💥1 概述
文献来源：
本文介绍了一种在实证数据分析（EDA）框架下自主异常检测的新方法。这种方法完全由数据驱动，没有阈值。采用非参数EDA估计器，该方法能够基于数据的相互分布和集成特性，客观自主检测异常。该方法首先根据两个EDA标准识别潜在的异常，然后将其划分为无形状的非参数数据云。最后，它识别与每个数据云（本地）有关的异常。基于综合数据集和基准数据集的数值算例验证了所提方法的有效性和有效性。
📚2 运行结果
部分代码：
%% Output %% Output.IDX - The indices of the identified anomalies %% Output.SystemParams - The identified anomalies data=Input.Data; Lorigin=size(data,1); Aver=mean(data,1); X=mean(sum(data.^2,2)); dist1=pdist(data,'euclidean'); Averdist=mean(dist1(find(dist1<=mean(dist1(find(dist1<=mean(dist1))))))); [UD,J,K]=unique(data,'rows'); F = histc(K,1:numel(J)); [L,W]=size(UD); GlobalDensity=F./(ones(L,1)+sum((UD-repmat(Aver,L,1)).^2,2)./((X-sum(Aver.^2)))); GlobalDensity=GlobalDensity(K,:); dist=pdist2(UD,data); LocalDensity=zeros(L,1); LPotenAbnorm=round(Lorigin/18); for i=1:1:L s0=find(dist(i,:)<Averdist); if length(s0)>1 data0=data(s0,:); Ave0=mean(data0,1); DELTA=mean(sum(data0.^2,2))-sum(Ave0.^2); LocalDensity(i)=F(i)/(1+sum((UD(i,:)-Ave0).^2)/DELTA)*(length(s0)-1)/(L); else LocalDensity(i)=0; end end LocalDensity=LocalDensity(K,:); [~,IDX1] = sort(LocalDensity,'ascend'); [~,IDX2] = sort(GlobalDensity,'ascend'); IDPA=unique([IDX1(1:1:LPotenAbnorm);IDX2(1:1:LPotenAbnorm)]); dataPA=data(IDPA,:); [~,~,IDX,Mnumber,~]=FormingDataCloud(dataPA); if isempty(Mnumber(Mnumber~=1))~=1 AMN=mean(Mnumber(Mnumber~=1)); else AMN=2; end seq=find(Mnumber<=AMN); AbnoID=[]; for i=1:1:length(seq) seq0=find(IDX==seq(i)); AbnoID=[AbnoID;seq0]; end AbnoIDX=sort(IDPA(AbnoID),'ascend'); AbnoData=data(AbnoIDX,:); Output.IDX=AbnoIDX; Output.Anomaly=AbnoData; end function [NoC,center,IDX,Mnumber,LocalX]=FormingDataCloud(data) %% [L,W]=size(data); %% [UD,J,K]=unique(data,'rows'); F = histc(K,1:numel(J)); LU=length(UD(:,1)); %% dist=pdist(UD,'euclidean'); dist=squareform(dist).^2; unidata_pi=sum(dist.*repmat(F',LU,1),2); unidata_density=unidata_pi'*F./(unidata_pi.*2*L); unidata_glodensity=unidata_density.*F; [~,pos]=max(unidata_glodensity); seq=1:1:LU; seq=seq(seq~=pos); Rank=zeros(LU,1); Rank(1,:)=pos; for i=2:1:LU [~,pos0]=min(dist(pos,seq)); pos=seq(pos0); Rank(i,:)=pos; seq=seq(seq~=pos); end UD1=UD(Rank,:); UGDen=unidata_glodensity(Rank); F1=F(Rank); Gradient=zeros(2,LU-2); Gradient(1,:)=UGDen(1:1:LU-2)-UGDen(2:1:LU-1); Gradient(2,:)=UGDen(2:1:LU-1)-UGDen(3:1:LU); seq2=2:1:LU-1; seq1=find(Gradient(1,:)<0&Gradient(2,:)>0); if Gradient(2,LU-2)<0 seq3=[1,seq2(seq1),LU]; else seq3=[1,seq2(seq1)]; end %% LU2=length(seq3); UD2=UD1(seq3,:); dist1=pdist2(UD2,data); [~,seq4]=min(dist1,[],1); centre=zeros(LU2,W); Mnumber=zeros(LU2,1); for i=1:1:LU2 seq5=find(seq4==i); Mnumber(i)=length(seq5); centre(i,:)=mean(data(seq5,:)); end seq0=find(Mnumber==1); M0=length(seq0); LU2=LU2-M0; C0=centre(seq0,:); seq0=find(Mnumber>1); centre=centre(seq0,:);
🌈3 Matlab代码+数据
🎉4 参考文献
部分理论来源于网络，如有侵权请联系删除。
[1] X. Gu, P. Angelov, “Autonomous anomaly detection”, in IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS), 2017, pp. 1-8.
[2] X. Gu, "Self-organising Transparent Learning System," Phd Thesis, Lancaster University, 2018.
