This document discusses data analysis techniques for credit card fraud detection. It introduces logistic regression models for fraud prediction and evaluates their performance based on accuracy metrics and financial costs. Cost-sensitive logistic regression directly incorporates financial costs into the model training process, achieving lower total costs compared to models optimized for accuracy alone. In conclusion, fraud detection algorithms should evaluate and optimize models based on real financial impacts rather than traditional accuracy metrics.

1. Data Analysis for Credit Card
Fraud Detection
Alejandro Correa Bahnsen
Luxembourg University

2. Introduction
€ 500
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2007 2008 2009 2010 2011E 2012E
Europe fraud evolution
Internet transactions (millions of euros)

3. Introduction
$-
$1.0
$2.0
$3.0
$4.0
$5.0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
US fraud evolution
Online revenue lost due to fraud (Billions of dollars)

4. Simplify transaction flow
Fraud??
Network

5. • Introduction
• Database
• Evaluation of algorithms
• Logistic Regression
• Financial measure
• Cost Sensitive Logistic Regression
Agenda

6. Database
• Larger European card processing
company
• 2012 card present transactions
• 750,000 Transactions
• 3500 Frauds
• 0.467% Fraud rate
• 148,562 EUR lost due to fraud on
test dataset
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
Jan
Test
Train

7. • Raw attributes
• Other attributes:
Age, country of residence, postal code, type of card
Database
TRXID Client ID Date Amount Location Type
Merchant
Group
Fraud
1 1 2/1/12 6:00 580 Lux Internet Airlines No
2 1 2/1/12 6:15 120 Lux Present Car Renting No
3 2 2/1/12 8:20 12 Bel Present Hotel Yes
4 1 3/1/12 4:15 60 Lux ATM ATM No
5 2 3/1/12 9:18 8 Fra Present Retail No
6 1 3/1/12 9:55 1210 Lux Internet Airlines Yes
7

8. • Derived attributes
Combination of
following criteria:
Database
ID
Num
CC
Date Amt Location Type
Merchant
Group
Fraud
No. of Trx –
same client –
last 6 hour
Sum – same
client – last 7
days
1 1 2/1/12 6:00 580 Lux Internet Airlines No 0 0
2 1 2/1/12 6:15 120 Lux Present Car Renting No 1 580
3 2 2/1/12 8:20 12 Bel Present Hotel Yes 0 0
4 1 3/1/12 4:15 60 Lux ATM ATM No 0 700
5 2 3/1/12 9:18 8 Fra Present Retail No 0 12
6 1 3/1/12 9:55 1210 Lux Internet Airlines Yes 1 760
By Group Last Function
Client None hour Count
Credit Card Transaction Type day Sum(Amount)
Merchant week Avg(Amount)
Merchant Category month
Merchant Group 1 3 months
Merchant Group 2
Merchant Country
8

9. • Misclassification = 1 −
𝑇𝑃+𝑇𝑁
𝑇𝑃+𝑇𝑁+𝐹𝑃+𝐹𝑁
• Recall =
𝑇𝑃
𝑇𝑃+𝐹𝑁
• Precision =
𝑇𝑃
𝑇𝑃+𝐹𝑃
• F-Score = 2
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 ∗ 𝑅𝑒𝑐𝑎𝑙𝑙
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+𝑅𝑒𝑐𝑎𝑙𝑙
Evaluation
True Class (𝑦𝑖)
Fraud (𝑦𝑖=1) Legitimate (𝑦𝑖=0)
Predicted class
(𝑝𝑖)
Fraud (𝑝𝑖=1) TP FP
Legitimate (𝑝𝑖=0) FN TN
• Confusion matrix

10. • Introduction
• Database
• Evaluation of algorithms
• Logistic Regression
• Financial measure
• Cost Sensitive Logistic Regression
Agenda

11. True Class (𝑦𝑖)
Fraud (𝑦𝑖=1) Legitimate (𝑦𝑖=0)
Predicted class
(𝑝𝑖)
Fraud (𝑝𝑖=1) 0 1
Legitimate (𝑝𝑖=0) 1 0
• Model
• Cost Function
• Cost Matrix
Logistic Regression

12. 1% 5% 10% 20% 50%
Logistic Regression
Under sampling procedure
0.467%
Select all the frauds and a random sample of the legitimate transactions.

13. Logistic Regression
Results
0%
10%
20%
30%
40%
50%
60%
70%
No Model All 1% 5% 10% 20% 50%
Recall Precision Miss-cla F1-Score

14. • Motivation
• False positives carry a different cost than false
negatives
• Frauds range from few to thousands of euros
(dollars, pounds, etc)
Financial evaluation
There is a need for a real comparison measure

15. • Cost matrix
where:
Financial evaluation
Ca Administrative costs
Amt Amount of transaction i
True Class (𝑦𝑖)
Fraud (𝑦𝑖=1) Legitimate (𝑦𝑖=0)
Predicted class
(𝑝𝑖)
Fraud (𝑝𝑖=1) Ca Ca
Legitimate (𝑝𝑖=0) Amt 0
• Evaluation measure

16. Logistic Regression
Results
€ 148,562€ 148,196€ 142,510
€ 112,103
€ 79,838
€ 65,870
€ 46,530
€ -
€ 20,000
€ 40,000
€ 60,000
€ 80,000
€ 100,000
€ 120,000
€ 140,000
€ 160,000
0%
10%
20%
30%
40%
50%
60%
70%
No Model All 1% 5% 10% 20% 50%
Cost Recall Precision F1-Score
Selecting the algorithm by F1-Score
Selecting the algorithm by Cost

17. Logistic Regression
• Best model selected using traditional F1-Score does not give
the best results in terms of cost
• Model selected by cost, is trained using less than 1% of the
database, meaning there is a lot of information excluded
• The algorithm is trained to minimize the miss-classification
(approx.) but then is evaluated based on cost
• Why not train the algorithm to minimize the cost instead?

18. True Class (𝑦𝑖)
Fraud (𝑦𝑖=1) Legitimate (𝑦𝑖=0)
Predicted class
(𝑝𝑖)
Fraud (𝑝𝑖=1) Ca Ca
Legitimate (𝑝𝑖=0) Amt 0
• Cost Matrix
Cost Sensitive Logistic Regression
• Cost Function
• Objective
Find 𝜃 that minimized the cost function (Genetic Algorithms)

19. € 148,562
€ 31,174
€ 37,785
€ 66,245 € 67,264
€ 73,772
€ 85,724
€ -
€ 20,000
€ 40,000
€ 60,000
€ 80,000
€ 100,000
€ 120,000
€ 140,000
€ 160,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
No
Model
All 1% 5% 10% 20% 50%
Cost Recall Precision F1-Score
Cost sensitive Logistic Regression
Results

20. Cost sensitive Logistic Regression
Results
€ 148,562
€ 46,530
€ 31,174
€ -
€ 20,000
€ 40,000
€ 60,000
€ 80,000
€ 100,000
€ 120,000
€ 140,000
€ 160,000
0%
10%
20%
30%
40%
50%
60%
70%
80%
No Model Logistic Regression Cost Sensitive
Logistic Regression
Cost Recall Precision F1-Score

21. Conclusion
• Selecting models based on traditional statistics does not
give the best results in terms of cost
• Models should be evaluated taking into account real
financial costs of the application
• Algorithms should be developed to incorporate those
financial costs

22. Thank you!

23. Contact information
Alejandro Correa Bahnsen
University of Luxembourg
Luxembourg
al.bahnsen@gmail.com
http://www.linkedin.com/in/albahnsen
http://www.slideshare.net/albahnsen