Digital marketing program design based on abnormal consumer behavior data classification and improved homomorphic encryption algorithm

Classification of consumption data based on improved Catboost

In order to effectively classify online consumer abnormal behavior data, this study employs a CatBoost-RBF-based method. CatBoost is utilized to address the primary challenge of enhancing the efficiency and accuracy of the classification function. By avoiding overfitting during the calculation of leaf nodes, CatBoost improves the algorithm’s generalization capability and ensures effective learning and prediction on the entire dataset (Hancock & Khoshgoftaar, 2020). The sample training set undergoes testing by randomly shuffling the sample data features and converting classification features into data value features, as illustrated in Eq. (1): (1)${\displaystyle x_{i,k}=\frac{\sum _{j=1}^{p-1}\left[x_{{\sigma }_{j,k}}=x_{{\sigma }_{p,k}}\right]\cdot Y_j+a\cdot p}{\sum _{j=1}^{p-1}\left[x_{{\sigma }_{j,k}}=x_{{\sigma }_{p,k}}\right]+a}}$ where p denotes the average target value in the dataset, a denotes the weighting factor. x_σj,k, x_σp,k and Y _j denote the average target value in the training sample k of σ_j − th and σ_p − th feature. The CatBoost algorithm utilizes a symmetric decision tree structure and transforms processable class features into processed label values. By combining features during partitioning, it effectively addresses data bias issues and optimizes the model using ranking boosting techniques.

The CatBoost algorithm is based on BoostingTree and employs a unique approach to calculating leaf node values. It utilizes oblivious trees as the basic predictor and constructs nodes layer by layer using complete binary trees (Chen & Han, 2021). This approach allows for efficient storage of all leaf nodes and enables effective mining of the original data to generate new classification features. These features serve as input data for RBF neural networks, significantly improving the learning efficiency while mitigating the risk of overfitting (Gopi, Jyothi & Narayana, 2023). As shown in Fig. 2. The training process of the CatBoost-RBF fusion model involves feature crossover operations. In this study, GridSearch is utilized to fine-tune the parameters of CatBoost, ensuring optimal performance. The leaf nodes obtained after CatBoost training are saved, and the output layer produces the probability of user repurchase behavior.

The process of classifying and identifying abnormal online consumer behavior data involves several stages. In the first stage, feature extraction is performed on the original data. Initially, consumer features are extracted, followed by the application of principal component analysis to analyze these features. This analysis aids in reducing the initial feature set to an optimized number of features. Subsequently, a self-encoder network is utilized to compress the initial feature set, resulting in a compressed feature set. Transitioning to the second stage, the sample set that has undergone dimensionality reduction is used to construct a classification model for abnormal online consumer behavior data. The model’s parameters are fine-tuned using the grid search method. The evaluation index is then employed to identify the most suitable model. Finally, the chosen model is applied to classify and identify the abnormal online consumer behavior dataset, yielding the final classification results for such data.

A self-encoder typically refers to a neural network comprising three layers. However, when performing dimensionality reduction with a self-encoder, it’s crucial to ensure effective utilization of the output feature data in subsequent modeling tasks. Yet, a basic three-layer network can be sensitive to the initially set artificial values, potentially impacting the output feature data. To address this, the article employs the stacked self-encoder method, involving training the layers sequentially. The parameters learned from the self-encoding transformation between two layers are used as starting values for subsequent layers. This approach results in more stable feature data output from the network. Given the resource-intensive nature of training multi-layer neural networks and the low dimensionality of the data in this study, a stacked self-encoder structure with only two layers of encoders is adopted.

Improved homomorphic encryption algorithm

When the traditional homomorphic encryption algorithm was proposed, there were four schemes, one of which can be expressed as follows: set two large prime numbers as p and q, let m = pq, a group of integers Z_m is selected as the unencrypted space of the consumption information, the operations that can be performed on the consumption information include F =  + m,  − m × m. The space of encrypted consumer information is Z_p × Z_q, based on this space we can derive F is equivalent to F′ is equivalent. The key of the encrypted consumption information is defined as k = (pq), which is expressed as a function of Ek(a) = [amodp, amodp].

Based on the previous section’s exposition on homomorphic encryption, the decryption of consumer information can be achieved through the utilization of the Chinese remainder theorem. However, the conventional homomorphic encryption algorithm, as demonstrated, fails to meet the desired standards of security concerning known consumer information. Thus, the purpose of this study is to enhance the traditional homomorphic encryption approach by employing an encryption algorithm possessing homomorphic characteristics.

When the homomorphic encryption of a consumer message is arranged in a sequential manner, it becomes arduous to withstand the impact of the encrypted consumer message. Consequently, within the scope of this investigation, we propose the following improvements to the conventional homomorphic encryption algorithm:

(1) First, set M,N (1) Firstly, set the number of large prime numbers in the network information to be secure, then let P = M^∗N;

(2) set Q represent the security parameters of the network information;

(3) the space of the end-encrypted consumer information can be expressed as X = Y _P. The encrypted consumption information space can be expressed as ${\mathrm{X}}^{{}^{\prime }}={\left({\mathrm{Y}}_{\mathrm{M}}\ast {\mathrm{Y}}_{\mathrm{N}}\right)}^{\mathrm{q}}$;

(4) Select any two prime numbers in the network information, and denote them as D_M and D_N, and also satisfy D_M ∈ Y _M, D_N ∈ Y _N;

(5) Determine the encryption key of the network message, and denote the key as $\mathrm{K}=\left(\mathrm{M},\mathrm{N},{\mathrm{D}}_{\mathrm{M}},{\mathrm{D}}_{\mathrm{N}}\right)$;

(6) Execute the homomorphic encryption algorithm,

Set the end of the encrypted network information M ∈ Z_M, let X be randomly divided into N copies, i.e., . X₁, X₂, X₃, …X_N.X_i ∈ Z_M, i = 1, 2, 3, …, N. (2)${\displaystyle \mathrm{X}=\sum _{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{X}}_{\mathrm{i}}\mathrm{mod}\left(\mathrm{m}\right)}$ (3)${\displaystyle {\mathrm{E}}_{\mathrm{k}}\left(\mathrm{X}\right)=\left\{\left[{\mathrm{X}}_1{\mathrm{D}}_{\mathrm{M}}\text{modM},{\mathrm{X}}_1{\mathrm{D}}_{\mathrm{N}}\text{modN}\right]\right.\left.,\dots ,\left[{\mathrm{X}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{M}}^{\mathrm{N}}\text{modM},{\mathrm{X}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{N}}^{\mathrm{N}}\text{modN}\right]\right\}}$ where mod(m) represents the modulo operation, which divides the sum by m and takes the remainder to produce the final result.

(7) Decrypt the network information, i.e., (4)${\displaystyle \begin{array}{cc}\hfill & \hfill \left[{\mathrm{X}}_1{\mathrm{D}}_{\mathrm{M}}{\mathrm{D}}_{\mathrm{M}}^{-1}\text{modM},{\mathrm{X}}_1{\mathrm{D}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{N}}^{-1}\text{modN}\right],\\ \hfill {\mathrm{D}}_{\mathrm{k}}\left(\mathrm{X}\right)=& \hfill \left[{\mathrm{X}}_2{\mathrm{D}}_{\mathrm{M}}{\mathrm{D}}_{\mathrm{M}}^{-2}\text{modM},{\mathrm{X}}_2{\mathrm{D}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{N}}^{-2}\text{modN}\right],\dots ,\\ \hfill & \hfill \left[{\mathrm{X}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{M}}{\mathrm{D}}_{\mathrm{M}}^{-\mathrm{N}}\text{modM},{\mathrm{X}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{N}}{\mathrm{D}}_{\mathrm{N}}^{-\mathrm{N}}\text{modN}\right]\end{array}}$ where ${\mathrm{D}}_{\mathrm{M}}^{-\mathrm{N}}$ and ${\mathrm{D}}_{\mathrm{N}}^{-\mathrm{N}}$ are the multiplicative inverse ofthe corresponding powers of D_MmodM and D_NmodN. (5)${\displaystyle \sum _{i=1}^N\left[X_i\mathrm{mod}M,X_i\mathrm{mod}N\right]=\left[\sum _{i=1}^N{X}_i\mathrm{mod},\sum _{i=1}^N{X}_i\mathrm{mod}N\right]=\left[X\mathrm{mod}M,X\mathrm{mod}N\right].}$

Using the Chinese residual theorem, we can calculate that (6)${\displaystyle D\left(X\right)=\left(XN{N}^{-1}+XM{M}^{-1}\right)\mathrm{mod}P}$ where NN⁻¹ = 1modM, MM⁻¹ = 1modM.

The process of consumer information security protection based on homomorphic encryption algorithm is shown in Fig. 3.

The aforementioned procedure elucidates the manipulation of decimal values for individual data entries. Since the consumption amount is exclusively measured in yuan, angle, and cent, the number of decimal places associated with the data is restricted to a maximum of two. In practical scenarios, it is customary to establish a predetermined number of decimal places, indicated as n = 2, to govern the precision of the data. Consequently, when the actual number of decimal places in a specific data entry falls below n, the remaining decimal places are supplemented with zeros. This approach is employed to facilitate accurate and efficient computations while ensuring uniformity in the representation of decimal values.

The implementation of a fixed number of decimal places, such as n = 2, enables standardized processing and eliminates any potential ambiguity arising from varying decimal representations. This consistency in decimal representation streamlines computational operations and enables seamless integration in various contexts. Furthermore, the inclusion of zero-fillers for decimal places below n guarantees conformity of all numerical values to a consistent format, thereby facilitating precision in subsequent calculations.

By adhering to these conventions in practical applications, the manipulation and analysis of decimal data become more streamlined and cohesive. The establishment of a defined number of decimal places, along with the implementation of zero-padding, enhances computational efficiency and minimizes the risk of errors or inconsistencies arising from inconsistent decimal precision.

Data set

The training set in this study comprises the data from the initial nine days of an e-commerce platform, while the data from the tenth day serves as the test set for evaluation. The dataset employed in this research is sourced from the publicly available dataset provided by Alibaba Tianchi Big Data Platform, consisting of real traffic logs from Taobao’s product recommendation system, dataset link is https://zenodo.org/record/8275743. After undergoing pre-processing steps such as data feature extraction and dimensionality reduction, the dataset utilized in this experiment encompasses a total of 630,008 records, with 267,652 data records representing 6,388 distinct users. Following repeated training, the model exhibits an average running time of 40 s.

Model comparison

The selection of logistic regression (LR), LightGBM, CatBoost, and CatBoost with the radial basis function (RBF) kernel (CatBoost-RBF) for performance comparison in a machine learning context can be attributed to a strategic choice aimed at comprehensively evaluating their suitability for the task at hand. Logistic regression is included as a baseline model due to its simplicity and interpretability, allowing for a fundamental understanding of the problem. LightGBM, a gradient boosting framework, is chosen for its ability to handle large datasets and deliver high predictive accuracy through ensemble methods. CatBoost is included for its specialization in handling categorical features efficiently and its reputation for robust performance. The introduction of CatBoost-RBF, incorporating a non-linear kernel, reflects an interest in assessing whether non-linear relationships between features and the target variable significantly impact predictive performance. This selection strategy enables a holistic examination of various model characteristics, such as simplicity, accuracy, efficiency, categorical feature support, and non-linear modeling capabilities, aiding in the informed choice of the most appropriate model for the specific dataset and problem domain.

When employing logistic regression (LR) to train the original dataset, the imbalanced nature of the sample data often results in low recall scores and consequently, poor recall performance. To address this issue, data balancing is necessary, achieved through the application of appropriate weights using a weighting method. The training process is then conducted based on the adjusted results. For imbalanced datasets, the training process of the model is adjusted by assigning different weights to each class. The weights are usually inversely proportional to the frequency of the categories, that is, the minority class is weighted more and the majority class is weighted less. In this article, the weights are calculated using the inverse class frequency. Figure 4 illustrates the comparison of training outcomes, showcasing the performance variations among different models.

The combined CatBoost-RBF model demonstrates higher accuracy compared to CatBoost, LR, and LightGBM. Furthermore, the fusion model exhibits superior accuracy and precision when compared to the single RBF model. These results suggest that the CatBoost-RBF model is highly effective in predicting users’ consumption behavior.

In terms of the ROC curve area AUC, the three algorithms (LR, LightGBM, and CatBoost-RBF fusion model) yield values of 0.48, 0.60, and 0.66, respectively. This indicates that the CatBoost-RBF fusion model outperforms the other two algorithms in terms of generalization performance, demonstrating better predictive value and greater generalization ability.

To validate the performance of the models, a comparison and analysis were conducted between the aforementioned models and the CatBoost-RBF classification model. Parameter tuning was carried out using a grid search method for each classification method. The results of the model and indicator measures are depicted in Fig. 5.

In Fig. 5, it is evident that except for LR, which exhibits the lowest accuracy, the other models demonstrate comparable accuracy levels. Among them, the CatBoost algorithm achieves the highest classification accuracy, indicating its superior classification performance. Regarding accuracy and recall, the random forest model displays high accuracy but low recall, suggesting its proficiency in identifying normal data but poor classification ability for abnormal data. On the other hand, the LightGBM model exhibits the highest precision rate, implying that it classifies the lowest percentage of normal data as abnormal. In contrast, the CatBoost-RBF model achieves the highest recall rate, indicating its ability to classify the lowest percentage of abnormal data as normal. In terms of F1-score, the CatBoost-RBF model exhibits the best overall performance.

Since this article primarily focuses on the classification of abnormal consumption data, with a greater emphasis on the error of classifying abnormal data as normal, the recall value assumes greater importance. Hence, the CatBoost-RBF algorithm, which performs well in both recall value and F1-score, is considered optimal. The experimental results showcase that this method attains a classification accuracy of 98.56%, precision of 97.47%, recall of 99.36%, and an F1-score of 98.41% for abnormal online shopping data. These results significantly outperform other algorithms and demonstrate superior classification recognition capabilities.

Encryption effect

Figure 6 illustrates that the running time of the CatBoost-RBF algorithm on ciphertexts exhibits a linear increase as the data volume expands. Upon testing various datasets, the enhanced clustering algorithm requires approximately 1 s to process 2000 sets of 20-bit ciphertexts for 2D data. Furthermore, the contour coefficient achieves a level of approximately 0.4, indicating satisfactory performance. From these observations, it can be deduced that as the data volume increases, the proposed algorithm’s processing time also extends. However, it is important to note that the classification effect remains consistently good and stable.

Figure 7 presents the comparison results between the privacy protection methods of the relevant schemes. In the figure, option 1 indicates the inclusion of all options, while option 2 represents their exclusion.

In the SecureML scheme, two cloud servers are required to directly reconstruct the model parameters during the training process. However, there is a potential risk of information leakage associated with this approach. On the other hand, the PPMLaas model adopts a strategy to avoid the computationally expensive bootstrap operation of homomorphic encryption. In this approach, the server checks the noise level in the ciphertext after each operation. If the noise level surpasses the threshold, the server transmits the ciphertext to the user for decryption. Subsequently, the server encrypts the modified ciphertext and transmits it back to the server.

The scheme proposed in this article ensures privacy protection for model parameters, user data, and inference results by maintaining the relevant computational data and original input data in a randomly split state during the training process. This approach restricts each cloud server involved in the computation to possess only a portion of the data. As a result, no single cloud server can access the complete information, thereby achieving privacy protection. In the experimental setup involving cloud servers, the strategy we adopted was to control each server to access and participate in data processing tasks. This is achieved through data sharding, which splits the synthetic dataset into smaller, more manageable partitions or shards. These partitions contain different subsets of data and form the basis for subsequent computation operations. In the experimental design, cloud servers are assigned by policy to process specific data partitions, thus ensuring that each server only operates on its assigned subset of the dataset. The allocation process considers the effects of randomization, workload distribution, and server capacity.