rbf神经网络（matlab代码，含数据和测试）

% RBF.m % Radial Basis Function Neural Network (RBFNN) designed to predict house prices in the Boston area % % Francis Poole % 16/04/15 % function RBF() %Initalise clear all close all clc dbstop if error %Initial Free Parameters M = 10; %Number of centres Sigma = 'cov'; %Variance of centres - 'cov' = covariance of k-means clusters, 'ave' = average distance between centres lambda = 0; %Regularisation parameter L = 3; %Number of committees %Setup %Get data t = getTrainingData(); %Training data p = getPredictionData(); %Prediction data %Split training data to input and target xStart = t(:,1:end-1); %Input data dStart = t(:,end); %Target data %K-fold setup I = randperm(size(xStart,1)); %Random indexes Error = []; xStart = preProcess(xStart, 1); %Optimisation %K-fold Cross Validation----------------------------------------------- n = 1; for k = 2:10 for run = 1:10 Error(run,n) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); %Initial run end n = n+1; end Error = mean(Error,1) figure(1) plot(Error) Error = []; %Reset Error k = 7; %Assign best number of folds - (7) %Number of centres----------------------------------------------------- M = 1; E = inf; working = 1; while working Error Error(M) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); if E > Error(M) E = Error(M); lower = 1; elseif lower lower = 0; else working = 0; end M = M+1; end Error figure(1) plot(Error) Error = []; M = 7; %Assign best number of centres - (7) %Variance of Centres--------------------------------------------------- for n = 1:2 Error(n,1) = RBFGaussian(xStart, dStart, k, M, 'avg', lambda, L, I); Error(n,2) = RBFGaussian(xStart, dStart, k, M, 'cov', lambda, L, I); end Error = mean(Error,1) bar(Error) Error = []; Sigma = 'cov'; %Assign best variance - (Covariance) %Regularisation-------------------------------------------------------- n = 1; for lambda = 0:0.01:0.2 Error(n) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); n = n+1; end plot(Error) Error Error = []; lambda = 0.06; %Assign best regularisation parameter - (0.06) %Pre-processing-------------------------------------------------------- %Normalisation xStart = t(:,1:end-1); %Get unprocessed input data Error(1) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); xStart = preProcess(xStart, 1); %NEED TO ADD PREDICTION DATA! Error(2) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); xStart = t(:,1:end-1); %Get unprocessed input data xStart = preProcess(xStart, 2); %NEED TO ADD PREDICTION DATA! Error(3) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); %Dimensionality Reduction xStart = t(:,1:end-1); %Get unprocessed input data xStart = preProcess(xStart, 3); Error(4) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); Error bar(Error) xStart = t(:,1:end-1); %Get unprocessed input data processedData = preProcess(xStart, 1); %Committee Machines---------------------------------------------------------------------- n = 1; for L = 1:8 Error(n) = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I); plot(Error) n = n+1; end Error Error = []; L = 4; %Assign best number of committies - (4) xStart = t(:,1:end-1); %Get unprocessed input data processedData = preProcess([xStart;p], 1); %Do best preprocessing - (Linear Rescaling) xStart = processedData(1:end-size(p,1), :); p = processedData(end-size(p,1)+1:end, :); Y = predict(p, xStart, dStart, M, Sigma, lambda, L) Y = Y.*1000; end function Y = predict(p, x, d, M, Sigma, lambda, L) for committee = 1:L %-----Stage 1 - Parameterise Hidden Layer [c, Sigma] = getCentres(x, M, Sigma); %-----Stage 2 - Find Weights Phi = ones(size(x,1),size(c,1)+1); %Bias if size(Sigma) > 1 for n = 1:size(x,1) for m = 1:size(c,1) Phi(n,m+1) = multiGaussianBasis(x(n,:)-c(m,:),Sigma(:,:,m)); %Multivariate gaussian basis function end end else for n = 1:size(x,1) for m = 1:size(c,1) Phi(n,m+1) = uniGaussianBasis(norm(x(n,:)-c(m,:)), Sigma); %Univariate gaussian basis function end end end W = pinv(pinv(Phi) * Phi + lambda * eye(size(c,1)+1)) * pinv(Phi) * d; %Using regularization theory %-----Stage 3 - Cross Validate pPhi = ones(size(p,1),size(c,1)+1); %Bias if size(Sigma) > 1 for n = 1:size(p,1) for m = 1:size(c,1) pPhi(n,m+1) = multiGaussianBasis(p(n,:)-c(m,:),Sigma(:,:,m)); %Multivariate gaussian basis function end end else for n = 1:size(vX,1) for m = 1:size(c,1) pPhi(n,m+1) = uniGaussianBasis(norm(p(n,:)-c(m,:)), Sigma); %Univariate gaussian basis function end end end y(:,committee)= pPhi * W; end Y = mean(y,2); end function Error = RBFGaussian(xStart, dStart, k, M, Sigma, lambda, L, I) N = size(xStart,1); foldSize = floor(N/k); %Number of data points in each fold for fold = 1:k %Split data for fold [x,vX] = kFold(xStart, fold, foldSize, I); [d,vD] = kFold(dStart, fold, foldSize, I); for committee = 1:L %-----Stage 1 - Parameterise Hidden Layer [c, Sigma] = getCentres(x, M, Sigma); %-----Stage 2 - Find Weights Phi = ones(size(x,1),size(c,1)+1); %Bias if size(Sigma) > 1 for n = 1:size(x,1) for m = 1:size(c,1) Phi(n,m+1) = multiGaussianBasis(x(n,:)-c(m,:),Sigma(:,:,m)); %Multivariate gaussian basis function end end else for n = 1:size(x,1) for m = 1:size(c,1) Phi(n,m+1) = uniGaussianBasis(norm(x(n,:)-c(m,:)), Sigma); %Univariate gaussian basis function end end end W = pinv(pinv(Phi) * Phi + lambda * eye(size(c,1)+1)) * pinv(Phi) * d; %Using regularization theory %-----Stage 3 - Cross Validate vPhi = ones(size(vX,1),size(c,1)+1); %Bias if size(Sigma) > 1 for n = 1:size(vX,1) for m = 1:size(c,1) vPhi(n,m+1) = multiGaussianBasis(vX(n,:)-c(m,:),Sigma(:,:,m)); %Multivariate gaussian basis function end end else for n = 1:size(vX,1) for m = 1:size(c,1) vPhi(n,m+1) = uniGaussianBasis(norm(vX(n,:)-c(m,:)), Sigma); %Univariate gaussian basis function end end end y(:,committee)= vPhi * W; ECom(committee, fold) = mean(abs(y(:,committee)-vD)); end Y = mean(y,2); E(fold) = mean(abs(Y-vD)); %Printout clc ECom mean(ECom) E k M lambda size(c,1) fold end Error = mean(E); end function x = preProcess(x, option) %---Input Normalisation %Linear Rescaling if option == 1 || option == 3