[人工智能]机器学习 K近邻算法_0(Matlab实现)

一、解析

KNN：
接收数据集以及聚点信息
返回聚点轨迹，聚点簇，迭代次数，偏差以及偏差和

Dis_Func：
接收两点的坐标
返回两点距离
此处为欧式距离(可根据需求修改)

A_Rand：
接收数据集大小，分组数量，每组数量以及离散程度
返回随机生成有规律分布的数据集

Show：
接收聚点簇轨迹，并作出聚点移动轨迹

二、效果

1、数据展示

2、聚点迭代路径

‘+’表示数据集分布
‘*’表示聚点起点
直线表示聚点迭代轨迹

三、代码

1、mian

%A:数据集
%size_A:数据集大小
%Points:聚点集
%nums_Points:聚点数量
%Error:误差和
%Max_Iteration:最大迭代次数


size_A=[20,2];
A=A_Rand(size_A,4,5,2);
%A=Temp;
plot(A(:,1),A(:,2),'+')
hold on;
nums_Points=4;
Points=50+5.*rand(nums_Points,size_A(2));
plot(Points(:,1),Points(:,2),'*')
Error=9;
Max_Iteration=20;


%Points:聚点轨迹
%Points_A:聚点簇
%flag:迭代次数
%Points_Centre_Variance:聚点簇偏差
%Points_Centre_Variance_Sum:聚点簇偏差和
[Track_Points,Points_A,flag, Points_Centre_Variance,Points_Centre_Variance_Sum]=KNN(A,size_A,Points,nums_Points,Error,Max_Iteration);
%聚点轨迹作图
Show(A,size_A,Track_Points, nums_Points,flag+1);


disp("最终聚点:");
disp(Track_Points((1+flag*nums_Points):(flag+1)*nums_Points,:));
disp("聚点簇:");
disp(Points_A);
disp("迭代次数:");
disp(flag);
disp("聚点簇偏差:");
disp(Points_Centre_Variance);
disp("聚点簇偏差和:");
disp(Points_Centre_Variance_Sum);

2、KNN

function [Track_Points,Points_A,flag, Points_Centre_Variance,Points_Centre_Variance_Sum] = KNN(A,size_A,Points,nums_Points,Error,Max_Iteration)
%A:���?�
%size_A:���?���С
%Points:�??
%nums_Points:�?���
%Error:���?�������

%聚点轨迹记录
Track_Points=[];
Track_Points=[Track_Points;Points];

%��������
flag=0;

%���?�?������ ���� 
Dist_A_P=zeros(size_A(1),1+nums_Points);
Dist_A_P(:,1)=(1:size_A(1))';
for i=1:size_A(1)
    for j=1:nums_Points
        Dist_A_P(i,j+1)=Dist_Func(A(i,:),Points(j,:),nums_Points);
    end
end

%�?����� ���� ��
Points_A=zeros(nums_Points,2+size_A(1));
Points_A(:,1)=(1:nums_Points)';
Points_A(:,2)=0;
for i=1:size_A(1)
    temp=find(Dist_A_P(i,2:1+nums_Points)==min(Dist_A_P(i,2:1+nums_Points)));
    Points_A(temp(1),2)=Points_A(temp(1),2)+1;
    Points_A(temp(1),2+Points_A(temp(1),2))=i;
end


%���?����� ���� �������?�����
Points_Centre=zeros(nums_Points,1+size_A(2));
Points_Centre(:,1)=(1:nums_Points)';
for i=1:nums_Points
    Sum=zeros(1,size_A(2));
    for j=1:Points_A(i,2)
        Sum=Sum+A(Points_A(i,2+j),:);
    end
    if(Points_A(i,2)~=0)
        Points_Centre(i,2:1+size_A(2))=Sum./Points_A(i,2);
    end
end


%?������ ���� ?��
Points_Centre_Variance=zeros(nums_Points,2);
Points_Centre_Variance(:,1)=(1:nums_Points)';
Points_Centre_Variance_Sum=0;
for i=1:nums_Points
    Sum=0;
    for j=1:Points_A(i,2)
        Sum=Sum+Dist_Func(Points(i,:),A(Points_A(i,2+j),:),nums_Points);
    end
    if(Points_A(i,2)~=0)
        Points_Centre_Variance(i,2)=Sum./Points_A(i,2);
    end
    Points_Centre_Variance_Sum=Points_Centre_Variance_Sum+Points_Centre_Variance(i,2);
end


while(Points_Centre_Variance_Sum>Error && flag<Max_Iteration)
    %����������1
    flag=flag+1;
    
    %����Points
    for i=1:nums_Points
        if(Points_A(i,2)~=0)
        Points(i,:)=Points_Centre(i,2:1+size_A(2));
        end
    end
    
    %聚点轨迹记录
    Track_Points=[Track_Points;Points];
    
    %���?�?������ ���� 
    for i=1:size_A(1)
        for j=1:nums_Points
            Dist_A_P(i,j+1)=Dist_Func(A(i,:),Points(j,:),nums_Points);
        end
    end
    
    %�?����� ���� ��
    Points_A(:,2)=0;
    for i=1:size_A(1)
        temp=find(Dist_A_P(i,2:1+nums_Points)==min(Dist_A_P(i,2:1+nums_Points)));
        Points_A(temp(1),2)=Points_A(temp(1),2)+1;
        Points_A(temp(1),2+Points_A(temp(1),2))=i;
    end
  
    %���?����� ���� �������?�����
    for i=1:nums_Points
        Sum=zeros(1,size_A(2));
        for j=1:Points_A(i,2)
            Sum=Sum+A(Points_A(i,2+j),:);
        end
        if(Points_A(i,2)~=0)
            Points_Centre(i,2:1+size_A(2))=Sum./Points_A(i,2);
        end
    end

    
    %?������ ���� ?��
    Points_Centre_Variance_Sum=0;
    for i=1:nums_Points
        Sum=0;
        for j=1:Points_A(i,2)
            Sum=Sum+Dist_Func(Points(i,:),A(Points_A(i,2+j),:),nums_Points);
        end
        if(Points_A(i,2)~=0)
            Points_Centre_Variance(i,2)=Sum./Points_A(i,2);
        end
        Points_Centre_Variance_Sum=Points_Centre_Variance_Sum+Points_Centre_Variance(i,2);
    end
end
end

3、Dist_Func

function [ret] = Dist_Func(A,B,nums_Points)
ret=round(sqrt(sum((A-B).^2)),3);
end

4、A_Rand

function [Ret_A] = A_Rand(size_A,nums1,nums2,Dispersion)
%size_A:数据集大小
%nums1:分组数量
%nums2:每组数量
%Dispersion:每组离散程度

temp=100.*rand(nums1,size_A(2));
Ret_A=Dispersion.*rand(size_A);

for i=1:nums1
    Ret_A((nums2*(i-1)+1):(nums2*i),:)=Ret_A((nums2*(i-1)+1):(nums2*i),:)+temp(i,:);
end
end

5、Show

function [Ret_A] = Show(A,size_A,Track_Points,nums_Point,nums)
%A:数据集
%size_A:数据集大小
%Track_Points:聚点轨迹
%nums_Point:聚点数量
%nums:聚点规模
for i=1:nums_Point
    temp1= Track_Points(nums_Point*[0:nums-1]+i,1);
    temp2= Track_Points(nums_Point*[0:nums-1]+i,2);
    plot(temp1,temp2);
    
end