Many fraud analysis systems have at their heart a rule-based engine for generating alerts about suspicious behaviors.The rules in the system are usually based on expert knowledge.Automatic rule discovery aims at using past examples of fraudulent and legitimate usage to find new patterns and rules to help distinguish between the two.Some aspects of the problem of finding rules suitable for fraud analysis make this problem unique.Among them are the following: the need to find rules combining both the properties of the customer (e.g., credit rating) and properties of the specific "behavior" which indicates fraud (e.g., number of international calls in one day); and the need for a new definition of accuracy: We need to find rules which do not necessarily classify correctly each individual "usage sample" as either fraudulent or not, but ensure the identification, with a minimum of wasted cost and effort, of most of the fraud "cases" (i.e., defrauded customers).These aspects require a special-purpose rule discovery system.We present as an example a two-stage system based on adaptation of the C4.5 rule generator, with an additional rule selection mechanism.Our experimental results indicate that this route is very promising.

Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an improvement to the standard local activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm, called activate, is uniform and does not assume that the network is tree-like. It can identify tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid local minima along these trees. For acyclic networks, the algorithm is guaranteed to converge to a global minimum from any initial state of the system (self-stabilization) and remains correct under various types of schedulers. On the negative side, we show that in the presence of cycles, no uniform algorithm exists that guarantees optimality even under a sequential asynchronous scheduler. An asynchronous scheduler can activate only one unit at a time while a synchronous scheduler can activate any number of units in a single time step. In addition, no uniform algorithm exists to optimize even acyclic networks when the scheduler is synchronous. Finally, we show how the algorithm can be improved using the cycle-cutset scheme. The general algorithm, called activate-with-cutset, improves over activate and has some performance guarantees that are related to the size of the network's cycle-cutset.

Connectionist networks with symmetric weights (like Hopfield networks and Boltzmann Machines) use gradient descent to find a minimum for quadratic energy functions. We show equivalence between the problem of satisfiability in propositional calculus and the problem of minimizing those energy functions. The equivalence is in the sense that for any satisfiable well-formed formula (WFF) we can find a quadratic function that describes it, such that the set of solutions that minimizes the function is equal to the set of truth assignments that satisfy the WFF. We also show that in the same sense every quadratic energy function describes some satisfiable WFF. Algorithms are given to transform any propositional WFF into an energy function that describes it and vice versa. High-order models that use sigma-pi units are shown to be equivalent to the standard quadratic models with additional hidden units. An algorithm to convert high-order networks to low-order ones is used to implement a satisfiability problem-solver on a connectionist network. The results give better understanding of the role of hidden units and of the limitations and capabilities of symmetric connectionist models. The techniques developed for the satisfiability problem may be applied to a wide range of other problems, such as associative memories, finding maximal consistent subsets, automatic deduction, and even nonmonotonic reasoning.