A CNN is a network model that can simulate human vision and recognize images, and was inspired by research on biological visual systems [22, 23]. The CNN can be used to process data such as characters, text, audio, images, and videos, and the 1D-CNN can also be used to deal with traditional data classification problems to achieve the fast learning of the pattern relationships between data [24].

Internet addiction influences are one-dimensional vectors, a multivariate sequential data, involving 20 aspects of influences, containing a total of 50 potential independent variables, and 2 dependent variables. Drawing inspiration from the classical Convolutional Neural Network (CNN) model, AlexNet, a series of experiments were conducted to refine the structure and hyper-parameters of the CNN, culminating in the development of a predictive model for Internet addiction.

This proposed model is architecturally composed of several layers: an input layer for initial data reception, a convolutional layer for feature extraction, a normalization layer to stabilize learning, an activation function layer to introduce non-linearity, a pooling layer for dimensionality reduction, a fully connected layer to synthesize learned features, and an output layer for final prediction. The structural layout of this model is illustrated in Fig. 1.

Figure 1 Source: The authors.

In Fig. 1, he input dimension of the input layer is 1×50, representing the 50 influencing factors of Internet addiction. After data normalization, the characteristics of Internet addiction in the input group with a size of t are x _t ={x _1t ,…x _2t ,…x _50t }. Each group of data corresponds to an addiction sample, and the sample labels are {y _t } ^N _t=0 , y _t ={0,1}, where y₀ corresponds to the normal Internet use sample, y₁ corresponds to the Internet addiction sample, and N denotes the total number of samples.

In a convolutional neural network model, the inter-layer relationships primarily facilitate data extraction. The concept of a weight matrix is central to this process. It embodies a subset of locally connected neurons from one layer to the next within the network, thereby generating a feature map. The convolutional layer's multiple feature maps, characterized by their respective weight matrices, are commonly referred to as convolution kernels. The mathematical representation of this convolution process is as follows [25]:

In this formula, the symbol * denotes the convolution operation. The term y^j signifies the j-th output neuron, xⁱ represents the i-th input feature, K^ij denotes the convolution kernel involved in the convolution operation of this specific layer, and b^j indicates the bias associated with the j-th feature.

The pooling layer, analogous to the complex cells in the primary visual cortex, exhibits robustness and insensitivity to positional shifts in input data. This layer's function compresses the data dimensions, enhancing the computational efficiency of the network model. There are two primary forms of pooling operations:

Average Pooling: This method calculates the mean value within the sampling window, thus determining the feature's eigenvalue.

In this research, the max pooling technique was employed, expressed as:

Here, eq. (2) utilizes max pooling for signal dimensionality reduction. It maps the feature Y, derived from the convolutional layer, into multiple non-overlapping regions X, with k representing indices 1 through K. Each region size is defined as 1×s.

Within Convolutional Neural Networks (CNNs), after undergoing a series of convolutional and pooling layer operations, feature maps are transformed into a one-dimensional vector. This vector subsequently passes through a fully connected layer, where it is assigned weights corresponding to different categories. The output from this layer is then matched against the true labels to assess the effectiveness of the model. The level of deviation between the predicted output and actual labels is calculated using the cross-entropy loss function, which is mathematically expressed in the following way [26]:

In this formulation, y_ic is a binary indicator used to denote whether the true class of the i-th sample corresponds to class c, taking the value of 1 if it does and 0 otherwise. The term p_ic signifies the model's predicted probability that the i-th sample observed falls into class c. Here, M represents the total count of categories within the dataset, while N denotes the total number of samples under consideration. E is used to represent the error value, with a lower E value indicative of a more successful learning outcome achieved by the model.

The model's weights and biases are updated using gradient descent after calculating the output category's error. The Adaptive Moment Estimation (Adam) algorithm optimizes this process, influencing the training speed and results [27].

The Internet addiction prediction model, which leverages deep learning techniques, underwent a comprehensive process of feature extraction and optimization of its weights before it was fully trained. This model is structured with an input layer, followed by five convolutional layers, three pooling layers, two layers for normalization, and culminates in a fully connected layer. The convolution kernels are designed with dimensions of 1×2 in the initial two layers, changing to 1×3 in the subsequent three layers. To address the potential problems of vanishing and exploding gradients, the Rectified Linear Unit (ReLU) function was chosen as the activation function. Additionally, batch normalization was introduced post the first and second convolutional layers to enhance the rate at which the model converges. Important parameters of the model include a learning rate set at 0.001, a batch size of 64, the employment of the Adam optimizer, and a training regimen spanning 500 epochs.

The network model was trained and evaluated on a local laptop equipped with a 12th generation Intel® Core™ i5-12500H processor, 16 GB of RAM, and a 1 TB SSD. It featured an NVIDIA GeForce RTX 3060 Laptop GPU with 4 GB of dedicated memory. The operating system used was Ubuntu 18.04, and the model was developed using Python 3.10 in conjunction with the PyTorch 1.10.0 deep learning framework.

The model's performance was assessed using four key metrics: accuracy, precision, recall, and the F1 score. Accuracy represents the ratio of correctly predicted instances to the overall number of instances. Precision is the measure of the proportion of true positive predictions in all positive predictions made. Recall reflects the proportion of actual positives that have been correctly identified. The F1 score, which is the harmonic mean of precision and recall, is scaled between 0 and 1, where higher values denote better performance of the model.

The efficacy of the proposed model for predicting Internet addiction is demonstrated in Fig. 2. During the training phase, the model's loss function initially decreased rapidly, signaling swift learning of the primary data features and robust data-fitting capability. As training progressed, the model reached a state of convergence. In the testing phase, the loss value steadily aligned with the training outcomes, eventually approaching zero, which underscores the model's enhanced predictive proficiency.

Figure 2 Source: The authors.

For practical evaluation, 118 samples were randomly selected as test data, with results detailed in the confusion matrix in Fig. 3. Of the normal Internet users, 51 were accurately identified, with 3 misclassifications. For users exhibiting Internet addiction, 60 were correctly predicted, with 4 misclassified. This resulted in a prediction accuracy of 94.07%, reflecting the model's substantial generalization capacity.

Figure 3 Source: The authors.

The effectiveness of the 1D-CNN model was compared with that of Support Vector Machine (SVM) and Multilayer Perceptron (MLP) algorithms in a detailed assessment. This comparison was based on identical training data and model parameters, focusing on predicting normal and Internet-addicted users. As per the data in Table 2, the 1D-CNN model achieved a 92.77% accuracy, outperforming the SVM and MLP models by 5.30% and 3.21%, respectively.

In terms of precision, recall, and F1 scores for normal Internet users, the 1D-CNN model scored 93.59%, 93.75%, and 0.937, respectively. For Internet-addicted users, the scores were 99.74%, 98.73%, and 0.992, respectively. The F1 scores for normal users predicted by the 1D-CNN were 0.05 and 0.036 higher than those of the SVM and MLP models, while for addicted users, the improvements were 0.07 and 0.06, respectively. These results establish the 1D-CNN model's superior predictive capabilities compared to SVM and MLP models, making it a viable tool for early detection and prevention of Internet addiction among college students.

In Table 1, influences with statistically significant differences were selected as input characteristics for the prediction model, namely, first grade (C1), second grade (C2), single-parent family (C3), non-single-parent family (C4), poor family (C5), rich family (C6), negative behavior (C7), withdrawal behavior (C8), neuroticism (C9), extraversion (C10), no depression (C11), depressed (C12), overly intrusive (C13), understanding and caring (C14), anxiety (C15), no anxiety (C16), poor social support (C17), and very good social support (C18).

Table 2

Model	A	Forecast result			Internet addiction
		P	R	F1	P	R	F1
SVM	87.47	83.78	93.67	0.884	91.67	93.45	0.925
MLP	89.56	87.46	93.85	0.901	95.85	92.72	0.932
1D-CNN	92.77	93.59	93.75	0.937	99.74	98.73	0.992

Note: A indicates Accuracy, P indicates Precision rate, R indicates Recall rate, F1 indicates F1 score.

As can be seen in Fig. 4, first grade (C1): there is no difference between Internet addiction and normal Internet users with an impact factor of 0; second grade (C2): the impact factor of 0.81 for Internet addiction is significantly higher than that of 0.27 for normal internet users; single-parent family (C3) and non-single-parent family (C4): the impact factor was less than 0.5, with no significant effect on Internet addiction; poor family (C5): the impact factor for normal Internet users is 0.6; rich family (C6): no difference between Internet addiction and normal Internet users; negative behavior (C7) and withdrawal behavior (C8): significant influence on Internet addiction with an impact factor of 0.75 and 0.83 respectively among Internet addiction, and a smaller weighting among normal Internet users; neuroticism (C9) and extraversion (C10): there is less influence between Internet addiction and normal Internet users; no depression (C11) and depressed (C12): those depressed are more likely to be Internet addicted with an impact factor of 1.0; overly intrusive (C13) and understanding and caring (C14): overly intrusive families have an effect on both Internet addiction and normal Internet users, and understanding and caring families have a positive effect on normal Internet users; anxiety (C15) and no anxiety (C16): those with anxiety have a greater impact on Internet addiction, with an impact factor of 0.55; poor social support (C17) and very good social support (C18): individuals with very good social support have a greater weight among normal Internet users.

Figure 4 Source: The authors.

Based on the above analyses, the priority of the influence factors of Internet addiction is: C12 (1.0) > C8 (0.83) > C2 (0.81) > C7 (0.75) > C13 (0.7) > C15 (0.55) > C11 (0.43) > C16 (0.42) > C18 (0.39) > C17 (0.34) > C9 (0.32) > C14 (0.31) > C10 (0.27) > C5 (0.25) > C4 (0.24) > C3 (0.2) > C6 (0.2) > C1 (0), and the priority of the influence factors of normal Internet users is: C13 (1.0) > C18 (0.79) > C14 (0.78) > C5 (0.6) > C8 (0.38) > C2 (0.29) > C3 (0.27) > C17 (0.23) > C11 (0.22) > C10 (0.17) > C4 (0.13) > C15 (0.12) > C12 (0.11) > C9 (0.09) > C16 (0.08) > C7 (0.07) > C6 (0.05) > C1 (0). This ranking can help to understand the different effects of the factors on Internet addiction and normal Internet users, and provide direction for future interventions and research.