Jing Gao 1, Feng Liang 1, Wei Fan 2, Chi Wang 1, Yizhou Sun 1, Jiawei i Han 1 University of Illinois, IBM TJ Watson.

Transcription

1 Jing Gao 1, Feng Liang 1, Wei Fan 2, Chi Wang 1, Yizhou Sun 1, Jiawei i Han 1 University of Illinois, IBM TJ Watson Debapriya Basu

2 Determine outliers in information networks Compare various algorithms which does the same 2

3 Eg Internet, t Social Networking Sites Nodes characterized by feature values Links - representative of relation between nodes 3

4 Outliers anomalies, novelties Different kinds of outliers Global Contextual 4

5 5

6 Unified model considering both nodes and links Community discovery and outlier detection are related processes 6

7 Treat each object as a multivariate data point Use K components to describe normal community behavior and one component to denote outliers Induce a hidden variable z i at each object indicating community Treat network information as a graph Model the graph as a Hidden Markov Random Field on z i Find the local l minimum i of the posterior probability potential energy of the model. 7

8 outlier community label Z node feature X link structure W K: number of communitie s high-income: mean: 116k std: 35k low-income: mean: 20k std: 12k 8 model parameters

9 Symbol I = {1,2,3.i,..M} Definition Indices of the objects V ={v1,v2.vv2 v m } Set of objects S = {s1,s2,.s m } Given attributes of objects W M*M = {w ij } Adjacency matrix containing the weights of the links Z={z 1,..,z m } RVs for hidden labels of objects X = {x 1,..,x m } RVs for observed data N i (i I) Neighborhood of object v i 1,.,k,.K Indices of normal communities Θ = {Θ 1, Θ 2,, Θ k } R.Vs for model parameters 9

10 Set of R.Vs X are conditionally independent given their labels P(X=S Z) = ΠP(x i =s i z i ) Kth normal community is characterized by a set of parameters P(x i =s i z i =k) = P(x i =s i Θ k ) Outliers are characterized by uniform distribution P(x i =s i z i =0) = ρ0 Markov random field is defined over hidden variable Z P(z i z I-{i} ) = P(z i z Ni ) The equivalent Gibbs distribution is P(Z) = exp(-u(z))*1/h 1 H 1 = normalizing i constant, t U(Z) = sum of clique potentials. ti Goal is to find the configuration of z that maximizes P(X=S Z)P(Z) for a given Θ 10

11 Continuous Data Is modeled as Gaussian distribution Model parameters: mean, standard deviation Text Data Is modeled as Multinomial distribution Model parameters: probability of a word appearing in a community 11

12 Initialize Z Θ : model parameters Z: community labels Given Z, find Θ that maximizes P(X Z) PARAMETER ESTIMATION Given Θ, find Z that maximizes P(Z X) INFERENCE 12

13 Calculate model parameters maximum likelihood estimation Continuous mean: sample mean of the community standard deviation: square root of the sample variance of the community Text probability of a word appearing in the community: empirical probability 13

14 Calculate Z i values Given Model parameters, Iteratively update the community labels of nodes at each timestep Select the label l that maximizes i P(Z X,Z Z N ) Calculate P(Z X,Z N ) values Both the node features and community labels of neighbors if Z indicates a normal community If the probability of a node belonging to any community is low enough, label it as an outlier 14

15 Setting Hyper parameters a 0 = threshold Λ = confidence in the network K = number of communities Initialization Group outliers in clusters. It will eventually get corrected. 15

16 Data Generation Generate continuous data based on Gaussian distributions and generate labels according to the model Define r: percentage of outliers, K: number of communities Baseline models GLODA: global outlier detection (based on node features only) DNODA: local outlier detection (check the feature values of direct neighbors) CNA: partition data into communities based on links and then conduct outlier detection in each community 16

17 GLODA DNODA CNA CODA r=1% K=5 r=5% K=5 r=1% K=8 r=5% K=8 17

18 Communities data mining, artificial intelligence, database, information analysis Sub network of Conferences Links: percentage of common authors among two conferences Node features: publication titles in the conference Sub network of Authors Links: co-authorship relationship Node features: titles of publications by an author 18

19 Community outliers: CVPR CIKM 19

20 Community Outliers Community Outlier Detection QUESTIONS 20

21 On Community Outliers and their Efficient Detection in Information Networks Gao, Liang, Fan, Wang, Sun, Han Outlier detection Irad Ben-Gal Automated detection of outliers in real-world data Last, Kandel Outlier Detection for High Dimensional Data Aggarwal, Yu 21