Do you have any suggestions on the methods of data mining used by credit card companies?
Credit card companies have actively used data mining techniques to address a variety of problems. On the marketing side of the business, decision trees have been a popular choice for predicting customer acquisition and retention targets. On the fraud prevention side, neural networks are commonly used. There isn't a hard and fast rule about which algorithms to use to solve a particular problem; analysts usually employ a variety of techniques and then select the best model that solves the problem at hand. If you are looking at a problem and are trying to determine which method to use, my suggestion is to try several and then evaluate them to choose a winner. You might want to make your choice of data mining software based on the ability of the software to automatically explore the space of possible techniques and present you with the best one.
For more information, check out SearchCRM's Best Web Links on Data Mining.