Datasets collection, experimental environment, and parameters setting

The dataset used in this study comes from the National Population Health Science Data Center, a professional institution under the China Academy of Medical Sciences; It is dedicated to collecting, sorting out, and sharing population health-related data nationwide. The dataset covers about 10,000 children’s health records, with a total of about 200,000 pieces of data, covering many aspects such as body shape, function, and quality. Its main features include basic information about children (such as age, gender, height, and weight), and physical fitness (such as the measurement data of key dimensions like strength, flexibility, and endurance). Meanwhile, it encompasses health assessment indicators (such as body mass indicator BMI and cardiopulmonary function test results). In addition, the dataset also contains information about environmental factors, such as living area, eating habits, and exercise frequency. To ensure the scientificity and validity of the data, this study has conducted strict preprocessing on the data, including data cleaning, data standardization, and dimensionality reduction. Data cleaning mainly deletes samples with too many missing or significant abnormal values. Data standardization adopts the Z-score method to normalize feature data. The dimension reduction process extracts the most representative features through PCA. Finally, the dataset is divided into training set (70%), verification set (15%), and test set (15%) to ensure that the training and evaluation of the model are representative. The dataset is downloaded through the National Population Health Science Data Center (https://www.ncmi.cn/).

The health and growth database of children and adolescents in China is led by the China Center for Disease Control and Prevention (China CDC). This dataset covers the physical health and growth data of 15,000 children and adolescents nationwide, with a total of about 300,000 records. Data features include basic information (e.g., height, weight, age, and gender), physical fitness (e.g., muscle strength, flexibility, and cardiopulmonary function), and behavior and living habits (e.g., diet frequency, sleep duration, and daily exercise). In the data preprocessing, this study uses the Interquartile Range (IQR) method to detect and remove abnormal values that deviate from the normal range. At the same time, it fills a few missing values by nearest neighbor interpolation. Then, the RF algorithm is employed to select features, and the key features that have a significant impact on the model are screened out, and the category data are sampled to balance the category distribution. The multidimensional characteristics of this dataset can provide rich information support for this study. The dataset can be obtained from the official website of China CDC (https://www.chinacdc.cn/).

The National Health and Nutrition Inspection Survey (NHANES) dataset is provided by the US Centers for Disease Control and Prevention, which is an open dataset focusing on health and nutrition surveys. This study selects the data from 1999 to now, of which the annual sample size is about 10,000, and the total data volume is huge. Its characteristics encompass physical health information (e.g., height, weight, and body fat percentage), health indicators (e.g., heart rate, vital capacity, and blood test results), and behavioral data (e.g., exercise frequency and dietary intake type). In data preprocessing, the data formats of different years are unified and integrated, and the numerical features are standardized by the Min-Max normalization method. Moreover, interactive features are constructed based on the original features, and noise data are removed by low-pass filtering. The diversity and scale of NHANES datasets provide reliable reference data for the study. The dataset is obtained through the NHANES official website (https://www.cdc.gov/nchs/nhanes/).

The European Adolescent Health Survey dataset is provided by the EU Health Data Sharing Program, covering more than 20 European countries and containing the health and behavior records of about 12,000 adolescents. The characteristics of this dataset include physical health data (height, weight, and BMI), physical activity records (weekly exercise time and exercise type), and mental health status (stress level and life satisfaction assessed by questionnaire). In the data preprocessing, this study codes and cleans up the abnormal values in the questionnaire records, and uses multiple interpolations to deal with the missing data. Then, the dimension of the data is reduced by factor analysis to reduce redundant information, and the feature dimension is unified for clustering and classification analysis. This dataset’s international perspective and multidimensional characteristics provide important supplementary data support for this study. Datasets are available through Eurostat (https://ec.europa.eu/eurostat).

In the experiment, the processor is Intel Core i9-12900 K, and the memory is Corsair Vengeance 64 GB DDR 5 4800 MHz. The graphics card is NVIDIA GeForce RTX 3090, and the hard disk is Samsung 980 Pro NVMe 1 TB SSD. The version of the operating system is Ubuntu 22.04 LTS 64-bit. The programming language version is Python 3.10, the deep learning framework version is TensorFlow 2.10, and the SOM library version is MiniSom 2.2.9. The mesh size of the optimized model is 30 × 30, the initial learning rate is 0.5, then gradually decays to 0.01, and the initial radius of the neighborhood radius is 5. With the training, it gradually shrinks to 1, the number of training iterations is 1000, and the distance metric is Euclidean distance. The contrast models of the experiment are T-distributed stochastic neighbor embedding (T-SNE), density peak clustering (DPC), and deep embedded clustering (DEC).

Performance evaluation

Comparative analysis of model performance

The comparison indicators selected in the performance comparison experiment are accuracy, precision, recall, F1 score, area under the receiver operating characteristic curve (AUC-ROC), and model training time. Firstly, the public dataset provided by the National Population Health Science Data Center is selected. The experimental data are indicated in (Fig. 2):

Figure 2 illustrates that in the proposed optimized model, the accuracy is 0.934 for strength, 0.851 for flexibility, and 0.863 for endurance, respectively, showing that the classification effect is superior to other models in all variables. In contrast, the DEC model’s accuracy is also excellent, especially in the strength dimension of 0.917. The DPC model’s flexibility is less than 0.799, and the T-SNE model’s strength is 0.876. The proposed model has the best precision in the strength dimension, which is 0.844, while the flexibility and endurance are 0.782 and 0.787 respectively, which has obvious advantages compared with other models. The precision of DEC in strength is 0.827, while the flexibility of T-SNE is weak, only 0.714. The proposed optimized model’s recall is still ahead in strength, flexibility, and endurance, which are 0.881, 0.803, and 0.809. The recall of DEC is also close to the optimized model, especially 0.865 in the strength dimension, and 0.749 in the flexibility of DPC, which is slightly lower than the optimized model. The F1 score of strength dimension, flexibility, and endurance of the optimized model are 0.862, 0.797, and 0.798, all of which are at the highest level. The DEC model has a score of 0.846 in F1 in the strength dimension, while T-SNE scores 0.722 in the flexibility dimension. The AUC-ROC reveals that the AUC values of the optimized model in strength, flexibility, and endurance are 0.944, 0.859, and 0.875, respectively, which shows a high classification ability. The AUC of the DEC model is 0.927 in the strength dimension, and the flexibility of DPC is 0.812, slightly lower than that of the optimized model. Finally, in the training time, the performance of the optimized model is significantly better than other models, with a training time of 6.729 s in the strength dimension, followed by 7.663 s in the DEC model. The training time of T-SNE and DPC is longer. Especially, the training time of the DPC model is 10.123 s in the endurance dimension. To further verify the performance of the optimized model on different datasets, this study selects four indicators: mean squared error (MSE), silhouette coefficient, model reasoning time, and classification balance. The experimental results are presented in (Fig. 3):

Performance comparison under different datasets ((a): MSE; (b): Silhouette coefficient; (c): Reasoning time; (d): Class balance ratio).

The results in Fig. 3 show that, in the MSE comparison, the optimized model performs best on the database of children and adolescents’ health and growth in China, with an MSE of 0.742, while the MSE of T-SNE and DPC models are 0.456 and 0.382. On NHANES and European adolescent health survey datasets, the optimized model reaches 0.765 and 0.753 respectively, significantly exceeding other models. In comparing silhouette coefficients, the optimized model performs best on the China dataset, with 0.552, while the DPC model is only 0.294. On the NHANES dataset, the optimized model reaches 0.575, which is better than DEC’s 0.389. The silhouette coefficient of the European dataset is 0.563, which continues to lead. The reasoning time of the optimized model is the lowest, and the China dataset is 0.293 s. In contrast, the reasoning time of DEC and T-SNE is 0.584 and 0.745 s, respectively. On NHANES and European datasets, the time to optimize the model is still the shortest, at 0.312 and 0.305 s, respectively. In the classification balance, the performance of the optimized model on the three datasets significantly outperforms other models. It reaches 0.718 on the China dataset, much higher than T-SNE’s 0.423 and DPC’s 0.381. The performance on NHANES and European datasets is 0.732 and 0.724 respectively, which is better than all other models.

Sensitivity analysis

To study the parameters of the model, the experiment also set up sensitivity analysis, and the experimental objectives are as follows:

1. (1)

   The impact of two core parameters, grid size, and learning rate, on the performance of the optimized model, is evaluated.

2. (2)

   It is necessary to verify whether the parameter changes significantly affect the classification performance, clustering effect, and operating efficiency.

3. (3)

   The best parameter configuration is found through sensitivity analysis to ensure a balance between model performance and efficiency.

The experimental grid size is set to 5 × 5, 10 × 10, 15 × 15 and 20 × 20 to evaluate the impact of mapping resolution of the SOM neural network. The learning rate is set to 0.01, 0.03, 0.05, 0.07, and 0.10, and the influence of the learning rate on the convergence speed and classification performance of the model is tested. The experiment uses the China database of children and adolescents’ health and growth. Each group of parameters is repeated 10 times to reduce the interference of randomness on the results. The experimental results of grid size are outlined in (Table 2):

In Table 2, with the increase of the grid size from 5 × 5 to 20 × 20, the performance indicator of the model has changed. Regarding accuracy and F1 score, the grid size reaches the highest value of 0.88 and 0.87 respectively when it is 15 × 15. However, it drops slightly when it is 20 × 20, indicating that the mapping accuracy may decrease if the grid size is too large. As grid size increases, the training time increases significantly, from 10.23 s to 25.34 s, illustrating that higher resolution brought about an increase in computational cost. In terms of the silhouette coefficient, the peak value is 0.58 when the grid size is 15 × 15, which indicates that the clustering effect is the best under this configuration. The experimental results of the learning rate are shown in (Table 3):

The results in Table 3 indicate that when the learning rate is 0.07, the accuracy and F1 score reach the highest values of 0.88 and 0.87, respectively, but too high learning rate (such as 0.1) leads to a slight decline in the model performance. In terms of training time, when the learning rate is high, the model converges faster, from 18.12 s of 0.01 to 15.67 s of 0.1, which shows the influence of the learning rate on calculation efficiency. When the learning rate is 0.07, the silhouette coefficient reaches the highest value of 0.57, suggesting that a moderate learning rate can better balance the convergence speed and clustering effect.

Cluster analysis experiment

The study also sets up a cluster analysis experiment to further analyze the model’s validity. The comparison indicators are silhouette coefficient, intra-class distance, inter-class distance, weighted average contour score, class distribution uniformity, and cluster number selection. The experimental results are suggested in (Fig. 4):

Cluster analysis experiment ((a): Silhouette coefficient; (b): Intra-class distance; (c): Inter-class distance; (d): Weighted average contour score; (e): Uniformity of class distribution; (f): Number of clusters selection).

The results of Fig. 4 show that the proposed optimized model performs best in the silhouette coefficient, with the scores of strengths, flexibility, and endurance of 0.655, 0.559, and 0.601 respectively, indicating that the clustering effect is significantly improved. In contrast, the silhouette coefficient of the DEC model in the strength dimension is 0.632, while the score of T-SNE in flexibility is low, only 0.481. In terms of intra-class distance, the performance of the optimized model is also superior, and the intra-class distances of strength, flexibility, and endurance are 3.201, 3.824, and 3.511 respectively. The DEC model’s intra-class distance reaches 3.312 in the strength dimension, which is slightly higher than that of the optimized model, and the flexibility of T-SNE is the worst, at 4.212. For the inter-class distance, the optimized model has the highest value in each dimension, and the inter-class distances of strength, flexibility, and endurance are 6.821, 6.012, and 6.421 respectively. The inter-class distance of DEC in the strength dimension is close to the optimized model, reaching 6.679, and that of DPC in flexibility is 5.671. The weighted average contour score also shows the leading performance of the optimized model, with a strength dimension of 0.629, flexibility of 0.542, and endurance of 0.584, which are higher than other models. DEC scored 0.603 in strength dimension, while T-SNE scored only 0.463 in flexibility. In the uniformity of category distribution, the uniformity scores of strengths, flexibility, and endurance of the optimized model are 0.859, 0.789, and 0.827, respectively, showing a relatively balanced distribution. The score of DEC in the strength dimension is 0.834, while the flexibility of T-SNE is 0.722. For the number selection of clusters, the optimized model selects 9 clusters in the strength dimension, with a flexibility of 7 and endurance of 8, all of which are more than other models. DEC chose 8 clusters in the strength dimension, while T-SNE chose fewer clusters in the flexibility and endurance dimensions.

Discussion

From the results of performance comparison experiments, the proposed optimized model performs well in many indicators, especially in the three dimensions of strength, flexibility, and endurance, which show high accuracy and stability. This reveals that the optimized model has obvious advantages in data dimensionality reduction and clustering effect while showing stronger robustness in classification performance. Although the DEC model is close to the optimized model in some indicators, its overall performance is slightly inferior, particularly in the flexibility and endurance dimensions, and its performance has not been fully surpassed. However, the performance of T-SNE and DPC models is insufficient, especially in training time and accuracy. This reflects that the traditional dimensionality reduction and clustering methods may have some limitations in effect and efficiency when handling complex health data. The advantage of the optimized model in training time is also very significant, especially when dealing with high-dimensional data, the training speed is remarkably faster than other models through reasonable parameter setting and optimization. This characteristic makes it have higher practical application value when processing large-scale data. At the same time, the comparison results of different datasets further verify the excellent performance of the optimized model in terms of MSE, silhouette coefficient, and classification balance. Among them, the performance of the optimized model in classification accuracy and balance exhibits its ability to solve the problem of uneven distribution of categories in health data analysis. In addition, in the efficiency indicator of reasoning time, the rapid response of the optimized model improves its practicability and provides feasibility for real-time analysis of health data.

From the results of cluster analysis experiments, the optimized model is outstanding in key indicators such as intra-class distance, silhouette coefficient, and inter-class distance. This shows that the model can effectively identify the differences between different categories. Meanwhile, it ensures the compactness of intra-class data and the separation of inter-class data, which reflects the strong clustering effect. Especially in the inter-class distance and the weighted average contour score, the numerical value of the optimized model is higher than other models, illustrating that it can distinguish different clustering categories more effectively. In contrast, the DEC model is close to the optimized model in silhouette coefficient and intra-class distance. However, it is insufficient in terms of inter-class distance and weighted contour score, especially in flexibility and endurance. However, the performance of T-SNE and DPC models lags the optimized model in many dimensions, especially in the intra-class distance and the balance of class distribution, and the effect of T-SNE is weak. In addition, the optimized model shows higher flexibility and adaptability in selecting cluster numbers, which can choose reasonable cluster numbers according to data characteristics and ensure the classification appropriateness of data with different dimensions. Generally speaking, the proposed optimized model has remarkable advantages in the clustering effect. It can effectively meet the analysis needs of high-dimensional and complex health data, and provide a scientific and efficient solution for evaluating children’s physical fitness.