Fraud - Consequences of Cutting Edge Solutions
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1 Detection using Peer Group analysis David Weston, Niall Adams, David Hand, Christopher Whitrow, Piotr Juszczak 19 September, /09/07 1 / 69
2 EPSRC Think Crime Peer Group Crime Prevention & Detection Funding 12 projects Also feasibilty studies and more Think Crime Project Develop Fraud Detection Tools Real Data 19/09/07 2 / 69
3 ThinkCrime Team Peer Group Members of the team are David Hand Niall Adams Christopher Whitrow Piotr Juszczak David Weston Gordon Blunt Collaborating banks Abbey National, Alliance and Leicester, Capital One, Lloyds TSB 19/09/07 3 / 69
4 Overview Peer Group Peer Group Applied to Time-Aligned Multivariate Continuous Data Peer Group Applied to Credit Card Transaction Data 19/09/07 4 / 69
5 Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group 19/09/07 5 / 69
6 Consequences of Fraud Consequences of Fraud Financial Consequences Financial Consequences UK: 428.0m Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group 19/09/07 6 / 69
7 Consequences of Fraud Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group Financial Consequences Financial Consequences UK: 428.0m Consumer Consequences Customer Inconvenience Fraud Detection Transactions falsely flagged as fraudulent 19/09/07 6 / 69
8 Patterns Of Fraud Fraud evolves to evade detection Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group 19/09/07 7 / 69
9 Patterns Of Fraud Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Fraud evolves to evade detection APACS 14/03/07 UK card fraud 309.8m ( 13%) Fraud abroad 118.2m (+43%) Peer Group 19/09/07 7 / 69
10 Patterns Of Fraud Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group Fraud evolves to evade detection APACS 14/03/07 UK card fraud 309.8m ( 13%) Fraud abroad 118.2m (+43%) The introduction of chip and PIN has made it more difficult for fraudsters to commit card fraud in the UK... create counterfeit magnetic stripe cards that can potentially be used in countries that haven t upgraded to chip and PIN. This has caused the increase in fraud abroad losses over the last 12 months. 19/09/07 7 / 69
11 Determining when Fraud has occurred Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Issuing Bank determines if fraud has taken place Can take several months Not necessarily correct Peer Group 19/09/07 8 / 69
12 Determining when Fraud has occurred Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Issuing Bank determines if fraud has taken place Can take several months Not necessarily correct Bad Debt Bankruptcy Peer Group 19/09/07 8 / 69
13 Determining when Fraud has occurred Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Issuing Bank determines if fraud has taken place Can take several months Not necessarily correct Bad Debt Bankruptcy Friendly Fraud Peer Group 19/09/07 8 / 69
14 Determining when Fraud has occurred Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group Issuing Bank determines if fraud has taken place Can take several months Not necessarily correct Bad Debt Bankruptcy Friendly Fraud 2001 US Banker magazine: over half online fraudulent transactions Account Holder declares a transaction they have performed is fraudulent 19/09/07 8 / 69
15 Challenges of Fraud Detection Fraud Evolution Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group 19/09/07 9 / 69
16 Challenges of Fraud Detection Consequences of Fraud Patterns Of Fraud Determining when Fraud has occurred Challenges of Fraud Detection Peer Group Fraud Evolution Data streams Timeliness Online System Back Office Imbalanced Classes Fraud as % of total value of number of transactions % (credit card, Australia) 19/09/07 9 / 69
17 Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Group 19/09/07 10 / 69
18 Approaches to Fraud Detection Broadly 2 approaches to statistical fraud detection Supervised or Anomaly Detection Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Group 19/09/07 11 / 69
19 Approaches to Fraud Detection Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Broadly 2 approaches to statistical fraud detection Supervised or Anomaly Detection Supervised Historical Instances of Fraud Less likely to falsely flag a transaction as fraudulent Approach Chris is taking Peer Group 19/09/07 11 / 69
20 Anomaly Detection Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Does not use historical Instances of Fraud Build a profile of usual behaviour Significant deviations considered as potential frauds More likely to falsely flag a transaction as fraudulent Potential to adapt to changing fraud patterns Approach Piotr is taking Peer Group 19/09/07 12 / 69
21 Peer Group Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Similar to anomaly detection methods Do not need to build a model of usual behaviour for account holder Determine a peer group Find other accounts that you expect will behave similarly to the account holder Find accounts that have behaved similarly in the past Monitor account holder s behaviour with respect to peer group Anomalous behaviour, should account holder deviate strongly from peer group Peer Group 19/09/07 13 / 69
22 Anomaly Detection to Peer Groups I Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example The weekly amount spent on a credit card for a particular account Week 1 to Week n y 1,...,y n 1,y n Target Account Wish to determine if the amount spent in week n is anomalous Anomaly Detection based on account profile y 1 y 2 y n 1 y n Peer Group 19/09/07 14 / 69
23 Anomaly Detection to Peer Groups II Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Population Normalised Anomaly Detection x m,1 x m,2 x m,n 1 x m,n. x 2,1 x 2,2 x 2,n 1 x 2,n x 1,1 x 1,2 x 1,n 1 x 1,n y 1 y 2 y n 1 y n Peer Group 19/09/07 15 / 69
24 Anomaly Detection to Peer Groups III Approaches to Fraud Detection Anomaly Detection Peer Group Anomaly Detection to Peer Groups I Anomaly Detection to Peer Groups II Anomaly Detection to Peer Groups III Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Groups Example Peer Group Sort accounts in order of decreasing similarity, π(i) x π(m),1 x π(m),2 x π(m),n 1 x π(m),n. x π(k),1 x π(k),2 x π(k),n 1 x π(k),n. x π(2),1 x π(2),2 x π(2),n 1 x π(2),n x π(1),1 x π(1),2 x π(1),n 1 x π(1),n y 1 y 2 y n 1 y n Peer Group size k. 19/09/07 16 / 69
25 Peer Groups Example /09/07 17 / 69
26 Peer Groups Example /09/07 18 / 69
27 Peer Groups Example /09/07 19 / 69
28 Peer Groups Example /09/07 20 / 69
29 Peer Groups Example /09/07 21 / 69
30 Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Peer Group Quality Whitening the Population 19/09/07 22 / 69
31 Detecting Anomalies Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Assuming we already have a peer group set of accounts for our target account. y n is multivariate (column vector) and continuous Mahalanobis distance of the target from the mean of its peer group µ is mean of x π(1),n,...,x π(k),n C is covariance matrix of x π(1),n,...,x π(k),n Mahalanobis distance of a target from its peer group (y n µ) T C 1 (y n µ) 19/09/07 23 / 69
32 Detecting Anomalies If the distance is above an externally selected threshold, then we flag the target as fraudulent. Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Peer Group Target /09/07 24 / 69
33 Robustifying Peer Groups Peer Group contaminated by fraudulent transactions Outlier Masking Outlier Swamping Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Peer Group Target /09/07 25 / 69
34 Robustifying Peer Groups Robustify the covariance matrix for the Mahalanobis Distance evaluation Use Heuristic Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population 19/09/07 26 / 69
35 Robustifying Peer Groups Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Robustify the covariance matrix for the Mahalanobis Distance evaluation Use Heuristic An account that has deviated strongly from its peer group at time t should not contribute to any peer group at time t 19/09/07 26 / 69
36 Robustifying Peer Groups Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Robustify the covariance matrix for the Mahalanobis Distance evaluation Use Heuristic An account that has deviated strongly from its peer group at time t should not contribute to any peer group at time t For each peer group select p% closest to their own peer groups 19/09/07 26 / 69
37 Peer Group Quality Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population It is not necessarily the case that peer group analysis can be successfully deployed on all accounts. q t = 1 k k (y t x π(i),t ) T (y t x π(i),t ) (1) i=1 where T is the transpose. This is a simple measure of how close the members of the peer group are to the target. A good quality peer group is one that closely follows the target over time. Q s,e = 1 t e t s t e t=t s q t. (2) 19/09/07 27 / 69
38 Whitening the Population Whitening the population to make the scatter of a peer group (of size 2) commensurate across time The smaller the value of Q s,e the better the peer group tracks the target over time. Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Members Population Target Peer Group Quality Whitening the Population t=1 t=2 t=3 19/09/07 28 / 69
39 Building Peer Groups Peer Group Detecting Anomalies Detecting Anomalies Robustifying Peer Groups Robustifying Peer Groups Peer Group Quality Whitening the Population Possible to know apriori the peer group membership Employee fraud detection, people with the same job description can be naturally grouped together. IBM FAMS. Health care fraud. Geography, speciality Infer peer group membership from the time series itself Measuring similarity of time series 19/09/07 29 / 69
40 Peer Group Real Data Transaction Details Merchant Category Codes 19/09/07 30 / 69
41 Real Data Peer Group Real credit card transaction history 4 month period Selected approximately 50,000 accounts No static data about the account holder Each account is a list of transactions Real Data Transaction Details Merchant Category Codes 19/09/07 31 / 69
42 Transaction Details Peer Group Real Data Transaction Details Merchant Category Codes Each Transaction is a record that includes Amount Time transaction took place Type of transaction, e.g. change pin code ATM or POS Card present / not present A Fraud flag was provided that gave the date (to the nearest day) when fraudulent behaviour began. 19/09/07 32 / 69
43 Merchant Category Codes Peer Group Real Data Transaction Details Merchant Category Codes Identify in which market segment the transaction was performed For example Book stores 4 digit number Fewer than 10,000 codes in use Merchant Category Groups 19/09/07 33 / 69
44 Peer Group Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts 19/09/07 34 / 69
45 Time Alignment & Feature Extraction Peer Group Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts Accounts transactions are asynchronous data streams Synchronise account time series by extracting features from the data streams at regular time intervals M(s, e, A) summarise transactions of account A occurring from day s to day e inclusive Mean amount spent Number of transactions Entropy of Merchant Category Groups 16 Groups +1 for ATMs Returns 1 point in 3 dimensional space 19/09/07 35 / 69
46 Time Alignment & Feature Extraction 100 Account A Amount Withdrawn Amount Withdrawn Day M(7,10,A) Account B Day M(7,10,B) 19/09/07 36 / 69
47 Outlier Detection from Peer Groups Peer Group Once a day at midnight Summary statistic for day t, behaviour of the past d days M(t d + 1,t,A) Smaller d, the more sensitive to new transactions Mahalanobis distance in 3 dimensional space Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts 19/09/07 37 / 69
48 Active and Inactive Accounts Peer Group Account inactive on day t if it has not performed any transactions on that day Do not test for outlierness for inactive accounts Unusually long periods of inactivity will not be considered fraudulent Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts 19/09/07 38 / 69
49 Active and Inactive Accounts Peer Group Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts Account inactive on day t if it has not performed any transactions on that day Do not test for outlierness for inactive accounts Unusually long periods of inactivity will not be considered fraudulent Account not active over entire summary statistic window Active peer group members. Closest k accounts that are active on at least one day of the summary statistic window 19/09/07 38 / 69
50 Building Peer Groups Peer Group Subdivide training data into n non-overlapping windows M(1, L n,a),...,m((n 1)L n + 1,L,A) Point in 3n dimensional space Complication, potential for bias Standardise each window by whitening Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts 19/09/07 39 / 69
51 Building Peer Groups 100 Account A Amount Withdrawn M(1,3 1 M(6 2 3,A) M(3 1 3,6 2 3,A) 3,10,A) 100 Account B Amount Withdrawn M(1,3 1 3,B) M(3 1 3,6 2 3,B) M(6 2 3,10,B) 19/09/07 40 / 69
52 Building Peer Groups Peer Group Find k nearest neighbours Large number of accounts Accounts that have high volume of transactions unlikely to be tracked by accounts with low volume First sort by number of transactions in training data Time Alignment & Feature Extraction Time Alignment & Feature Extraction Outlier Detection from Peer Groups Active and Inactive Accounts 19/09/07 41 / 69
53 Peer Group Performance Criteria Performance Metric Performance Curve Average Performance Curve 19/09/07 42 / 69
54 Performance Criteria Peer Group Reduce total amount lost to fraud Reduce number of fraudulent transactions Reduce the time between fraud starting and fraud detection Reduce the number of account holders affected by flagging legitimate transactions as fraud Number of possible performance metrics Performance Criteria Performance Metric Performance Curve Average Performance Curve 19/09/07 43 / 69
55 Performance Metric Peer Group Performance Criteria Performance Metric Performance Curve Average Performance Curve If an account has been flagged as containing fraudulent transactions. The card issuer would need to investigate this account. minimise the amount of fraud given the number of investigations the card company can make Performance Curve x-axis number of fraudulent accounts missed as a proportion of the number of fraudulent accounts y-axis number of fraud flags raised as a proportion of the number of accounts Different to ROC curve. The smaller the area under the curve the better the performance. Random classification is represented by a diagonal line from the top left to the bottom right. 19/09/07 44 / 69
56 Performance Curve 1 Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds not found The lower the curve the better the performance. Twice Area under Curve [0,1], smaller the area the better the performance 19/09/07 45 / 69
57 Average Performance Curve Produce one curve for each day Take the average of the curves. For a given proportion of fraud flags raised 1 Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds not found 19/09/07 46 / 69
58 Peer Group Experiments Effect of Fraud Contamination using an Oracle Effect of Fraud Contamination using an Oracle Varying Length of Summary Statistic 19/09/07 47 / 69 Window
59 Experiments Peer Group Data 4 months of data Accounts with > 80 transactions and fraud free for first 3 months. About 4000 accounts 6% defrauded in final month Performed Peer Group once a day for the remaining month Experiments Effect of Fraud Contamination using an Oracle Effect of Fraud Contamination using an Oracle Parameters Peer Group building 8 segments Summary Statistic window size 7 days Active Peer Group Size 100 Robustifying Peer Groups not used Varying Length of Summary Statistic 19/09/07 48 / 69 Window
60 Effect of Fraud Contamination using an Oracle With Fraud Contamination Twice Area Under Curve Peer Group Size 19/09/07 49 / 69
61 Effect of Fraud Contamination using an Oracle With Fraud Contamination Without Fraud Contamination Twice Area Under Curve Peer Group Size 19/09/07 50 / 69
62 Building Peer Groups The effect of changing the granularity of the description of the Peer Group building data. Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found 1 19/09/07 51 / 69
63 Building Peer Groups The effect of changing the granularity of the description of the Peer Group building data. Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found /09/07 52 / 69
64 Building Peer Groups The effect of changing the granularity of the description of the Peer Group building data. Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found /09/07 53 / 69
65 Building Peer Groups The effect of changing the granularity of the description of the Peer Group building data. Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found /09/07 54 / 69
66 Building Peer Groups The effect of changing the granularity of the description of the Peer Group building data. Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found /09/07 55 / 69
67 Varying Length of Summary Statistic Window day Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds not Found 19/09/07 56 / 69
68 Varying Length of Summary Statistic Window day 3 days Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds not Found 19/09/07 57 / 69
69 Varying Length of Summary Statistic Window Number of Fraud Flags Raised per Day as a Proportion of the Population day 3 days 5 days Proportion of Frauds not Found 19/09/07 58 / 69
70 Varying Length of Summary Statistic Window Number of Fraud Flags Raised per Day as a Proportion of the Population day 3 days 5 days 7 days Proportion of Frauds not Found 19/09/07 59 / 69
71 Varying Length of Summary Statistic Window Number of Fraud Flags Raised per Day as a Proportion of the Population day 3 days 5 days 7 days 14 days Proportion of Frauds not Found 19/09/07 60 / 69
72 Global Outlier Detector Is peer group analysis doing nothing more than finding outliers to the population? Special case, use largest possible peer group All accounts apart from target account Peer Group Experiments Effect of Fraud Contamination using an Oracle Effect of Fraud Contamination using an Oracle Varying Length of Summary Statistic 19/09/07 61 / 69 Window
73 Peer Groups Performance Non Robust Number of Fraud Flags Raised per Day as a Proportion of the Population Proportion of Frauds Not Found 19/09/07 62 / 69
74 Peer Groups Performance Number of Fraud Flags Raised per Day as a Proportion of the Population Non Robust Non Robust without Fraud Contamination Proportion of Frauds Not Found 19/09/07 63 / 69
75 Peer Groups Performance Number of Fraud Flags Raised per Day as a Proportion of the Population Non Robust Non Robust without Fraud Contamination Robust Proportion of Frauds Not Found 19/09/07 64 / 69
76 Peer Groups Performance Number of Fraud Flags Raised per Day as a Proportion of the Population Non Robust Non Robust without Fraud Contamination Robust Global Proportion of Frauds Not Found 19/09/07 65 / 69
77 Peer Groups Versus Global Outlier Detector Performance of the peer group analysis compared with global population outlier detector. Performance Difference Robustified Peer Group Peer Group Number of Fraud Flags Raised per Day as a Proportion of the Population 19/09/07 66 / 69
78 Peer Groups Versus Global Outlier Detector Performance of the robustified peer group analysis compared with global population outlier detector on screened data Performance Difference Number of Fraud Flags Raised per Day as a Proportion of the Population 19/09/07 67 / 69
79 Peer Group Conclusions 19/09/07 68 / 69
80 Conclusions Peer Group We have demonstrated there exist credit card transaction accounts that evolve sufficiently closely to enable fraudulent behaviour to be detected. Finding frauds that are not global outliers to the population. Current work Combining Methods Conclusions 19/09/07 69 / 69
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