基于自编码器的离群点检测算法的Matlab版实现

基于自编码器的无监督离群点检测算法的核心思想是：通过将待检测数据集输入自编码器进行训练，训练完成后，那些难以被重构的对象（即重构误差较大的对象）被认为是离群点。

基于AE的outlier detection存在的前提，也就是有一个假设条件存在，即：离群点难以被自编码器在输出层重构。

基于AE的outlier detection的Matlab版实现如下：

function [outputArg1,outputArg2] = GD_AE_OD(inputArg1,inputArg2)
%SIMPLEBP_MORENEURONMOREHIDDEN 此处显示有关此函数的摘要
%   此处显示详细说明
%通过计算待检测数据集的重构误差来计算样本的离群值，越大越有可能是离群点。
x=load('Normalization_wbc.txt')';%每一列是一个样本
y=load('Normalization_wbc.txt')';
Label=load('Label_wbc.txt');
ADLabels=load('Label_wbc.txt');
[m,n]=size(x);%m表示有多少个特征，n表示有多少个样本

%初始化
Layer2_hiddensize=5;%第一个隐藏层的神经元个数
Layer3_hiddensize=m;%第二个隐藏层的神经元个数
Layer2_w=rand(Layer2_hiddensize,m);%rand(m,n)表示随机生成m行n列的0-1之间的矩阵，如果rand(m)表示生成m*m的方阵的随机矩阵
Layer2_b=rand(Layer2_hiddensize,1);
Layer3_w=rand(Layer3_hiddensize,Layer2_hiddensize);
Layer3_b=rand(Layer3_hiddensize,1);
%初始化隐藏层的输出
Layer2_output=rand(Layer2_hiddensize,1);
Layer3_output=rand(Layer3_hiddensize,1);
%初始化隐藏层的梯度
Layer2_e=rand(Layer2_hiddensize,1);
Layer3_e=rand(Layer3_hiddensize,1);

iteration=1000;%迭代次数
LearningRate=0.1;
Abnormal_number=20;%异常点个数
for t=1:iteration
    %%%%%%%%%%%标准正向传播%%%%%%%%
    for i=1:n
        %%%%%正传%%%%%%%%%%%%
        Layer2_output = Sigmoid( Layer2_w * x(:,i) - Layer2_b);
        total_Layer2_output(:,i)=Layer2_output;
        Layer3_output = Sigmoid( Layer3_w * Layer2_output - Layer3_b);
        x(:,i)=Layer3_output;
        %%%%%%%反传%%%%%%%%%%%
        Layer3_e=Layer3_output .* (1-Layer3_output) .* (y(:,i)-Layer3_output);
        Layer2_e=Layer2_output .* (1-Layer2_output) .*  (Layer3_w' * Layer3_e);
        Layer3_w = Layer3_w + LearningRate  * Layer3_e * Layer2_output';
        Layer2_w = Layer2_w + LearningRate * Layer2_e * x(:,i)';
        Layer3_b = Layer3_b - LearningRate * Layer3_e;
        Layer2_b = Layer2_b - LearningRate * Layer2_e;
    end
    Loss=(y-x).*(y-x);%loss中每一列表示对应列的样本的损失值
    EverySample_Loss=sum(Loss,1);
    TotalLoss(t,:)=sum(EverySample_Loss)/n;
end

mse=sum(Loss,1)';
auc = Measure_AUC(mse, ADLabels);
disp(auc)
[OF_value,index_number]=sort(mse);
ODA_AbnormalObject_Number=index_number(n-Abnormal_number+1:end,:);%outlier detection algorithm 算法认定的异常对象的编号
ODA_NormalObject_Number=index_number(1:n-Abnormal_number,:);%outlier detection algorithm算法认定的正常对象的编号
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%算法实际的检测率/准确率/误报率等评价指标的计算%%%%%%%%%%%%%%%%%%%%%%%%
%%%%Real_NormalObject_Number表示数据集中真正的正常对象的编号，Real_AbnormalObject_Number表示数据集中真正异常对象的编号
[Real_NormalObject_Number,Real_Normal]=find(Label==0);
[Real_AbnormalObject_Number,Real_Abnormal]=find(Label==1);

%正例是异常对象，反例是正常对象
TP=length(intersect(Real_AbnormalObject_Number,ODA_AbnormalObject_Number));
FP=length(Real_AbnormalObject_Number)-TP;
TN=length(intersect(Real_NormalObject_Number,ODA_NormalObject_Number));
FN=length(Real_NormalObject_Number)-TN;

%准确率
ACC=(TP+TN)/(TP+TN+FP+FN);
fprintf('准确率ACC= %8.5f\n',ACC*100)
%检测率==查全率=R
DR=TP/(TP+FN);
fprintf('检测率DR= %8.5f\n',DR*100)
%查准率P
P=TP/(TP+FP);
fprintf('查准率P= %8.5f\n',P*100)
%误报率
FAR=FP/(TN+FP);
fprintf('误报率FAR= %8.5f\n',FAR*100)

%绘制混淆矩阵
Confusion_matrix=[TP,FN;FP,TN];
Figure_Confusion_matrix=heatmap(Confusion_matrix);


figure(2)
for j=0:iteration-1
    j=j+1;
    axis_x(j,:)=j;
end
plot(axis_x,TotalLoss,'LineWidth',2);

end

请配合我其他博客的计算AUC方法的函数一起使用