%% Get 2D data
close all; clc; tic;
if nargin == 0
load dataset.mat p;
train = p{1}; test = p{2};
% Kernel types and parameters:
ktype = 'rbf'; kpar = 1; % RBF kernel
%ktype = 'rbf'; kpar = 10; % RBF kernel
%ktype = 'rbf'; kpar = 0.9; % RBF kernel
%ktype = 'rbfpoly'; kpar = [1 1 0.65]; % mixed kernel
%ktype = 'poly'; kpar = 2; % polynomial kernel
%ktype = 'imquad'; kpar = 10; % inverse multiquadric kernel
%ktype = 'cauchy'; kpar = 5; % Cauchy kernel
end
%lax = [-15 15 -15 15];
lax = [-4 10 -3 6]; % Axes limits
N = length(train); M = length(test);
z0T = train; z1T = test; % Training and Test data
[xx,yy] = meshgrid(lax(1):0.05:lax(2),... % Meshgrid for contours
lax(3):0.05:lax(4));
z2T = [xx(:) yy(:)]; L = length(z2T); % Vectorize meshgrid points
K.type = ktype; K.p = kpar; % Kernel type and parameters
set(0,'defaultfigurecolor',[1 1 1]); % Set fig color to w
conf = 0.99; % Significance level (*100%)
% Normalize 2D Data
zm = mean(z0T); zs = std(z0T);
z0 = (z0T - zm(ones(N,1),:))./zs(ones(N,1),:); % Normalize training z
z1 = (z1T - zm(ones(N,1),:))./zs(ones(M,1),:); % Normalize test z
z2 = (z2T - zm(ones(L,1),:))./zs(ones(L,1),:); % Normalize surf z
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% KERNEL PRINCIPAL COMPONENTS ANALYSIS %
[K0c,K0,U0] = kerneltrain(z0,K); % Populate kernel matrix
K1c = kerneltest(z1,z0,K0,U0,K); % Project test data to RKHS
K2c = kerneltest(z2,z0,K0,U0,K); % Project surf data to RKHS
[V,D] = eig(K0c/N); % Eigenvalue decomposition
[S,sj] = sort(diag(D),'descend'); % Sort eigenvalues
V = V(:,sj); S = S'; % Re-arrange eigenvectors
S(S < 1e-7) = []; % Remove eigenvalues <= 0
P = V(:,1:length(S))*diag(S.^-0.5); % Projection matrix
if ~isreal(S)
disp('Complex eigenvalues detected.'); % Warn about complex eigs
end
%% Perform KPCA Monitoring
CS = cumsum(S)/sum(S)*100;
RP = find(CS >= 99.9,1); % Get eigenvalues by %CPV
disp([num2str(RP) ' principal'...
' components chosen.']);
t0 = K0c*P(:,1:RP); % Kernel subspace (train)
t1 = K1c*P(:,1:RP); % Kernel subspace (test)
t2 = K2c*P(:,1:RP); % Kernel subspace (surf)
T2 = sum((t0.^2)./S(ones(N,1),1:RP),2); % T2 statistics (train)
t0n = K0c*P; % Full kernel space
Q = abs(sum(t0n.^2,2) - sum(t0.^2,2)); % Q statistics (train)
if strcmp(ktype,'rbf') == 1
fprintf('\n At infinite fault magnitude:\n');
U1 = ones(1,N)/N;
tt = U1*K0*(U0 - eye(N))*P(:,1:RP);
fprintf(' T2 limit: %.2f\n',...
sum((tt.^2)./S(1:RP),2)); % Limit of T2 for RBF
tu = U1*K0*(U0 - eye(N))*P;
fprintf(' Q limit: %.2f\n\n',...
abs(sum(tu.^2,2) - sum(tt.^2,2))); % Limit of Q for RBF
end
T2t = sum((t1.^2)./S(ones(M,1),1:RP),2); % T2 statistics (test)
T2u = sum((t2.^2)./S(ones(L,1),1:RP),2); % T2 statistics (surf)
t1n = K1c*P; t2n = K2c*P;
Qt = abs(sum(t1n.^2,2) - sum(t1.^2,2)); % Q statistics (test)
Qu = abs(sum(t2n.^2,2) - sum(t2.^2,2)); % Q statistics (surf)
%% Plot monitoring charts
figure(3); subplot(211);
semilogy(1:N,T2,'b',1:M,T2t,'m','linewidth',1.2); % T2 monitoring chart
xlabel('Time'); ylabel('T^2'); subplot(212);
semilogy(1:N,Q,'b',1:M,Qt,'m','linewidth',1.2); % Q monitoring chart
xlabel('Time'); ylabel('Q');