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code/soft_rs/rks2017/RKS_classification.m

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+% Random Kitchen Sinks (RKS) for Least squares kernel classification
+% 
+% We are given the following training-test data matrices
+% Xtrain: N x d, Xtest: M x d
+% Ytrain: N x 1, Ytest: M x 1
+
+close all, clear, clc
+
+% synthetic sample data
+N = 1e4;M = 1e3;d = 2;
+Xtrain = [randn(N/2,d); 3+randn(N/2,d)];Ytrain = [ones(N/2,1); -ones(N/2,1)];
+Xtest = [randn(M/2,d); 3+randn(M/2,d)];Ytest = [ones(M/2,1); -ones(M/2,1)];
+
+% Training
+D      = 100; % number of random features
+lambda = 1e-9;    % regularization parameter
+sigma  = 2; % kernel parameter
+W      = (1/sigma)*randn(D,d);   % Random projection matrix
+Z      = exp(1i*Xtrain*W');  % Explicitly projected features, N x D
+alpha  = (Z'*Z + lambda*eye(D) )\(Z'*Ytrain);  % Primal weights, D x 1
+
+% Testing
+Ztest  = exp(1i*Xtest*W'); % M x D
+Ypred  = sign(real(Ztest*alpha)); % M x 1
+
+% Overall Accuracy
+acc = sum(Ypred == Ytest)/length(Ypred)
+
+% Plot
+figure,scatter(Xtrain(1:N/2,1),Xtrain(1:N/2,2),'+'), hold on,
+scatter(Xtrain(N/2+1:end,1),Xtrain(N/2+1:end,2),'ro')
+x=(min(Xtrain(:,1)):.05:max(Xtrain(:,1)))';
+y=(min(Xtrain(:,2)):.05:max(Xtrain(:,2)))';
+for i=1:length(x)
+    for j=1:length(y)
+        if abs(real(exp(1i*[x(i) y(j)]*W')*alpha)) < 1e-1
+            plot(x(i),y(j),'k-')
+        end
+    end
+end
+xlabel('feature 1'), ylabel('feature 2')
+legend('class +1', 'class -1','decission boundary'),grid on

code/soft_rs/rks2017/RKS_regression.m

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+% Random Kitchen Sinks (RKS) for Least squares kernel regression
+% 
+% We are given the following training-test data matrices
+% Xtrain: N x d, Xtest: M x d
+% Ytrain: N x 1, Ytest: M x 1
+
+close all, clear, clc
+
+% synthetic sample data
+N = 1e4;M = 1e3;d = 1;
+Xtrain = randn(N,d);Ytrain = sin(Xtrain) + .1*randn(N,d);
+Xtest = randn(M,d);Ytest = sin(Xtest) + .1*randn(M,d);
+
+% Training
+D      = 100; % number of random features
+lambda = 1e-3;    % regularization parameter
+sigma  = 1; % kernel parameter
+W      = (1/sigma)*randn(D,d);   % Random projection matrix
+Z      = exp(1i*Xtrain*W');  % Explicitly projected features, N x D
+alpha  = (Z'*Z + lambda*eye(D) )\(Z'*Ytrain);  % Primal weights, D x 1
+
+% Testing
+Ztest  = exp(1i*Xtest*W'); % M x D
+Ypred  = real(Ztest*alpha); % M x 1
+
+% RMSE
+norm(Ypred - Ytest)/sqrt(length(Ypred))
+
+figure,plot(Xtrain,Ytrain,'.'), hold on,
+x=(min(Xtrain):.01:max(Xtrain))';
+plot(x,real(exp(1i*x*W')*alpha),'r-','linewidth',2)
+legend('training set', 'fitted curve'), grid on

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