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Kriging surrogate model has demonstrated a powerful ability to be applied to a variety of engineering challenges by emulating time-consuming simulations. However, when it comes to problems with high-dimensional input variables, it may be difficult to obtain a model with high accuracy and efficiency due to the curse of dimensionality. To meet this challenge, an improved high-dimensional Kriging modeling method based on maximal information coefficient (MIC) is developed in this work.

The hyperparameter domain is first derived and the dataset of hyperparameter and likelihood function is collected by Latin Hypercube Sampling. MIC values are innovatively calculated from the dataset and used as prior knowledge for optimizing hyperparameters. Then, an auxiliary parameter is introduced to establish the relationship between MIC values and hyperparameters. Next, the hyperparameters are obtained by transforming the optimized auxiliary parameter. Finally, to further improve the modeling accuracy, a novel local optimization step is performed to discover more suitable hyperparameters.

The proposed method is then applied to five representative mathematical functions with dimensions ranging from 20 to 100 and an engineering case with 30 design variables.

The results show that the proposed high-dimensional Kriging modeling method can obtain more accurate results than the other three methods, and it has an acceptable modeling efficiency. Moreover, the proposed method is also suitable for high-dimensional problems with limited sample points.

Internet marketing underground industry users refer to people who use technology means to simulate a large number of real consumer behaviors to obtain marketing activities rewards illegally, which leads to increased cost of enterprises and reduced effect of marketing. Therefore, this paper aims to construct a user risk assessment model to identify potential underground industry users to protect the interests of real consumers and reduce the marketing costs of enterprises.

Method feature extraction is based on two aspects. The first aspect is based on traditional statistical characteristics, using density-based spatial clustering of applications with noise clustering method to obtain user-dense regions. According to the total number of users in the region, the corresponding risk level of the receiving address is assigned. So that high-quality address information can be extracted. The second aspect is based on the time period during which users participate in activities, using frequent item set mining to find multiple users with similar operations within the same time period. Extract the behavior flow chart according to the user participation, so that the model can mine the deep relationship between the participating behavior and the underground industry users.

Based on the real underground industry user data set, the features of the data set are extracted by the proposed method. The features are experimentally verified by different models such as random forest, fully-connected layer network, SVM and XGBOST, and the proposed method is comprehensively evaluated. Experimental results show that in the best case, our method can improve the F1-score of traditional models by 55.37%.

This paper investigates the relative importance of static information and dynamic behavior characteristics of users in predicting underground industry users, and whether the absence of features of these categories affects the prediction results. This investigation can go a long way in aiding further research on this subject and found the features which improved the accuracy of predicting underground industry users.