Q2_final.m
代码语言：javascript复制%% Take Home Exam 4: Question 2
% Anja Deric | April 13, 2020
% Clear all variables and generate new training and testing data
clc; clear;
[train_data,train_labels] = generateMultiringDataset(2,1000,1);
title('Training Data');
[test_data,test_labels] = generateMultiringDataset(2,10000,2);
title('Validation Data');
%% Initial Training
% Train a Gaussian kernel SVM with cross-validation to select
% hyperparameters that minimize probability of error
% Hyperparameter initialization
CList = 10.^linspace(-3,7,11);
sigmaList = 10.^linspace(-2,3,13);
lossVal = zeros(length(sigmaList),length(CList));
% Loop through all hyperparameters to find best combination
for sigmaCounter = 1:length(sigmaList)
sigma = sigmaList(sigmaCounter);
for CCounter = 1:length(CList)
C = CList(CCounter);
% Train SVM model for hyperparameter combination
SVMModel = fitcsvm(train_data',train_labels,'BoxConstraint',C,...
'KernelFunction','rbf','KernelScale',sigma);
% Get cross-validated model (10-fold cross validation)
CVSVMModel = crossval(SVMModel);
% Store loss for SVM model
lossVal(sigmaCounter,CCounter) = kfoldLoss(CVSVMModel);
end
end
%% Final Training
% Find best sigma and C combination
minLoss = min(lossVal(:));
[sigmaBest_ind, CBest_ind] = find(lossVal == minLoss);
% Train final SVM and predict labels on test data
best_SVMModel = fitcsvm(train_data',train_labels,'BoxConstraint',...
CList(CBest_ind),'KernelFunction','rbf','KernelScale',...
sigmaList(sigmaBest_ind));
prediction = best_SVMModel.predict(test_data');
% Calculate accuracy of model
incorrect = sum(prediction' ~= test_labels);
accuracy = ((length(test_data) - incorrect)/length(test_data))*100
%% Plot Classified Labels
% Find and plot all correctly and incorrectly classified test samples
indINCORRECT = find(prediction' ~= test_labels); % incorrectly classified
indCORRECT = find(prediction' == test_labels); % correctly classified
plot(test_data(1,indCORRECT),test_data(2,indCORRECT),'g.'); hold on;
plot(test_data(1,indINCORRECT),test_data(2,indINCORRECT),'r.'); axis equal;
title('Training Data (RED: Incorrectly Classified)');
xlabel('X_1'); ylabel('X_2');
%% Functions
function [data,labels] = generateMultiringDataset(numberOfClasses,numberOfSamples,fig)
% Generates N samples from C ring-shaped class-conditional pdfs with equal priors
% Randomly determine class labels for each sample
thr = linspace(0,1,numberOfClasses 1); % split [0,1] into C equal length intervals
u = rand(1,numberOfSamples); % generate N samples uniformly random in [0,1]
labels = zeros(1,numberOfSamples);
for l = 1:numberOfClasses
ind_l = find(thr(l)<u & u<=thr(l 1));
labels(ind_l) = repmat(l,1,length(ind_l));
end
a = [1:numberOfClasses].^3; b = repmat(2,1,numberOfClasses); % parameters of the Gamma pdf needed later
% Generate data from appropriate rings
% radius is drawn from Gamma(a,b), angle is uniform in [0,2pi]
angle = 2*pi*rand(1,numberOfSamples);
radius = zeros(1,numberOfSamples); % reserve space
for l = 1:numberOfClasses
ind_l = find(labels==l);
radius(ind_l) = gamrnd(a(l),b(l),1,length(ind_l));
end
data = [radius.*cos(angle);radius.*sin(angle)];
if 1
colors = rand(numberOfClasses,3);
figure(fig); clf;
for l = 1:numberOfClasses
ind_l = find(labels==l);
plot(data(1,ind_l),data(2,ind_l),'.','MarkerFaceColor',colors(l,:));
axis equal; hold on;
xlabel('X_1'); ylabel('X_2');
end
end
end
