num?=?20;
[height?width]?=?size（imread（‘data\1.pgm‘））;
Data（height*widthnum）?=?0;?%convert?one?image?data?into?a?column

for?i=1:num
????path?=?[‘data\‘num2str（i）‘.pgm‘];
????temp?=?imread（path）;
????temp?=?im2double（temp）;
????Data（:i）?=?reshape（temp?[]?1）;???%convert?one?image?data?into?a?column
end

%setp?2:Subtract?the?mean
MeanValue?=?mean（Data?2）;
OriginalMean?=?repmat（MeanValue1?size（Data2））;
DataAdjust?=?Data?-?OriginalMean;

%step?3:Calculate?the?covariance?matrix
%?注意這里的cov函數(shù)，如果傳入?yún)?shù)是矩陣，那么行代表了維度，也就是上面的x1x2x3xn。
%?所以，這里DataAdjust需要轉(zhuǎn)置一下。
%?Covariance?=?cov（DataAdjust‘）;
%?Covariance_2?=?（DataAdjust?*?DataAdjust‘）./（size（Data2）-1）;?%驗(yàn)證了A*A‘/（N-1）等于協(xié)方差矩陣

%step?4:calculate?the?eigenvectors?and?eigenvalues
%?[EigenVectors?EigenValues]?=?eig（Covariance）;?%返回值EigenValues按照從小到大排序的，所以，從靠后的列選擇主成分

%step?5:choosing?components?and?forming?a?feature?vector.
[row?col]?=?size（Data）;
if?row?>=?col
????length?=?col;
else
????length?=?row;
end
%?SortEigenVectors?=?fliplr（EigenVectors）;?%特征向量排序，第一列對(duì)應(yīng)的特征值最大，依次往后
%?FeatureVectors?=?SortEigenVectors（:1:length-1）;?%%select?part?the?EigenVectors?as?the?components?here?is?the?first?length-1?columns

%用另外一種方法得到FeatureVectors針對(duì)的是數(shù)據(jù)維數(shù)較大的情況這種方法更快
C1?=?DataAdjust‘?*?DataAdjust;
[C1_EigenVectors?C1_EigenValues]?=?eig（C1）;
V?=?DataAdjust?*?C1_EigenVectors;
%進(jìn)行歸一化?這一步在好多敘述里都沒(méi)有提及到
EigenVectors_2?=?V?./?（ones（size（V?1）1）?*?sqrt（sum（V?.*?V）））;
%選取pricipal?components
SortEigenVectors_2?=?fliplr（EigenVectors_2）;
FeatureVectors?=?SortEigenVectors_2（:1:length-1）;?

%選取一個(gè)特征向量進(jìn)行展示，即所謂的特征臉，目前一共有20-1=19個(gè)特征臉
%?EigenFace_1?=?reshape（FeatureVectors（:2）height?width）;
%?figure
%?imshow（EigenFace_1?[]）;

%圖像數(shù)據(jù)投影到特征空間上
PatternVectors?=?FeatureVectors‘?*?DataAdjust;?%每一列代表一幅圖像投影到n-1維的空間里。


%測(cè)試圖像
%將一張圖像映射到特贈(zèng)空間后得到的模式向量，也就是在n-1維上的各個(gè)投影
TestData?=?imread（‘D:\Matlab\3_eigenface\study\orl_faces\s20\2.pgm‘）;
temp?=?im2double（TestData）;
TestData?=?reshape（temp?[]?1）;
TestDataPatternVector?=?FeatureVectors‘?*?（TestData?-?MeanValue）;?
%利用歐氏距離進(jìn)行比較。
result（1?length）?=?0;
for?i=1:length
????temp?=?（PatternVectors（:i）?-?TestDataPatternVector）.^2;
????result（1i）?=?sqrt（sum（temp））;
end
[minimum?index]?=?min（result）;
X?=?[‘Match?the?s‘?num2str（index）?‘?successfully.??Congratulations!‘];
disp（X）

?屬性????????????大小?????日期????時(shí)間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2016-12-07?19:17??data\
?????文件???????10318??2016-12-07?16:01??data\1.pgm
?????文件???????10318??2016-12-07?16:01??data\10.pgm
?????文件???????10318??2016-12-07?16:01??data\11.pgm
?????文件???????10318??2016-12-07?16:01??data\12.pgm
?????文件???????10318??2016-12-07?16:01??data\13.pgm
?????文件???????10318??2016-12-07?16:01??data\14.pgm
?????文件???????10318??2016-12-07?16:01??data\15.pgm
?????文件???????10318??2016-12-07?16:01??data\16.pgm
?????文件???????10318??2016-12-07?16:01??data\17.pgm
?????文件???????10318??2016-12-07?16:01??data\18.pgm
?????文件???????10318??2016-12-07?16:01??data\19.pgm
?????文件???????10318??2016-12-07?16:01??data\2.pgm
?????文件???????10318??2016-12-07?16:01??data\20.pgm
?????文件???????10318??2016-12-07?16:01??data\3.pgm
?????文件???????10318??2016-12-07?16:01??data\4.pgm
?????文件???????10318??2016-12-07?16:01??data\5.pgm
?????文件???????10318??2016-12-07?16:01??data\6.pgm
?????文件???????10318??2016-12-07?16:01??data\7.pgm
?????文件???????10318??2016-12-07?16:01??data\8.pgm
?????文件???????10318??2016-12-07?16:01??data\9.pgm
?????文件????????2676??2016-12-15?16:02??main_4_1.m
?????文件????????2722??2016-12-16?21:09??main_4_2.m