LOF(local outlier factor)算法的Matlab版本实现

LOF算法是一种基于密度的无监督离群点检测算法，其核心思想是：通过比较对象xi与其邻居密度的相似性程度，如果越不相似，即xi的LOF值越大于1，则其是离群点的可能性越高。

下面给出了LOF算法的Matlab版本实现，可直接粘贴复制，并将代码稍作修改即可运行。

function [outputArg1,outputArg2] = LOF(inputArg1,inputArg2)
x=load ('Normalization_wbc.txt');%装载要检测的数据集
Label=load('Label_wbc.txt');%数据集X所对应的标签
ADLabels=load('Label_wbc.txt');%这是为了计算AUC值加的标签
%样本个数为n,后续计算混淆矩阵是要用的，别和其他算法混淆
n=size(x,1);
%近邻个数
k=20;
%异常对象个数
Abnormal_number=20;
x2=sum(x.^2,2);%按列求和 便于后续步骤进行计算
[s,t]=sort(sqrt(repmat(x2,1,n)+repmat(x2',n,1)-2*x*x'),2);
%进行异常检测
for i=1:k+1
    for j=1:k
        RD(:,j)=max(s(t(t(:,i),j+1),k),s(t(:,i),j+1));
    end
    LRD(:,i)=1./mean(RD,2);
end
LOF=mean(LRD(:,2:k+1),2)./LRD(:,1);
[value_outlier,index_outlier]=sort(LOF,'ascend');
%LOF算法最终判定的离群点对象编号
outlier=index_outlier(1:Abnormal_number,:);
auc = Measure_AUC(LOF, ADLabels);
disp(auc)

ODA_AbnormalObject_Number=index_outlier(n-Abnormal_number+1:end,:);%outlier detection algorithm 算法认定的异常对象的编号
ODA_NormalObject_Number=index_outlier(1:n-Abnormal_number,:);%outlier detection algorithm算法认定的正常对象的编号
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%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);
end

请配合计算AUC值的函数一起使用（如果不需要计算AUC，可在代码中注释掉即可运行）

function AccumAuc = Measure_AUC(Scores, Labels)
% Area Under Curve for Amonaly
% 
% Scores: predicted scores;
% Labels: groundtruth labels, PosLabel = 1& NegLabel = 0;

NumInst = length(Scores);

% sort Scores and Labels
[Scores, index] = sort(Scores, 'descend');
Labels = Labels(index);

PosLabel = 1;
NegLabel = 0;

NumPos = length(find(Labels == PosLabel));
NumNeg = length(find(Labels == NegLabel));

AccumPos = 0;
AccumNeg = 0;
AccumAuc = 0;

UnitPos = 1 / NumPos;
UnitNeg = 1 / NumNeg;

i = 1;
while i <= NumInst
    temp = AccumPos;
    if (i < NumInst - 1) && (Scores(i) == Scores(i + 1))
        while (i < NumInst - 1) && (Scores(i) == Scores(i + 1))
            if Labels(i) == NegLabel
                AccumNeg = AccumNeg + 1;
            elseif Labels(i) == PosLabel
                AccumPos = AccumPos + 1;
            else
                disp('Label is not defined!');
            end
            i = i + 1;
        end

        if Labels(i) == NegLabel
            AccumNeg = AccumNeg + 1;
        elseif Labels(i) == PosLabel
            AccumPos = AccumPos + 1;
        else
            disp('Label is not defined!');
        end

        AccumAuc = AccumAuc + (AccumPos + temp) * UnitPos * AccumNeg * UnitNeg / 2;
        AccumNeg = 0;
    else
        if Labels(i) == NegLabel
            AccumNeg = AccumNeg + 1;
            AccumAuc = AccumAuc + AccumPos * UnitPos * AccumNeg * UnitNeg;
            AccumNeg = 0;
        elseif Labels(i) == PosLabel
            AccumPos = AccumPos + 1;
        else
            disp('Label is not defined');
        end
    end
    i = i + 1;
end