利用nsga2进行进行特征选择其主要思想是：将子集的选择看作是一个搜索寻优问题(wrapper方法)，生成不同的组合，对组合进行评价，再与其他的组合进行比较。这样就将子集的选择看作是一个是一个优化问题。

需要优化的两个目标为特征数和精度。

nsga2是一个多目标优化算法。

具体的特征选择代码在上述代码的基础上改了两个①主函数②评价函数，增加了一个数据分成训练集和测试集的函数：

MATLAB

function divide_datasets()

load Parkinson.mat;

dataMat=Parkinson_f;

len=size(dataMat,1);

%归一化

maxV = max(dataMat);

minV = min(dataMat);

range = maxV-minV;

newdataMat = (dataMat-repmat(minV,[len,1]))./(repmat(range,[len,1]));

Indices = crossvalind('Kfold', length(Parkinson_label), 10);

site = find(Indices==1|Indices==2|Indices==3);

train_F = newdataMat(site,:);

train_L = Parkinson_label(site);

site2 = find(Indices~=1&Indices~=2&Indices~=3);

test_F = newdataMat(site2,:);

test_L =Parkinson_label(site2);

save train_F train_F;

save train_L train_L;

save test_F test_F;

save test_L test_L;

end

%what doesn't kill you makes you stronger, stand a little taller,doesn't mean i'm over cause you're gonw.

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functiondivide_datasets()

loadParkinson.mat;

dataMat=Parkinson_f;

len=size(dataMat,1);

%归一化

maxV=max(dataMat);

minV=min(dataMat);

range=maxV-minV;

newdataMat=(dataMat-repmat(minV,[len,1]))./(repmat(range,[len,1]));

Indices=crossvalind('Kfold',length(Parkinson_label),10);

site=find(Indices==1|Indices==2|Indices==3);

train_F=newdataMat(site,:);

train_L=Parkinson_label(site);

site2=find(Indices~=1&Indices~=2&Indices~=3);

test_F=newdataMat(site2,:);

test_L=Parkinson_label(site2);

savetrain_Ftrain_F;

savetrain_Ltrain_L;

savetest_Ftest_F;

savetest_Ltest_L;

end

%what doesn't kill you makes you stronger, stand a little taller,doesn't mean i'm over cause you're gonw.

MATLAB代码主函数:

MATLAB

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%此处可以更改

%更多机器学习内容请访问omegaxyz.com

clc;

clear;

pop = 500; %种群数量

gen = 100; %迭代次数

M = 2; %目标数量

V = 22; %维度

min_range = zeros(1, V); %下界

max_range = ones(1,V); %上界

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%特征选择

divide_datasets();

global answer

answer=cell(M,3);

global choice %选出的特征个数

choice=0.8;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

chromosome = initialize_variables(pop, M, V, min_range, max_range);

chromosome = non_domination_sort_mod(chromosome, M, V);

for i = 1 : gen

pool = round(pop/2);

tour = 2;

parent_chromosome = tournament_selection(chromosome, pool, tour);

mu = 20;

mum = 20;

offspring_chromosome = genetic_operator(parent_chromosome,M, V, mu, mum, min_range, max_range);

[main_pop,~] = size(chromosome);

[offspring_pop,~] = size(offspring_chromosome);

clear temp

intermediate_chromosome(1:main_pop,:) = chromosome;

intermediate_chromosome(main_pop + 1 : main_pop + offspring_pop,1 : M+V) = offspring_chromosome;

intermediate_chromosome = non_domination_sort_mod(intermediate_chromosome, M, V);

chromosome = replace_chromosome(intermediate_chromosome, M, V, pop);

if ~mod(i,100)

clc;

fprintf('%d generations completed\n',i);

end

end

if M == 2

plot(chromosome(:,V + 1),chromosome(:,V + 2),'*');

xlabel('f_1'); ylabel('f_2');

title('Pareto Optimal Front');

elseif M == 3

plot3(chromosome(:,V + 1),chromosome(:,V + 2),chromosome(:,V + 3),'*');

xlabel('f_1'); ylabel('f_2'); zlabel('f_3');

title('Pareto Optimal Surface');

end

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%此处可以更改

%更多机器学习内容请访问omegaxyz.com

clc;

clear;

pop=500;%种群数量

gen=100;%迭代次数

M=2;%目标数量

V=22;%维度

min_range=zeros(1,V);%下界

max_range=ones(1,V);%上界

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%特征选择

divide_datasets();

globalanswer

answer=cell(M,3);

globalchoice%选出的特征个数

choice=0.8;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

chromosome=initialize_variables(pop,M,V,min_range,max_range);

chromosome=non_domination_sort_mod(chromosome,M,V);

fori=1:gen

pool=round(pop/2);

tour=2;

parent_chromosome=tournament_selection(chromosome,pool,tour);

mu=20;

mum=20;

offspring_chromosome=genetic_operator(parent_chromosome,M,V,mu,mum,min_range,max_range);

[main_pop,~]=size(chromosome);

[offspring_pop,~]=size(offspring_chromosome);

cleartemp

intermediate_chromosome(1:main_pop,:)=chromosome;

intermediate_chromosome(main_pop+1:main_pop+offspring_pop,1:M+V)=offspring_chromosome;

intermediate_chromosome=non_domination_sort_mod(intermediate_chromosome,M,V);

chromosome=replace_chromosome(intermediate_chromosome,M,V,pop);

if~mod(i,100)

clc;

fprintf('%d generations completed\n',i);

end

end

ifM==2

plot(chromosome(:,V+1),chromosome(:,V+2),'*');

xlabel('f_1');ylabel('f_2');

title('Pareto Optimal Front');

elseifM==3

plot3(chromosome(:,V+1),chromosome(:,V+2),chromosome(:,V+3),'*');

xlabel('f_1');ylabel('f_2');zlabel('f_3');

title('Pareto Optimal Surface');

end

评价函数(利用林志仁SVM进行训练)：

MATLAB

function f = evaluate_objective(x, M, V, i)

f = [];

global answer

global choice

load train_F.mat;

load train_L.mat;

load test_F.mat;

load test_L.mat;

temp_x = x(1:V);

inmodel = temp_x>choice;%%%%%设定恰当的阈值选择特征

f(1) = sum(inmodel(1,:));

answer(i,1)={f(1)};

model = libsvmtrain(train_L,train_F(:,inmodel), '-s 0 -t 2 -c 1.2 -g 2.8');

[predict_label, ~, ~] = libsvmpredict(test_L,test_F(:,inmodel),model,'-q');

error=0;

for j=1:length(test_L)

if(predict_label(j,1) ~= test_L(j,1))

error = error+1;

end

end

error = error/length(test_L);

f(2) = error;

answer(i,2)={error};

answer(i,3)={inmodel};

end

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functionf=evaluate_objective(x,M,V,i)

f=[];

globalanswer

globalchoice

loadtrain_F.mat;

loadtrain_L.mat;

loadtest_F.mat;

loadtest_L.mat;

temp_x=x(1:V);

inmodel=temp_x>choice;%%%%%设定恰当的阈值选择特征

f(1)=sum(inmodel(1,:));

answer(i,1)={f(1)};

model=libsvmtrain(train_L,train_F(:,inmodel),'-s 0 -t 2 -c 1.2 -g 2.8');

[predict_label,~,~]=libsvmpredict(test_L,test_F(:,inmodel),model,'-q');

error=0;

forj=1:length(test_L)

if(predict_label(j,1)~=test_L(j,1))

error=error+1;

end

end

error=error/length(test_L);

f(2)=error;

answer(i,2)={error};

answer(i,3)={inmodel};

end

选的的数据集请从UCI上下载。

结果：

①pareto面

最后粒子的数据(选出的特征数和精确度)