F LO LOW S CO COPE : : S PO POTTING M ONE ONEY L AU AUNDERING B AS ON G RAP ASED ED ON RAPHS Xiangfeng Li 1 , Shenghua Liu 2 , Zifeng Li 3 , Xiaotian Han 4 , Chuan Shi 1 , Bryan Hooi 5 , He Huang 6 , Xueqi Cheng 2 1 Beijing University of Post and Telecommunication 2 Institute of Computing Technology, Chinese Academy of Sciences 3 University of Surrey 4 Texas A&M University 5 School of Computer Science, National University of Singapore 6 China Citic Bank
Introduction Model Algorithm Experiments Conclusion Motivation • Typical method of money laundering (ML) save Our Focus dirty money enters the financial system illegal income integration consumption 2/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion ML Forms a Multipartite Dense Subgraph Inner account Outer account � � � � � Inner account Inner account � Outer account � ? � Adjacency Matrix 3/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Problem: Natural Dense Subgraph Inner account Outer account � � � � � suspicious dense blocks Inner account formed by fraudsters Inner account natural dense blocks (core, community, etc.) � Outer account � l Question. How can we ? distinguish them? � Adjacency Matrix 5/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Solution: Multipartite Dense Subgraph • Natural dense transfer not always form a multipartite dense subgraph Inner account Outer account ML characteristic � � � � � Inner account Both dense in and out of the bank Inner account Only dense in � transfer out Outer account � ? � Only dense in receive 6/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Solution: Multipartite Dense Subgraph (cont.) • Our FlowScope catches exactly multipartite dense subgraph HoloScope- ! Fraudar Our FlowScope 7/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Problem formulation • Given ◦ ! = ( " , # ): a graph of money transfers ◦ " : accounts as nodes ◦ # : money amount as edges weight ◦ $ : number of middle layers • Find ◦ a dense flow of money transfers (i.e. a subgraph of ! ), • Such that ◦ 1) the flow involves high-volume money transfers into the bank, and out of the bank to the destinations; ◦ 2) it maximizes density as defined in our ML metric. dense flow detection ! = suspicious flow in the graph $ + 1 matrices 8/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Requirements • Our goal is to design an algorithm which is Fast : runs in near-linear time Accurate : provides an accuracy guarantee Effective : produces meaningful results in practice 0 FlowScope , our proposed method, satisfies all the requirements 9/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Model • Graph $ = ( % , & ) , % = " ⋃ ! ⋃ # ◦ ! is the inner accounts of the bank, and " and # are sets of outer accounts • Generate multipartite graph % k = " ⋃ ! ⋃ … ⋃ ! ⋃ # $ k = ( % k , & k ) , Inner account (W) Outer account (Y) ( - 2 � � � � Inner account (W) Outer account (Y) Inner account(W) Inner account (W) � � � � � � � Inner account (W) � � Inner account (W) Inner account Outer account (X) � � � Outer account (X) � � � ? � Duplicate for k-3 times 10/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Model (cont.) • Out/in degree of each middle-layer node # $ = ∑ ' ( ∈* +,- ⋀ ",0 ∈1 2 "0 ! " 3 $ = ∑ ' 4 ∈* +5- ⋀ 6," ∈1 2 6" ! " • Definition of min and max flow # $ , ! " 3 $ }, ∀ > " ∈ ? @ 7 " $ = min{ ! " # $ , ! " 3 $ }, ∀ > " ∈ ? @ A " $ = max { ! " ~ flow • Suspicious metric balance parameter 63I = 1 D 6 $ $ F F 7 " $ − L(A " $ − 7 " $ ) retention/deficit @GH ' J ∈* + 63I 1 = $ F F (L + 1)7 " $ − LA " $ , P ≥ 3 @GH ' J ∈* + 11/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Algorithm • Input: Graph ! = ( " , # ) • Output: Node set of dense multipartite flow: $ • Key idea: priority tree and greedy deletion Step 1. initialize Step 2. greedy deletion Step 3. get the result 12/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Algorithm (cont.) ◦ Step 1. initialize § 1. generate the ! -partite graph, " ← $ , % & ← ' , … , % ()* ← ' , + ← , § 2. initialize subset - ← " ⋃% & ⋃ … ⋃ M ()* ⋃ + § 3. calculate the priority of node 8 2 3 S = 5 6 3 - − 8 + 1 ; 3 - , if ? 3 ∈ % A , B ∈ {1, 2, … , ! − 2} ; 3 - = F 3 - , if ? 3 ∈ " ⋃ + § 4. build priority tree for S with 2 3 S Outer account( # ) Inner account( " ) Priority tree Outer account( ! ) Inner account( " ) 20 10 10 20 10 10 1 1 2 13/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Algorithm (cont.) ◦ Step 2. greedy deletion § 1. get the node ! with minimum weight § 2. delete the selected node, update the value of " # and update node’s weight that corelated with ! § 3. repeat 1 and 2 until one of $, & ' , … , & )*+ , , is empty Update priority of node Outer account( # ) Inner account( " ) 0 Outer account( ! ) 20 Inner account( " ) 4 10 10 20 0 40 20 0 0 40 ∞ 20 4 10 10 ∞ 20 0 4 0 40 ∞ ∞ 2 1 1 0.2 2 20 20 0 4 4 ∞ 0 0 40 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 1 1 40 4 4 0.2 Delete minimum 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 weighted node A M C 0.2 Update " # 5.5 0.2 40 5.3 2 0.2 40 ∞ Density 5.1 20 2 0.2 1 40 ∞ ∞ ∞ 4.9 20 20 2 4 4 0.2 1 1 40 ∞ ∞ ∞ ∞ ∞ ∞ ∞ new ! ( " ) after 4.7 the first deletion 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 4.5 0 1 2 3 4 5 6 7 8 9 M A C Iteration 14/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Algorithm (cont.) ◦ Step 3. get the result § 1. find the maximum value of ! " § 2. recover correspond node set Ŝ corresponding to maximum ! " 9 8 Outer account( # ) Inner account( " ) 7 6 Outer account ( ! ) Density Inner account ( " ) 5 Recover Ŝ 20 10 10 4 maximum of 3 20 10 10 2 ! " ： 8 1 1 1 2 0 0 1 2 3 4 5 6 7 8 9 Result Ŝ: Iteration $ : {0,1}, % # # & : {0,1}, ' : {2} 15/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Algorithm (cont.) • Theorem [Approximation Guarantee] ◦ in 3-step ML (tripartite) middle counts in # ʹ g ( Ŝ ) ≥ Ｍ ’ # ’ ( g ( # *) - $% ) amount of camouflage FlowScope transfers node set just before the optimal first optimal node removed Properties of FlowScope: Fast : runs in near-linear time Accurate : provides an accuracy guarantee Effective : produces meaningful results in practice 0 16/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Real-world performance FlowScope Wins With ground-truth labelled Performance on synthetic data 17/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Effectiveness: one middle layer Good performance under variety of topologies 18/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Effectiveness: one middle layer (cont.) Summary in table s n i W e p o c S w o l F 19/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Robustness against longer transfer chains 20/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Effectiveness: varies topologies and labelled data Properties of FlowScope: Fast : runs in near-linear time Accurate : provides an accuracy guarantee Effective : produces meaningful results in practice 0 21/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Sensitivity and Scalability FlowScope is robustness to FlowScope runs in near-linear parameter time with the # of edges 22/28 FlowScope: Spotting Money Laundering Based on Graphs
Introduction Model Algorithm Experiments Conclusion Conclusion • FlowScope detects money laundering fast and effectively Accurate Fast g ( Ŝ ) = Ｍ ’ " ’ ( g ( " *) - #$ ) Reproducible Effective https://github.com/aplaceof/FlowScope 24/28 FlowScope: Spotting Money Laundering Based on Graphs
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