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🔥 内容介绍
在机器学习领域，支持向量机（Support Vector Machine，SVM）是一种常用的监督学习方法，被广泛应用于分类和回归问题。然而，传统的SVM模型在处理回归问题时存在一些局限性，例如对噪声敏感、模型复杂度难以确定等。为了克服这些问题，研究者们提出了基于最小二乘支持向量机（Least Squares Support Vector Machine，LSSVM）的回归模型。
LSSVM回归模型通过最小化目标函数来寻找最佳的超平面，从而实现对数据的回归预测。然而，由于目标函数的复杂性和高维空间中的数据分布，传统的优化算法在求解LSSVM模型时往往效果不佳。为了进一步提高LSSVM模型的性能，研究者们引入了蛇群算法（Snake Optimization Algorithm，SO）来对LSSVM模型进行优化。
蛇群算法是一种基于自然界中蛇群行为的优化算法，具有全局搜索能力和收敛速度快的优点。通过模拟蛇群的觅食行为和捕食行为，蛇群算法能够在搜索空间中寻找最优解。在LSSVM回归预测中，蛇群算法可以通过调整模型参数和优化目标函数来提高模型的拟合能力和泛化性能。
在实际应用中，基于蛇群算法优化的LSSVM模型在数据回归预测方面表现出色。首先，蛇群算法能够全局搜索最优解，避免了传统优化算法陷入局部最优解的问题。其次，蛇群算法具有较快的收敛速度，能够在较短的时间内找到最优解。最后，蛇群算法能够通过调整模型参数和优化目标函数，提高模型的预测精度和泛化性能。
然而，基于蛇群算法优化的LSSVM模型也存在一些挑战和限制。首先，蛇群算法的性能受到初始参数设置和迭代次数的影响，需要进行合理的调参和优化。其次，蛇群算法在处理大规模数据时可能面临计算复杂度较高的问题。因此，在实际应用中，需要根据具体问题进行适当的算法选择和参数调整。
📣 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
⛳️ 运行结果
🔗 参考文献
[1] 孙峰超.基于最小二乘支持向量机的非线性预测控制[D].中国石油大学[2023-09-28].DOI:10.7666/d.y1709445.
[2] 杨钊,路超凡,刘安黎.基于PSO-LSSVM算法的表面粗糙度预测模型与应用[J].机床与液压, 2021, 49(6):5.
[3] 刘云,易松.基于双参数最小二乘支持向量机(TPA-LSSVM)的风电时间序列预测模型的优化研究[J].北京化工大学学报：自然科学版, 2019, 46(2):6.DOI:CNKI:SUN:BJHY.0.2019-02-015.
[4] 殷樾.基于粒子群算法最小二乘支持向量机的日前光伏功率预测[J].分布式能源, 2021, 6(2):7.DOI:10.16513/j.2096-2185.DE.2106019.
