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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.IEEE TRANSACTIONS ON DEPEDABLE AND SECURE COMPUTINGvalue for the ST approach has become negative even for μ = 0.5. For our approach, the TP-FPvalue became negative only after μ = 2.5.80TP_OA TP_ST FP_OA FP_STTP and FP (%)60402000.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Malicious Transaction Distribution Mean8(a)TP - FP Spread andAccuracy (%)100806040200-200.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0-40SP_OA SP_ST AC_OA AC_STMalicious Transaction Distribution Mean8(b)Figure 8. Performance variation of the two systems (OA and ST) with Mean (μ) of MaliciousTransaction Distribution for mixed profile (a) TP and FP (b) TP-FP spread (SP) and Accuracy(AC)From the above results, it can be concluded that the proposed system has an overall Accuracy of80% even under large input condition variations, which is much higher than the overall Accuracyof the method proposed by Stolfo et al [6]. Our system can, therefore, correctly detect most ofthe transactions. However, when there is no profile information at all, the system shows some29
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.IEEE TRANSACTIONS ON DEPEDABLE AND SECURE COMPUTINGperformance degradation in terms of TP-FP. This observation highlights the importance ofprofile selection as explained in Section 4. Also, when there is little difference between genuinetransactions and malicious transactions, most of the credit card fraud detection systems sufferperformance degradation, either due to a fall in the number of true positives or a rise in thenumber of false positives.6. CONCLUSIONS AND DISCUSSIONSIn this paper, we have proposed an application of Hidden Markov Model in credit card frauddetection. The different steps in credit card transaction processing are represented as theunderlying stochastic process of an HMM. We have used the ranges of transaction amount as theobservation symbols, while the types of item have been considered to be states of the HMM. Wehave suggested a method for finding the spending profile of cardholders as well as application ofthis knowledge in deciding the value of observation symbols and initial estimate of the modelparameters. It has also been explained how the HMM can detect whether an incomingtransaction is fraudulent or not. Experimental results show the performance and effectiveness ofour system and demonstrate the usefulness of learning the spending profile of the cardholders.Comparative studies reveal that the Accuracy of the system is close to 80% over a wide variationin the input data. The system is also scalable for handling large volumes of transactions.ACKNOWLEDGMENTSWe are thankful to the anonymous reviewers for their constructive and useful comments. This work ispartially supported by a research grant from the Department of Information Technology, Ministry ofCommunication and Information Technology, Government of India, under Grant No. 12(34)/04-IRSDdated 07/12/2004.30
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