For real-world customer classification data, data structures are often highly uncertain. The constructed models may not match the data structure characteristics, which can lead to unsatisfactory classification performance. Further, the class distribution characteristics of data sets are usually highly imbalanced, which can also weaken the classification performance. To solve the above problems, we construct a complex-valued group method of data handling (CGMDH) neural network-based data characteristic-driven adaptive decision support system. First, we introduce the linearly separable discriminant method to analyze the data structure characteristics. Second, we extend the circular linear CGMDH neural network model and propose a circular quadratic nonlinear CGMDH (QCGMDH) neural network model. Finally, according to the data structure characteristics and resampling technique, we adaptively select and train the most appropriate CGMDH neural network model from two types of CGMDH. To analyze the effectiveness of the constructed system, the experimental results of 16 real-valued classification data sets show both linearly separable discrimination and random oversampling technology can help to improve the classification performance. Further, to verify its customer classification performance, we conduct an empirical analysis on 14 real-valued customer classification data sets and find that its customer classification performance is significantly better than that of the other nine models and comparable to that of the circular QCGMDH neural network model.

The security of credit card fraud detection (CCFD) models based on machine learning is important but rarely considered in the existing research. To this end, we propose a black-box attack-based security evaluation framework for CCFD models. Under this framework, the semisupervised learning technique and transfer-based black-box attack are combined to construct two versions of a semisupervised transfer black-box attack algorithm. Moreover, we introduce a new nonlinear optimization model to generate the adversarial examples against CCFD models and a security evaluation index to quantitatively evaluate the security of them. Computing experiments on two real data sets demonstrate that, facing the adversarial examples generated by the proposed attack algorithms, all six supervised models considered largely lose their ability to identify the fraudulent transactions, whereas the two unsupervised models are less affected. This indicates that the CCFD models based on supervised machine learning may possess substantial security risks. In addition, the evaluation results for the security of the models generate important managerial implications that help banks reasonably evaluate and enhance the model security. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported in part by the National Natural Science Foundation of China [Grants 72171160 and 71988101], Key Program of National Natural Science Foundation of China and Quebec Research Foundation (NSFC-FRQ) Joint Project [Grant 7191101304], Key Program of NSFC-FRQSC Joint Project [Grant 72061127002], Excellent Youth Foundation of Sichuan Province [Grant 2020JDJQ0021], and National Leading Talent Cultivation Project of Sichuan University [Grant SKSYL2021-03]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1297 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0076 ) at ( http://dx.doi.org/10.5281/zenodo.7631457 ).

Recently, applications of complex-valued neural networks (CVNNs) to real-valued classification problems have attracted significant attention. However, most existing CVNNs are black-box models with poor explanation performance. This study extends the real-valued group method of data handling (RGMDH)-type neural network to the complex field and constructs a circular complex-valued group method of data handling (C-CGMDH)-type neural network, which is a white-box model. First, a complex least squares method is proposed for parameter estimation. Second, a new complex-valued symmetric regularity criterion is constructed with a logarithmic function to represent explicitly the magnitude and phase of the actual and predicted complex output to evaluate and select the middle candidate models. Furthermore, the property of this new complex-valued external criterion is proven to be similar to that of the real external criterion. Before training this model, a circular transformation is used to transform the real-valued input features to the complex field. Twenty-five real-valued classification data sets from the UCI Machine Learning Repository are used to conduct the experiments. The results show that both RGMDH and C-CGMDH models can select the most important features from the complete feature space through a self-organizing modeling process. Compared with RGMDH, the C-CGMDH model converges faster and selects fewer features. Furthermore, its classification performance is statistically significantly better than the benchmark complex-valued and real-valued models. Regarding time complexity, the C-CGMDH model is comparable with other models in dealing with the data sets that have few features. Finally, we demonstrate that the GMDH-type neural network can be interpretable.