matlab 基于黏菌算法优化最小二乘支持向量机SMA-lssvm实现数据回归预测

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文章探讨了如何利用黏菌算法(SMA)优化最小二乘支持向量机(LSSVM)，以提高数据回归预测的性能和准确性，特别针对大规模数据集中的挑战。通过模拟黏菌行为调整模型参数，实现更高效的参数组合搜索。

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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