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🔥 内容介绍
在机器学习领域，支持向量机（Support Vector Machines，SVM）是一种常用的分类算法。它通过在特征空间中构建一个最优超平面来实现数据分类。然而，传统的SVM算法在处理大规模数据集时存在一些问题，比如计算复杂度较高、内存消耗大等。为了解决这些问题，研究者们提出了一种基于最小二乘支持向量机（Least Squares Support Vector Machines，LSSVM）的改进算法，即BES-LSSVM。
BES-LSSVM算法是一种基于秃鹰算法（Bald Eagle Strategy）优化的LSSVM算法。秃鹰算法是一种模拟秃鹰捕食行为的优化算法，它通过模拟秃鹰的搜寻和捕食策略来寻找最优解。BES-LSSVM算法通过应用秃鹰算法来优化LSSVM的参数，从而提高分类性能。
BES-LSSVM算法的核心思想是通过优化LSSVM的超参数来提高分类准确性。LSSVM算法的超参数包括正则化参数和核函数参数，它们的选择对于算法的性能至关重要。传统的方法通常是通过交叉验证来选择最优的超参数，但这种方法计算复杂度较高且耗时。BES-LSSVM算法通过应用秃鹰算法来自动选择最优的超参数，从而减少了计算复杂度和时间消耗。
BES-LSSVM算法的具体步骤如下：
- 初始化一群秃鹰，并随机生成初始解。
- 根据当前解计算适应度值，并选择适应度最高的秃鹰作为当前最优解。
- 根据当前最优解更新其他秃鹰的位置，并计算新的适应度值。
- 重复步骤2和步骤3，直到达到停止条件（如迭代次数达到设定值）。
- 返回最优解作为LSSVM的超参数。
通过BES-LSSVM算法优化后的LSSVM模型在数据分类任务中具有较高的准确性和鲁棒性。与传统的SVM算法相比，BES-LSSVM算法能够更好地处理大规模数据集，并且在计算复杂度和时间消耗上更加高效。因此，BES-LSSVM算法在实际应用中具有广泛的潜力。
总结起来，BES-LSSVM算法是一种基于秃鹰算法优化的最小二乘支持向量机算法，用于实现数据分类任务。它通过优化LSSVM的超参数来提高分类准确性，并且在处理大规模数据集时具有较高的效率。未来，我们可以进一步研究BES-LSSVM算法在其他机器学习任务中的应用，并探索其更多的优化潜力。
📣 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.
