Detecting credit card fraud by Modified Fisher Discriminant Analysis

• We introduce Fisher Linear Discriminant Analysis (FLDA).
• We modify it to be sensitive toward profitable instances.
• We applied them together in credit card fraud detection problem.
• The results are compared in terms of total obtained profit with three well-known models.
• Modified fisher outperforms the other models in attaining high profit.

In parallel to the increase in the number of credit card transactions, the financial losses due to fraud have also increased. Thus, the popularity of credit card fraud detection has been increased both for academicians and banks. Many supervised learning methods were introduced in credit card fraud literature some of which bears quite complex algorithms. As compared to complex algorithms which somehow over-fit the dataset they are built on, one can expect simpler algorithms may show a more robust performance on a range of datasets. Although, linear discriminant functions are less complex classifiers and can work on high-dimensional problems like credit card fraud detection, they did not receive considerable attention so far. This study investigates a linear discriminant, called Fisher Discriminant Function for the first time in credit card fraud detection problem. On the other hand, in this and some other domains, cost of false negatives is very higher than false positives and is different for each transaction. Thus, it is necessary to develop classification methods which are biased toward the most important instances. To cope for this, a Modified Fisher Discriminant Function is proposed in this study which makes the traditional function more sensitive to the important instances. This way, the profit that can be obtained from a fraud/legitimate classifier is maximized. Experimental results confirm that Modified Fisher Discriminant could eventuate more profit.