【lssvm回归预测】基于龙格库塔算法优化最小二乘支持向量机RUN-lssvm实现数据回归预测附matlab代码-优快云博客

本文探讨了传统支持向量机在处理大规模数据时的挑战，介绍了基于最小二乘支持向量机的回归预测方法，以及如何通过引入龙格库塔算法优化求解过程，显著提高处理效率。

✅作者简介：热爱科研的Matlab仿真开发者，修心和技术同步精进，matlab项目合作可私信。

🍎个人主页：Matlab科研工作室

🍊个人信条：格物致知。

更多Matlab完整代码及仿真定制内容点击👇

智能优化算法神经网络预测雷达通信无线传感器电力系统

信号处理图像处理路径规划元胞自动机无人机

🔥 内容介绍

在机器学习领域中，支持向量机（Support Vector Machine，SVM）是一种常用的监督学习方法，它在分类和回归问题中都取得了很好的效果。然而，传统的SVM算法在处理大规模数据时会面临一些挑战，例如计算复杂度高、内存消耗大等问题。为了解决这些问题，研究人员提出了一种基于最小二乘支持向量机（Least Squares Support Vector Machine，LSSVM）的回归预测方法。

LSSVM回归预测方法通过将回归问题转化为一个最小化目标函数的优化问题，通过求解这个优化问题得到回归模型。在LSSVM中，通过引入松弛变量和惩罚项来控制模型的复杂度和泛化能力。然而，传统的LSSVM算法在求解优化问题时也存在一些问题，例如对于大规模数据的处理效率较低。为了解决这个问题，我们可以通过引入龙格库塔算法对LSSVM进行优化。

龙格库塔算法是一种常用的数值求解微分方程的方法，它通过迭代逼近来求解方程的数值解。在LSSVM中，我们可以将龙格库塔算法应用于优化问题的求解过程中，通过迭代逼近来求解最优解。这种方法可以大大提高LSSVM算法的求解效率，尤其是在处理大规模数据时。

📣 部分代码

function [model,Yt] = prelssvm(model,Xt,Yt)% Preprocessing of the LS-SVM%% These functions should only be called by trainlssvm or by% simlssvm. At first the preprocessing assigns a label to each in-% and output component (c for continuous, a for categorical or b% for binary variables). According to this label each dimension is rescaled:% %     * continuous: zero mean and unit variance%     * categorical: no preprocessing%     * binary: labels -1 and +1% % Full syntax (only using the object oriented interface):% % >> model   = prelssvm(model)% >> Xp = prelssvm(model, Xt)% >> [empty, Yp] = prelssvm(model, [], Yt)% >> [Xp, Yp] = prelssvm(model, Xt, Yt)% %       Outputs    %         model : Preprocessed object oriented representation of the LS-SVM model%         Xp    : Nt x d matrix with the preprocessed inputs of the test data%         Yp    : Nt x d matrix with the preprocessed outputs of the test data%       Inputs    %         model : Object oriented representation of the LS-SVM model%         Xt    : Nt x d matrix with the inputs of the test data to preprocess%         Yt    : Nt x d matrix with the outputs of the test data to preprocess% % % See also:%   postlssvm, trainlssvm% Copyright (c) 2011,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.be/sista/lssvmlabif model.preprocess(1)~='p', % no 'preprocessing  if nargin>=2, model = Xt;  end   returnend% % what to do% if model.preprocess(1)=='p',   eval('if model.prestatus(1)==''c'',model.prestatus=''unschemed'';end','model.prestatus=''unschemed'';');end  if nargin==1, % only model rescaling      %  % if UNSCHEMED, redefine a rescaling  %  if model.prestatus(1)=='u',% 'unschemed'    ffx =[];            for i=1:model.x_dim,      eval('ffx = [ffx model.pre_xscheme(i)];',...     'ffx = [ffx signal_type(model.xtrain(:,i),inf)];');    end    model.pre_xscheme = ffx;       ff = [];    for i=1:model.y_dim,      eval('ff = [ff model.pre_yscheme(i)];',...     'ff = [ff signal_type(model.ytrain(:,i),model.type)];');    end    model.pre_yscheme = ff;    model.prestatus='schemed';  end    %  % execute rescaling as defined if not yet CODED  %  if model.prestatus(1)=='s',% 'schemed'      model=premodel(model);     model.prestatus = 'ok';  end    %  % rescaling of the to simulate inputs  %elseif model.preprocess(1)=='p'  if model.prestatus(1)=='o',%'ok'     eval('Yt;','Yt=[];');    [model,Yt] = premodel(model,Xt,Yt);  else     warning('model rescaling inconsistent..redo ''model=prelssvm(model);''..');  endendfunction [type,ss] = signal_type(signal,type)%% determine the type of the signal,% binary classifier ('b'), categorical classifier ('a'), or continuous% signal ('c')%%ss = sort(signal);dif = sum(ss(2:end)~=ss(1:end-1))+1;% binaryif dif==2,  type = 'b';% categoricalelseif dif<sqrt(length(signal)) || type(1)== 'c',  type='a';% continuelse  type ='c';end  %% effective rescaling%function [model,Yt] = premodel(model,Xt,Yt)%%%if nargin==1,  for i=1:model.x_dim,    % CONTINUOUS VARIABLE:     if model.pre_xscheme(i)=='c',      model.pre_xmean(i)=mean(model.xtrain(:,i));      model.pre_xstd(i) = std(model.xtrain(:,i));      model.xtrain(:,i) = pre_zmuv(model.xtrain(:,i),model.pre_xmean(i),model.pre_xstd(i));      % CATEGORICAL VARIBALE:     elseif model.pre_xscheme(i)=='a',      model.pre_xmean(i)= 0;      model.pre_xstd(i) = 0;      model.xtrain(:,i) = pre_cat(model.xtrain(:,i),model.pre_xmean(i),model.pre_xstd(i));      % BINARY VARIBALE:     elseif model.pre_xscheme(i)=='b',            model.pre_xmean(i) = min(model.xtrain(:,i));      model.pre_xstd(i) = max(model.xtrain(:,i));      model.xtrain(:,i) = pre_bin(model.xtrain(:,i),model.pre_xmean(i),model.pre_xstd(i));    end    end    for i=1:model.y_dim,    % CONTINUOUS VARIABLE:     if model.pre_yscheme(i)=='c',      model.pre_ymean(i)=mean(model.ytrain(:,i),1);      model.pre_ystd(i) = std(model.ytrain(:,i),1);      model.ytrain(:,i) = pre_zmuv(model.ytrain(:,i),model.pre_ymean(i),model.pre_ystd(i));    % CATEGORICAL VARIBALE:     elseif model.pre_yscheme(i)=='a',            model.pre_ymean(i)=0;      model.pre_ystd(i) =0;      model.ytrain(:,i) = pre_cat(model.ytrain(:,i),model.pre_ymean(i),model.pre_ystd(i));    % BINARY VARIBALE:     elseif model.pre_yscheme(i)=='b',            model.pre_ymean(i) = min(model.ytrain(:,i));      model.pre_ystd(i) = max(model.ytrain(:,i));      model.ytrain(:,i) = pre_bin(model.ytrain(:,i),model.pre_ymean(i),model.pre_ystd(i));    end    endelse %if nargin>1, % testdata Xt,   if ~isempty(Xt),    if size(Xt,2)~=model.x_dim, warning('dimensions of Xt not compatible with dimensions of support vectors...');end    for i=1:model.x_dim,      % CONTINUOUS VARIABLE:       if model.pre_xscheme(i)=='c',  Xt(:,i) = pre_zmuv(Xt(:,i),model.pre_xmean(i),model.pre_xstd(i));      % CATEGORICAL VARIBALE:       elseif model.pre_xscheme(i)=='a',  Xt(:,i) = pre_cat(Xt(:,i),model.pre_xmean(i),model.pre_xstd(i));      % BINARY VARIBALE:       elseif model.pre_xscheme(i)=='b',        Xt(:,i) = pre_bin(Xt(:,i),model.pre_xmean(i),model.pre_xstd(i));      end      end  end    if nargin>2 & ~isempty(Yt),    if size(Yt,2)~=model.y_dim, warning('dimensions of Yt not compatible with dimensions of training output...');end    for i=1:model.y_dim,      % CONTINUOUS VARIABLE:       if model.pre_yscheme(i)=='c',  Yt(:,i) = pre_zmuv(Yt(:,i),model.pre_ymean(i), model.pre_ystd(i));      % CATEGORICAL VARIBALE:       elseif model.pre_yscheme(i)=='a',        Yt(:,i) = pre_cat(Yt(:,i),model.pre_ymean(i),model.pre_ystd(i));      % BINARY VARIBALE:       elseif model.pre_yscheme(i)=='b',        Yt(:,i) = pre_bin(Yt(:,i),model.pre_ymean(i),model.pre_ystd(i));      end    end  end    % assign output  model=Xt;endfunction X = pre_zmuv(X,mean,var)%% preprocessing a continuous signal; rescaling to zero mean and unit% variance % 'c'%X = (X-mean)./var;function X = pre_cat(X,mean,range)%% preprocessing a categorical signal;% 'a'%X=X;function X = pre_bin(X,min,max)%% preprocessing a binary signal;% 'b'%if ~sum(isnan(X)) >= 1 %--> OneVsOne encoding    n = (X==min);    p = not(n);    X=-1.*(n)+p;end