Interaction of two systems with saddle-node bifurcations on invariant circles. I. Foundations and the mutualistic case

The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system. It governs the transition from resting behaviour to periodic spiking in many class I neurons, for example. Here, as a first step towards theory of networks of such units the effect of weak coupling between two systems with a SNIC is analysed. Two crucial parameters of the coupling are identified, which we call \delta_1 and \delta_2. Global bifurcation diagrams are obtained here for the "mutualistic" case \delta_1 \delta_2 > 0. According to the parameter regime, there may coexist resting and periodic attractors, and there can be quasiperiodic attractors of torus or cantorus type, making the behaviour of even such a simple system quite non-trivial. In a second paper we will analyse the mixed case \delta_1 \delta_2 < 0 and summarise the conclusions of this study.Comment: 37 pages, 27 figure

ITER: An algorithm for predictive regression rule extraction. Data warehousing and knowledge discovery. Proceedings.

Various benchmarking studies have shown that artificial neural networks and support vector machines have a superior performance when compared to more traditional machine learning techniques. The main resistance against these newer techniques is based on their lack of interpretability: it is difficult for the human analyst to understand the motivation behind these models' decisions. Various rule extraction techniques have been proposed to overcome this opacity restriction. However, most of these extraction techniques are devised for classification and only few algorithms can deal with regression problems.

Modeling customer loyalty using customer lifetime value.

The definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution will be to redefine the notion of customer's loyalty by considering it from a customer-centric point-of-view instead of a product-centric point-of-view. We will hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer's activity. Hence, a churner will be defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease will be used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we will compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classirfiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures or prediction need to be revised and a more profit oriented focus may be desirable.Churn prediction; Classification; Customer lifetime value; Prediction models;

Post-processing of association rules.

In this paper, we situate and motivate the need for a post-processing phase to the association rule mining algorithm when plugged into the knowledge discovery in databases process. Major research effort has already been devoted to optimising the initially proposed mining algorithms. When it comes to effectively extrapolating the most interesting knowledge nuggets from the standard output of these algorithms, one is faced with an extreme challenge, since it is not uncommon to be confronted with a vast amount of association rules after running the algorithms. The sheer multitude of generated rules often clouds the perception of the interpreters. Rightful assessment of the usefulness of the generated output introduces the need to effectively deal with different forms of data redundancy and data being plainly uninteresting. In order to do so, we will give a tentative overview of some of the main post-processing tasks, taking into account the efforts that have already been reported in the literature.

A modified Pareto/NBD approach for predicting customer lifetime value.

Valuing customers is a central issue for any commercial activity. The customer lifetime value (CLV) is the discounted value of the future profits that this customer yields to the company. In order to compute the CLV, one needs to predict the future number of transactions a customer will make and the profit of these transactions. With the Pareto/NBD model, the future number of transactions of a customer can be predicted, and the CLV is then computed as a discounted product between this number and the expected profit per transaction. Usually, the number of transactions and the future profits per transaction are estimated separately. This study proposes an alternative. We show that the dependence between the number of transactions and their profitability can be used to increase the accuracy of the prediction of the CLV. This is illustrated with a new empirical case from the retail banking sector.Customer lifetime value; Value; Yield; Companies; Order; Model; Product; Expected;

Using rule extraction to improve the comprehensibility of predictive models.

Whereas newer machine learning techniques, like artifficial neural net-works and support vector machines, have shown superior performance in various benchmarking studies, the application of these techniques remains largely restricted to research environments. A more widespread adoption of these techniques is foiled by their lack of explanation capability which is required in some application areas, like medical diagnosis or credit scoring. To overcome this restriction, various algorithms have been proposed to extract a meaningful description of the underlying `blackbox' models. These algorithms' dual goal is to mimic the behavior of the black box as closely as possible while at the same time they have to ensure that the extracted description is maximally comprehensible. In this research report, we first develop a formal definition of`rule extraction and comment on the inherent trade-off between accuracy and comprehensibility. Afterwards, we develop a taxonomy by which rule extraction algorithms can be classiffied and discuss some criteria by which these algorithms can be evaluated. Finally, an in-depth review of the most important algorithms is given.This report is concluded by pointing out some general shortcomings of existing techniques and opportunities for future research.Models; Model; Algorithms; Criteria; Opportunities; Research; Learning; Neural networks; Networks; Performance; Benchmarking; Studies; Area; Credit; Credit scoring; Behavior; Time;

A modified Pareto/NBD approach for predicting customer lifetime value.

Systems; Applications; Customer lifetime value; Value;

Modeling churn using customer lifetime value.

The definition and modeling of customer loyalty have been central issues in customer relationship management since many years. Recent papers propose solutions to detect customers that are becoming less loyal, also called churners. The churner status is then defined as a function of the volume of commercial transactions. In the context of a Belgian retail financial service company, our first contribution is to redefine the notion of customer loyalty by considering it from a customer-centric viewpoint instead of a productcentric one. We hereby use the customer lifetime value (CLV) defined as the discounted value of future marginal earnings, based on the customer's activity. Hence, a churner is defined as someone whose CLV, thus the related marginal profit, is decreasing. As a second contribution, the loss incurred by the CLV decrease is used to appraise the cost to misclassify a customer by introducing a new loss function. In the empirical study, we compare the accuracy of various classification techniques commonly used in the domain of churn prediction, including two cost-sensitive classifiers. Our final conclusion is that since profit is what really matters in a commercial environment, standard statistical accuracy measures for prediction need to be revised and a more profit oriented focus may be desirable.Data mining; Decision support systems; Marketing; Churn prediction;