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🔥 内容介绍
在机器学习领域，数据回归预测是一个重要的任务，它可以帮助我们从已知数据中推断出未知数据的值。最小二乘支持向量机（Least Squares Support Vector Machine，简称LSSVM）是一种常用的回归预测模型，它通过最小化误差平方和来拟合数据。
然而，LSSVM模型在处理大规模数据集时可能会面临一些挑战。为了解决这个问题，我们可以引入黏菌算法（Slime Mould Algorithm，简称SMA）来优化LSSVM模型，以提高其性能和准确性。
黏菌算法是一种基于自然界中黏菌的行为机制而设计的优化算法。黏菌是一种单细胞生物，它具有自主移动和感知环境的能力。黏菌通过释放化学物质来吸引或排斥其他黏菌，并通过这种相互作用来寻找最佳路径或解决问题。
在基于黏菌算法优化的SMA-LSSVM中，我们首先使用LSSVM模型来拟合数据。然后，我们将黏菌算法引入到模型中，以优化模型参数。黏菌算法通过模拟黏菌的行为，通过释放化学物质来吸引或排斥其他模型参数，以寻找最佳的参数组合。
SMA-LSSVM模型的优化过程可以分为以下几个步骤：
- 初始化黏菌群体：根据LSSVM模型的参数空间，初始化一群黏菌。每个黏菌代表一个参数组合。
- 计算适应度函数：根据LSSVM模型的性能指标（如均方误差或决定系数），计算每个黏菌的适应度值。适应度值越高，表示该参数组合越优秀。
- 释放化学物质：根据适应度值，每个黏菌释放化学物质来吸引或排斥其他黏菌。适应度值高的黏菌释放的化学物质浓度较高，吸引其他黏菌靠近；适应度值低的黏菌释放的化学物质浓度较低，排斥其他黏菌。
- 移动和更新参数：黏菌根据化学物质的浓度移
📣 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.
