人脸识别实验结论
1、关于MSE
背景：看过文章《SRDA: An Efficient Algorithm for Large Scale Discriminant Analysis》之后呢，总感觉这个SRDA在使用ridge回归时，其方程公式22和MSE（minimum square error）算法非常相似，所以专门将SRDA与MSE进行了比较。
先说说不同之处吧：SRDA中的投影向量 是利用LSQR一列一列来优化的， 而MSE呢，直接求解一个逆矩阵就可以了（X'*X+lambda*I）\X'*Y;（LSQR solves Ax = b or min ||b - Ax||_2 if damp = 0,）
SRDA给每个特征都添加了1，MSE没有；
SRDA中的类标列数为c-1，而MSE的类标列数为c；
SRDA中的识别过程为 测试预测类标 与 训练预测类标之间的欧式距离， 而 MSE一般用测试预测类标 与 真实类标的欧式距离
MSE的类标一般为，[1,0,0,0,0,0,], 而SRDA的类标为由一个随机矩阵的QR分解求得！！！
下面说说识别结果吧：
在用同样大小的lambda惩罚因子情况下，对于Isolet数据集，SRDA的识别率最好，其中SRDA_NCC_ridge: 10.88, SRDA_NN_ridge:10.88, SRDA_Laso(NN为10.49，NCC为10.84),
而原始MSE为14.95，换成都是预测类标值后为11.23，而将类标换成SRDA方法生成的类标且用预测类标之间的距离度量时为11.03
个人感觉，这个类标如SRDA这么定义没有必要，效果并不明显，不过可以试试吧！！！
另外，值得说明的是，在求解 AX=B的问题上，LSQR和原始MSE的（X'*X+lambda*I）\X'*Y;结果基本上一样
norm(MSE_projection-eigvector,'fro') ans = 6.6695e-04
这里，我们贴上我们测试过程中使用的主函数代码
% The main function of Cai deng
% http://www.cad.zju.edu.cn/home/dengcai/Data/ReproduceExp.html#SRDA
clc,clear;
clear all;
clear memory;
addpath('SLEP package');
addpath('data set');
%%----------- 这个主函数是专门调用论文中Isolet1等数据集而写 ----------%
fea_train = [];
gnd_train = [];
load Isolet1
fea_train = [fea_train;fea];
gnd_train = [gnd_train;gnd];
clear fea gnd
load Isolet2
fea_train = [fea_train;fea];
gnd_train = [gnd_train;gnd];
clear fea gnd
fea_test = [];
gnd_test = [];
load Isolet4
fea_test = [fea_test;fea];
gnd_test = [gnd_test;gnd];
clear fea gnd
load Isolet5
fea_test = [fea_test;fea];
gnd_test = [gnd_test;gnd];
clear fea gnd
sele_num = 20; % select training samples
% % ***************** PCA降维 *********************
% options = [];
% options.PCARatio = 0.98;
% [~,~,~,new_data] = PCA(fea,options);
% fea = new_data;
% % ***********************************************
nnClass = length(unique(gnd_train)); % The number of classes;
num_Class = [];
for i = 1:nnClass
num_Class = [num_Class length(find(gnd_train==i))]; % The number of samples of each class
end
Train_Ma = [];
Train_Lab = [];
Test_Ma = fea_test;
Test_Lab = gnd_test;
for j = 1:nnClass
idx = find(gnd_train==j);
% randIdx = 1:num_Class(j); % select the first sele_num training samples
randIdx=randperm(num_Class(j)); % radomly select the sele_num training samples
%--------------------------------------------------------------------
Train_Ma = [Train_Ma; fea_train(idx(randIdx(1:sele_num)),:)]; % Random select select_num samples per class for training
Train_Lab = [Train_Lab;gnd_train(idx(randIdx(1:sele_num)))];
end
Train_Ma = Train_Ma';
Train_Ma = Train_Ma./repmat(sqrt(sum(Train_Ma.^2)),[size(Train_Ma,1) 1]);
Test_Ma = Test_Ma';
Test_Ma = Test_Ma./repmat(sqrt(sum(Test_Ma.^2)),[size(Test_Ma,1) 1]);
%% ---------- Training SRDA with L2-regularization --------------%
tic;
options = [];
options.ReguType = 'Ridge';
options.ReguAlpha = 1; % 这个是L2 的约束项 ridge regression
model = SRDAtrain(Train_Ma',Train_Lab, options);
TimeTrain = toc;
tic;
%-------------Use nearest center classifer ------ %
accuracy = SRDApredict(Test_Ma', Test_Lab, model);
TimeTest = toc;
disp(['SRDA,',num2str(sele_num),' Training, Errorrate: ',num2str((1-accuracy)*100),' TrainTime: ',num2str(TimeTrain),' TestTime: ',num2str(TimeTest)]);
% -------- use NN to classify the samples -------------%
feaTrain = SRDAtest(Train_Ma', model);
feaTest = SRDAtest(Test_Ma', model);
D = EuDist2(feaTest,feaTrain,0);
[dump,idx] = min(D,[],2);
predictlabel = Train_Lab(idx);
errorrate = (length(find(predictlabel-Test_Lab))/length(Test_Lab))*100;
disp(['SRDA,',num2str(sele_num),' Train, NN Errorrate: ',num2str(errorrate)]);
%% Training SRDA with L1-regularization (use LARs), (Sparse LDA)
options = [];
options.ReguType = 'Lasso';
options.LASSOway = 'LARs';
options.ReguAlpha = 0.01;
options.LassoCardi = 50:10:200;
model_Lasso = SRDAtrain(Train_Ma',Train_Lab, options);
%-------------Use nearest center classifer ------ %
accuracy_Lasso = SRDApredict(Test_Ma', Test_Lab, model_Lasso);
for i = 1:length(model_Lasso.LassoCardi)
% disp(['Sparse SRDA,',num2str(sele_num),' Train, Cardi=',num2str(model_Lasso.LassoCardi(i)),' NC Errorrate: ',num2str((1-accuracy_Lasso(i))*100)]);
end
Lasso = min((1-accuracy_Lasso)*100);
% ----- Use nearest neighbor classifer ----- %
feaTrain = SRDAtest(Train_Ma', model_Lasso);
feaTest = SRDAtest(Test_Ma', model_Lasso);
for i = 1:length(model_Lasso.LassoCardi)
D = EuDist2(feaTest{i},feaTrain{i},0);
[dump,idx] = min(D,[],2);
predictlabel = Train_Lab(idx);
errorrate(i) = (length(find(predictlabel-Test_Lab))/length(Test_Lab))*100;
% disp(['Sparse SRDA,',num2str(sele_num),' Train, Cardi=',num2str(model_Lasso.LassoCardi(i)),' NN Errorrate: ',num2str(errorrate(i))]);
end
Lasso_NN = min(errorrate)
Lasso
% 因为感觉这个就跟MSE特别像 所以 试一下 MSE的识别率
addpath('G:\机器学习\代码和数据集\看论文编写代码\MSE');
lambda = 1;
[MSE_projection,Y_Class,Y] = MSE(Train_Ma',Train_Lab,lambda);
Predict_train = Train_Ma'*MSE_projection;
Predict_test = Test_Ma'*MSE_projection;
count = 0;
for i = 1:size(Test_Ma,2)
temp = Predict_test(i,:);
for j = 1:size(Y_Class,1)
res(j) = norm(temp-Y_Class(j,:));
end
[rr,dd] = min(res);
if dd == Test_Lab(i);
count = count + 1;
end
end
error_MSE = (1 - count/size(Test_Ma,2))*100
D = EuDist2(Predict_test,Predict_train,0);
[dump,idx] = min(D,[],2);
predictlabel_test = Train_Lab(idx);
errorrate_MSE = (length(find(predictlabel_test-Test_Lab))/length(Test_Lab))*100
% [MSE_projection2,Y2] = MSE_2(Train_Ma',Train_Lab,lambda);
% Train_Ma = [ones(1,size(Train_Ma,2));Train_Ma];
% Test_Ma = [ones(1,size(Test_Ma,2));Test_Ma];
% Predict_train2 = Train_Ma'*MSE_projection2;
% Predict_test2 = Test_Ma'*MSE_projection2;
% D = EuDist2(Predict_test2,Predict_train2,0);
% [dump,idx] = min(D,[],2);
% predictlabel_test2 = Train_Lab(idx);
% errorrate_MSE2 = (length(find(predictlabel_test2-Test_Lab))/length(Test_Lab))*100
%% --- 调用LSQR 来 求解 这个 Ax=b的问题
options.ReguAlpha = 1;
[eigvector, istop] = lsqr2(Train_Ma',Y, options.ReguAlpha, 20);
Predict_train_LSQR = Train_Ma'*eigvector;
Predict_test_LSQR = Test_Ma'*eigvector;
D = EuDist2(Predict_test_LSQR,Predict_train_LSQR,0);
[dump,idx] = min(D,[],2);
predictlabel_test = Train_Lab(idx);
errorrate_MSE_LSQR = (length(find(predictlabel_test-Test_Lab))/length(Test_Lab))*100
