【回归预测-lssvm分类】基于最小二乘支持向量机lssvm实现数据分类代码

1 内容介绍

在信息爆炸的新时代,由于全球科技与经济迅猛发展,数据充斥在各行各业,数据的结构也变得多样化.其中对于数据的分类最常见,伴随着数据分类的同时出现两大处理难点,一个是非均衡问题,另一个就是高维问题.但是传统的数据方法在进行数据挖掘时,低维平衡数据被重点关注,传统分类方法有线性判别分析,Logistic判别模型,支持向量机算法,K近邻算法,决策树算法,随机森林算法,神经网络学习,等.但是目前各个领域充斥着大量高维非均衡数据,而传统方法对非均衡数据分类问题的关注比较缺失.目前对于非均衡数据分类时,由于数量本身的严重偏斜,分类器整体的分类准确度良好恰恰归功于多数类样本的正确分类.

​

2 仿真代码

%LS-SVM模型参数初始化

clc

clear

aa=xlsread('数据集.xlsx')

%% 重构矩阵

P=aa(:,1:2);

T=aa(:,3);

type = 'f';

kernel='RBF_kernel';

preprocess='original';

gam = 3;

sig2 = 0.6;

%进行模型训练

model = initlssvm(P,T,type,gam,sig2,kernel);

model = trainlssvm(model);

%回归预测

predictlabel = simlssvm(model,P);

%% 预测结果分析

[m,n]=size(predictlabel);

figure

subplot(2,1,1)

plot(1:m,predictlabel,'ob',1:m,T,'*r');

legend('预测值','实际值');

ylabel('分类','FontSize',12);

title('SVM')

grid on;

subplot(2,1,2)

plot(1:m,predictlabel-T,'-*r');

ylabel('error','FontSize',12);

legend('预测值error');

[M,b,r]=postreg(predictlabel,T)

function [sig_e, bay,model] = bay_errorbar(model,Xt, type, nb, bay)

% Compute the error bars for a one dimensional regression problem

%

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2}, Xt)

% >> sig_e = bay_errorbar(model, Xt)

%

% The computation takes into account the estimated noise variance

% and the uncertainty of the model parameters, estimated by

% Bayesian inference. sig_e is the estimated standard deviation of

% the error bars of the points Xt. A plot is obtained by replacing

% Xt by the string 'figure'.

%

%

% Full syntax

%

% 1. Using the functional interface:

%

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, Xt)

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, Xt, type)

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, Xt, type, nb)

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, 'figure')

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, 'figure', type)

% >> sig_e = bay_errorbar({X,Y,'function',gam,sig2,kernel,preprocess}, 'figure', type, nb)

%

% Outputs

%sig_e: Nt x 1 vector with the [$ \sigma^2$] errorbands of the test data

% Inputs

%X : N x d matrix with the inputs of the training data

%Y : N x 1 vector with the inputs of the training data

%type: 'function estimation' ('f')

%gam: Regularization parameter

%sig2: Kernel parameter

%kernel(*) : Kernel type (by default 'RBF_kernel')

%preprocess(*) : 'preprocess'(*) or 'original'

%Xt: Nt x d matrix with the inputs of the test data

%type(*) : 'svd'(*), 'eig', 'eigs' or 'eign'

%nb(*): Number of eigenvalues/eigenvectors used in the eigenvalue decomposition approximation

%

% 2. Using the object oriented interface:

%

% >> [sig_e, bay, model] = bay_errorbar(model, Xt)

% >> [sig_e, bay, model] = bay_errorbar(model, Xt, type)

% >> [sig_e, bay, model] = bay_errorbar(model, Xt, type, nb)

% >> [sig_e, bay, model] = bay_errorbar(model, 'figure')

% >> [sig_e, bay, model] = bay_errorbar(model, 'figure', type)

% >> [sig_e, bay, model] = bay_errorbar(model, 'figure', type, nb)

%

% Outputs

%sig_e : Nt x 1 vector with the [$ \sigma^2$] errorbands of the test data

%model(*) : Object oriented representation of the LS-SVM model

%bay(*) : Object oriented representation of the results of the Bayesian inference

% Inputs

%model : Object oriented representation of the LS-SVM model

%Xt : Nt x d matrix with the inputs of the test data

%type(*) : 'svd'(*), 'eig', 'eigs' or 'eign'

%nb(*) : Number of eigenvalues/eigenvectors used in the eigenvalue decomposition approximation

%

% See also:

% bay_lssvm, bay_optimize, bay_modoutClass, plotlssvm

% Copyright (c) 2002, KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlab

if iscell(model), model = initlssvm(model{:}); end

if model.type(1)~='f',

error(['confidence bounds only for function estimation. For' ...

' classification, use ''bay_modoutClass(...)'' instead;']);

end

eval('type;','type=''svd'';');

eval('nb;','nb=model.nb_data;');

if ~(strcmpi(type,'svd') | strcmpi(type,'eig') | strcmpi(type,'eigs') | strcmpi(type,'eign')),

error('Eigenvalue decomposition via ''svd'', ''eig'', ''eigs'' or ''eign''...');

end

if strcmpi(type,'eign')

warning('The resulting errorbars are most probably not very usefull...');

end

if ~isstr(Xt),

eval('[sig_e, bay] = bay_confb(model,Xt,type,nb,bay);',...

'[sig_e, bay] = bay_confb(model,Xt,type,nb);');

else

grid = 50;

[X,Y] = postlssvm(model,model.xtrain,model.ytrain);

eval('[sig_e, bay] = bay_confb(model,X,type,nb,bay);',...

'[sig_e, bay] = bay_confb(model,X,type,nb);');

% plot the curve including confidence bound

sige = sqrt(sig_e);

Yt = simlssvm(model,X);

figure;

hold on;

title(['LS-SVM_{\gamma=' num2str(model.gam(1)) ', \sigma^2=' num2str(model.kernel_pars(1)) ...

'}^{' model.kernel_type(1:3) '} and its 95% (2\sigma) error bands']);

if model.x_dim==1,

xlabel('X');

ylabel('Y');

[~,si] = sort(X);

plot(X(si),Yt(si),'k'); hold on;

plot(X(si),Yt(si)+2.*sige(si),'-.r');

plot(X(si),Yt(si)-2.*sige(si),':r');

plot(X(si),Y(si),'k*'); hold off;

else

xlabel('time');

ylabel('Y');

plot(Yt,'k'); hold on;

plot(Yt+2.*sige,'-.r');

plot(Yt-2.*sige,':r');

plot(Y,'k*'); hold off;

end

end

function [sig_e, bay] = bay_confb(model,X,type,nb,bay)

% see formula's thesis TvG blz 126

nD = size(X,1);

%tol = .0001;

%

% calculate the eigenvalues

%

eval('bay;','[c1,c2,c3,bay] = bay_lssvm(model,1,type,nb);');

omega = kernel_matrix(model.xtrain(model.selector,1:model.x_dim), ...

model.kernel_type, model.kernel_pars);

oo = ones(1,model.nb_data)*omega;

% kernel values of X

theta = kernel_matrix(model.xtrain(model.selector, 1:model.x_dim), ...

model.kernel_type, model.kernel_pars, X);

for i=1:nD,

kxx(i,1) = feval(model.kernel_type, X(i,:),X(i,:), model.kernel_pars);

end

Zc = eye(model.nb_data) - ones(model.nb_data)./model.nb_data;

Hd = (Zc*bay.Rscores);

Hd = Hd*diag(1./bay.mu - (bay.mu+ bay.zeta*bay.eigvals).^-1)*Hd';

% forall x

for i=1:nD,

term1(i,1) = bay.zeta^-1 + kxx(i)/bay.mu - theta(:,i)'*Hd*theta(:,i);

term2(i,1) = 2/model.nb_data*sum(theta(:,i)'*Hd*omega) - 2/bay.mu/model.nb_data* sum(theta(:,i));

end

% once

term3 = 1/(bay.zeta*model.nb_data) ...

+ 1/(bay.mu*model.nb_data^2)* sum(oo) ...

-1/(model.nb_data^2)* oo*Hd*oo';

sig_e = term1+term2+term3;

function model = changelssvm(model,option, value)

% Change a field of the object oriented representation of the LS-SVM

%

%

% The different options of the fields are given in following table:

%

% 1. General options representing the kind of model:

%

%type: 'classifier' ,'function estimation'

% implementation: 'CMEX' ,'CFILE' ,'MATLAB'

%status: Status of this model ('trained' or 'changed' )

%alpha: Support values of the trained LS-SVM model

% b: Bias term of the trained LS-SVM model

% duration: Number of seconds the training lasts

%latent: Returning latent variables ('no' ,'yes' )

% x_delays: Number of delays of eXogeneous variables (by default 0 )

% y_delays: Number of delays of responses (by default 0 )

%steps: Number of steps to predict (by default 1 )

%gam: Regularisation parameter

% kernel_type: Kernel function

% kernel_pars: Extra parameters of the kernel function

%

%

% 2. Fields used to specify the used training data:

%

% x_dim: Dimension of input space

% y_dim: Dimension of responses

% nb_data: Number of training data

% xtrain: (preprocessed) inputs of training data

% ytrain: (preprocessed,coded) outputs of training data

% selector: Indexes of training data effectively used during training

%

%

% 3. Options used in the Conjugate Gradient (CG) algorithm:

%

% cga_max_itr: Maximum number of iterations in CG

%cga_eps: Stopcriterium of CG, largest allowed error

% cga_fi_bound: Stopcriterium of CG, smallest allowed improvement

% cga_show: Show the results of the CG algorithm (1 or 0)

% cga_startvalues: Starting values of the CG algorithm

%

%

% 4. Fields with the information for pre- and post-processing (only given if appropriate):

%

% preprocess: 'preprocess' or 'original'

% schemed: Status of the preprocessing

% ('coded' ,'original' or 'schemed' )

% pre_xscheme: Scheme used for preprocessing the input data

% pre_yscheme: Scheme used for preprocessing the output data

% pre_xmean: Mean of the input data

% pre_xstd: Standard deviation of the input data

% pre_ymean: Mean of the responses

% pre_ystd: Standard deviation of the reponses

%

%

% 5. The specifications of the used encoding (only given if appropriate):

%

%code: Status of the coding

% ('original' ,'changed' or 'encoded')

% codetype: Used function for constructing the encoding

% for multiclass classification (by default 'none')

% codetype_args: Arguments of the codetype function

% codedist_fct: Function used to calculate to which class a

% coded result belongs

% codedist_args: Arguments of the codedist function

% codebook2: Codebook of the new coding

% codebook1: Codebook of the original coding

%

% Full syntax

%

% >> model = changelssvm(model, field, value)

%

% Outputs

%model(*) : Obtained object oriented representation of the LS-SVM model

% Inputs

%model : Original object oriented representation of the LS-SVM model

%field : Field of the model one wants to change (e.g. 'preprocess')

%value : New value of the field of the model one wants to change

%

% See also:

% trainlssvm, initlssvm, simlssvm, plotlssvm.

% Copyright (c) , KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlab

%

% alias sigma^2

%

if (strcmpi(option,'sig2')) option = 'kernel_pars'; end

%

% selector -> nb_data

% nb_data -> selector

%

if strcmp(option,'selector'),

model.nb_data = length(value);

end

if strcmp(option,'nb_data'),

model.selector = 1:value;

end

%

% xtrain

%

if strcmp(option,'xtrain'),

[nb,model.x_dim] = size(value);

model.nb_data = nb;%min(nb,model.nb_data);

model.selector = 1:model.nb_data;

if length(model.gam)>model.y_dim & length(model.gam)~=size(value,1),

warning('Discarting different gamma''s...');

model.gam = max(model.gam);

end

eval('value=prelssvm(model,value);',...

'warning(''new trainings inputdata not comform with used preprocessing'');');

end

%

% ytrain

%

if strcmp(option,'ytrain'),

if size(value,2)~=size(model.ytrain,2),

model.y_dim = size(value,2);

end

eval('value = codelssvm(model,[],value);',...

'warning(''new trainings outputdata not comform with used encoding;'');');

eval('[ff,value] = prelssvm(model,[],value);',...

'warning(''new trainings outputdata not comform with used preprocessing;'');');

[nb,model.y_dim] = size(value);

model.nb_data = min(nb,model.nb_data);

model.selector = 1:model.nb_data;

end

%

% switch between preprocessing - original data

% model.prestatus = {'changed','ok'}

%

if (strcmpi(option,'preprocess')) & model.preprocess(1)~=value(1),

model.prestatus = 'changed';

end

%

% change coding

%

if strcmpi(option,'codetype') | strcmpi(option,'codebook2') | ...

strcmpi(option, 'codeargs') | strcmpi(option, 'codedistfct'),

model.code = 'changed';

elseif strcmpi(option,'codebook1'),

warning('change original format of the classifier; the toolbox will be unable to return results in the original format');

end

%

% final change

%

eval(['old_value = model.' lower(option) ';'],'old_value=[];');

eval(['model.' lower(option) '=value;']);

if (isempty(value) | isempty(old_value)),

different = 1;

else

eval('different = any(old_value~=value);','different=1;');

end

if different & ~strcmpi(option,'implementation'),

model.status = 'changed';

end

3 运行结果

4 参考文献

[1]李飞. 基于改进粒子群算法的支持向量机参数优化[D]. 河北工业大学.

[1]沈会. 基于最小二乘支持向量机方法的统计优化预测模型[D]. 武汉理工大学, .

博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。

部分理论引用网络文献，若有侵权联系博主删除。