1.完整项目描述和程序获取
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2.部分仿真图预览
3.算法概述
LSSVM（Least Square SVM）是将Kernel应用到ridge regression中的一种方法，它通过将所有样本用最小二乘误差进行拟合（这个拟合是在kernel变换过的高维空间），但是LSSVM的缺陷是计算复杂度大概是样本数的三次方量级，计算量非常大。为了解决这个问题于是提出了SVR（支持向量回归），SVR通过支持向量减小了LSSVM的计算复杂度，并且具备LSSVM的能够利用kernel在高纬度拟合样本。
4.部分源码
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x = model.xtrain; y = model.ytrain;
% train model
if isempty(model.gam) && isempty(model.kernel.pars)
error('Please tune model first with ''tunelssvm'' to obtain tuning parameters');
end
model = trainlssvm(model);
s = smootherlssvm(model);
Yhat = simlssvm(model,x);
% bias: double smoothing with fourt order kernel RBF4
modelb = initlssvm(x,y,'f',[],[],'RBF4_kernel','o');
modelb = tunelssvm(modelb,'simplex','crossvalidatelssvm',{10,'mse'});
modelb = trainlssvm(modelb);
biascorr = (s-eye(size(x,1)))*simlssvm(modelb,x);
% construct approximate 100(1-alpha)% confidence interval
%1) estimate variance nonparametrically
sigma2 = varest(model);
%2) calculate var-cov matrix
s = s*diag(sigma2)*s';
%2b) find standardized absolute maxbias
delta = max(abs(biascorr./sqrt(diag(s))));
%3) pointwise or simultaneous?
if conftype(1)=='s'
z = tbform(model,alpha) + delta;
elseif conftype(1)=='p'
z = norminv(alpha/2);
Yhat = Yhat - biascorr;
else
error('Wrong type of confidence interval. Please choose ''pointwise'' or ''simultaneous''');
end
ci = [Yhat+z*sqrt(diag(s)) Yhat-z*sqrt(diag(s))];
function [var,modele] = varest(model)
% if preprocessed data, construct original data
if model.preprocess(1)=='p'
[x,y] = postlssvm(model,model.xtrain,model.ytrain);
else
x = model.xtrain; y = model.ytrain;
end
model = trainlssvm(model);
Yh = simlssvm(model,x);
% Squared normalized residuals
e2 = (y-Yh).^2;
% Make variance model
if model.nb_data <= 200
costfun = 'leaveoneoutlssvm'; costargs = {'mae'};
else
costfun = 'crossvalidatelssvm'; costargs = {10,'mae'};
end
modele = initlssvm(x,e2,'f',[],[],'RBF_kernel');
modele = tunelssvm(modele,'simplex',costfun,costargs);
modele = trainlssvm(modele);
% variance model
var = max(simlssvm(modele,x),0);
% make estimate of var unbiased in homoscedastic case if regression
% estimate is unbiased
L = smootherlssvm(model);
S = smootherlssvm(modele);
var = var./(ones(size(x,1),1)+S*diag(L*L'-L-L'));
A313
