rng(0,'twister'); % For reproducibility
N = 100;
X = rand(N,20);
y = -ones(N,1);
y(X(:,3).*X(:,9)./X(:,15) < 0.4) = 1;
mdl = fscnca(X,y,'Solver','sgd','Verbose',1);
figure()
plot(mdl.FeatureWeights,'ro')
grid on
xlabel('Feature index')
ylabel('Feature weight')
clear
load('twodimclassdata.mat');
figure()
gscatter(X(:,1),X(:,2),y)
xlabel('x1')
ylabel('x2')
n = size(X,1);
rng('default')
XwithBadFeatures = [X,randn(n,100)*sqrt(20)];
XwithBadFeatures=(XwithBadFeatures-min(XwithBadFeatures))./range(XwithBadFeatures,1);
X = XwithBadFeatures;
ncaMdl = fscnca(X,y,'FitMethod','exact','Verbose',1,...
'Solver','lbfgs');
% 'FitMethod','exact' 使用所有的数据进行拟合
% 'Verbose',1 信息显示
% 'Solver','lbfgs' 求解器的设置，'lbfgs' — Limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm
figure
semilogx(ncaMdl.FeatureWeights,'ro');
xlabel('Feature index');
ylabel('Feature weight');
grid on;
figure % 和上面的图作对比
plot(ncaMdl.FeatureWeights,'ro');
xlabel('Feature index');
ylabel('Feature weight');
grid on;
% 对于每一折来说cvpartition将 4/5的数据作为训练集，另外1/5作为测试集
cvp = cvpartition(y,'kfold',5);
numtestsets = cvp.NumTestSets;
lambdavalues = linspace(0,2,20)/length(y);
lossvalues = zeros(length(lambdavalues),numtestsets);
for i = 1:length(lambdavalues) % 对lambda的数值进行循环
for k = 1:numtestsets % 对测试集进行循环
% 提取训练集
Xtrain = X(cvp.training(k),:);
ytrain = y(cvp.training(k),:);
% 提取测试集
Xtest = X(cvp.test(k),:);
ytest = y(cvp.test(k),:);
% 使用训练集训练nca模型
ncaMdl = fscnca(Xtrain,ytrain,'FitMethod','exact',...
'Solver','lbfgs','Lambda',lambdavalues(i));
% 使用nca模型对测试集的损失函数进行计算。
lossvalues(i,k) = loss(ncaMdl,Xtest,ytest,...
'LossFunction','quadratic');
end
end
figure()
plot(lambdavalues,mean(lossvalues,2),'ro-');
xlabel('Lambda values');
ylabel('Loss values');
grid on;
[~,idx] = min(mean(lossvalues,2)); % Find the index
bestlambda = lambdavalues(idx) % Find the best lambda value
ncaMdl = fscnca(X,y,'FitMethod','exact','Verbose',1,...
'Solver','lbfgs','Lambda',bestlambda);
figure
semilogx(ncaMdl.FeatureWeights,'ro');
xlabel('Feature index');
ylabel('Feature weight');
grid on;
