3.1. Visualization of Basketball Game Data Based on Random Forest Algorithm

With the rapid development of the economy, the application fields of computer technology are becoming more extensive. In terms of data visualization, computer technology can use different techniques to visualize data, and people can also obtain basketball game data through various channels. However, traditional algorithms are prone to poor data visualization effects when visualizing basketball game data. Therefore, the study introduces the RF to visualize basketball game data, as RF can extract feature data from a large amount of data, classify and regress the feature data ^{[15, 17]}. The steps for visualizing basketball game data are shown in Fig. 1.

Fig. 1. Data visualization process.

Fig. 1 shows the core flow of basketball game data visualization. The View layer interacts with the user through the ARI interface and designs the mechanics map to map key game metrics (such as scoring efficiency and defensive line). The rendering and interaction module of the force mapping component is responsible for dynamically presenting multidimensional data (such as player position hot zone). The database interface connects the open source knowledge graph database in the data layer with the basketball knowledge graph database to extract and fuse structured data. This process provides infrastructure support for subsequent TRRF algorithm feature classification and clustering optimization, ensuring accurate segmentation and visual presentation of high-dimensional data. When using the RF algorithm to visualize basketball game data, the first step is to calculate the function of the input vector based on the decision tree that classifies and plans the data, as shown in Eq. (1).

In Eq. (1), $A_k(\cdot)$ represents the average value. $I(\cdot)$ represents the function value. Then, the error value of the RF algorithm is calculated through the input function, as shown in Eq. (2).

In Eq. (2), $P^*$ represents the error value. Combined with the number of decision trees, convergence analysis is performed on the error values, as shown in Eq. (3).

In Eq. (3), $h(X,\Theta)$ represents the classifier. Then, the limit value of the RF error value is determined, as expressed in Eq. (4).

In Eq. (4), $\rho$ represents the value of the correlation coefficient. $S$ represents the classification strength value. Finally, the coefficient of multiple decision trees is calculated, as shown in Eq. (5).

In Eq. (5), $p^2(0 \mid T)$ and $p^2(1 \mid T)$ represent the sample ratio. Based on the proportion between different samples, the visualization effect between different samples is judged, as shown in Eq. (6).

In Eq. (6), $N$, $N_1$, and $N_r$ all represent the number of samples. After visualizing the basketball game data through the above steps, the process of visualizing the basketball game data using the RF algorithm is obtained, as shown in Fig. 2.

Fig. 2. The process of visualizing data in a random forest.

Fig. 2 shows the flow of basketball data visualization based on RF algorithm. Taking a specific sample in the experimental data set as an example (such as a team's game data in a certain year), the algorithm first extracts key features from the large-scale data, including a player's shooting percentage (such as a player's 45.6%), defensive rebounding efficiency (such as a team's 7.2 times per game), and passing success rate (such as a player's 82%). Then, multiple decision trees are used to perform parallel classification and regression analysis of features. For example, decision tree 1 ranks offensive efficiency based on shooting percentage, and decision tree 2 evaluates defensive stability based on defensive rebound data. After integrating the results of the decision tree using the Bagging method, the improved TRRF algorithm introduces a clustering strategy to screen high-precision sub libraries. Ultimately, the best prediction result is selected through a majority voting mechanism. Clustering algorithms can cluster unlabeled data samples based on their similarity, and assign the classified data to the same cluster based on the classified data ^{[18, 20]}. When clustering algorithms classify data without similarity in decision trees, they first select the initial cluster center in the decision tree, and then select the next cluster center based on the initial cluster center ^{[21, 23]}. The expression is shown in Eq. (7).

In Eq. (7), $D(x)$ represents the distance. Then, based on the selected central clustering points, the optimal K value of the clustering center is calculated, as shown in Eq. (8).

In Eq. (8), $a_i$ represents the distance between the sample and the classification cluster. $b_i$ represents the average distance. Finally, the sample contour coefficient is used to limit the K value, as shown in Eq. (9).

In Eq. (9), $n$ represents the number of samples. After improving the RF through the above steps, the improved RF algorithm, namely TRRF algorithm, is obtained. The improved RF algorithm is used to visualize and analyze basketball game data to obtain the best visualization results. The specific process of visualizing basketball game data using this algorithm is shown in Fig. 3.

Fig. 3. The process of visualizing data by the TRRF algorithm.

As shown in Fig. 3, the TRRF algorithm first samples the training set data for visual analysis of basketball game data, and classifies the sampled game data. Then, features are extracted from different categories of game data based on the improved high-precision decision tree to obtain high-precision game data sub forests. The high-precision sub forests are then divided into different clusters and combined into random sub forests. Finally, the best sub forest is found in the random sub forest as the final visualization result. For basketball game data with no features or sparse features, TRRF algorithm uses an improved high-precision decision tree to divide the original data into multi-granularity, such as dividing time series data into discrete intervals, and counting key indicators in each interval. The clustering algorithm is used to analyze the similarity of unlabeled data and generate cluster labels as new features. Multiple sub forests are generated by the Bagging method. Each sub forest generates differentiated features based on different clustering centers or feature combinations. The TRRF algorithm can automatically mine the hidden features from the original data and effectively classify featureless data.

3.2. Random Forest Data Visualization Prediction Model Integrating Voting Ensemble Learning Algorithm

The improved RF algorithm can effectively visualize and analyze basketball game data. However, when there are a large number of training sets in the basketball game dataset, it is easy to be unable to classify feature data ^{[24, 26]}. In response to this issue, the research introduces the Voting ensemble learning algorithm for visualizing basketball game data, mainly because this learning algorithm can process the data in the dataset according to different voting methods to determine the final prediction effect ^{[27, 28]}. The basic principle of the Voting ensemble learning algorithm is shown in Fig. 4.

Fig. 4. Basic principle of the Voting ensemble learning algorithm.

In Fig. 4, the Voting ensemble learning algorithm combines multiple classifiers in the training set. Different models in the dataset are predicted and analyzed based on different classifiers. All results are fused to obtain the final prediction result in the dataset. When visualizing basketball game data using the Voting ensemble algorithm, different categories are first calculated based on different voting methods, as shown in Eq. (10).

In Eq. (10), $p_k$ represents the probability. $E_k$ represents the weighted probability. $w_i$ represents the weight value. Then, the final probability value is calculated through category probability, as shown in Eq. (11).

In Eq. (11), $y_{i-predict-voting}$ represents the probability result. Then, the feature data in the dataset is selected and the error relationship between different classifiers is calculated, as shown in Eq. (12).

In Eq. (12), $f$ represents the mapping relationship. $\varepsilon$ represents the error value. The error value after voting is calculated based on the relationship between different error values, as shown in Eq. (13).

In Eq. (13), $T$ represents the total number of classifiers. Finally, the weight is calculated by computing the individual extremum, as expressed in Eq. (14).

In Eq. (14), $p_{iD}$ represents the individual extremum. The expression for calculating the global extremum through individual extremum is shown in Eq. (15).

In Eq. (15), $p_{gD}$ represents the global optimal solution. Finally, by obtaining the extremum, the update speed and position of the data particles are calculated, as shown in Eq. (16).

In Eq. (16), $\omega$ represents the inertia factor. $C_1$ and $C_2$ represent constant values. $\gamma$ represents a random number. After visualizing basketball game data using the Voting ensemble learning algorithm, the specific process of visualizing basketball game data is obtained, as shown in Fig. 5.

Fig. 5. The process of ensemble learning to visualize data.

As shown in Fig. 5, when visualizing basketball game data, the Voting ensemble learning algorithm first extracts the feature data of basketball games from a large dataset. The feature data of basketball games is input into different training sets created by the Voting ensemble learning algorithm. The feature data of basketball games is predicted based on the models in different training sets, and then combined the prediction results with the feature function. Finally, by analyzing and processing the final prediction results, the visualization of basketball game data is obtained. The Voting ensemble learning algorithm can obtain the optimal visualization results of basketball game data. Voting ensemble learning improves the model performance by fusing the prediction results of multiple classifiers ^{[29, 30]}. Its core mechanism can be divided into Hard Voting and Soft Voting. In basketball game data, hard voting directly selects the highest frequency prediction category through the majority voting mechanism. For example, when predicting the outcome of an offense (score/turnover), if the three base classifiers output “score”, “score”, and “turnover”, respectively, hard voting will determine the final result as “score”. This method is suitable for scenarios where category labels are clear (such as event type classification). Soft voting outputs weighted fusion results based on the probability of the classifier. The optimization strategy of hard voting and soft voting is realized through feature classification optimization, numerical prediction optimization, and anti-noise enhancement. In feature classification optimization, hard voting is used for discrete events (such as foul decision) to ensure that the classification results are consistent with the actual referee records. In numerical prediction optimization, soft voting is used for continuous indicators (such as shooting percentage). The contribution of high-precision decision tree is dynamically adjusted by combining weight coefficients. To obtain more accurate visualization results, a mixed prediction model combining Voting ensemble learning algorithm with TRRF algorithm for basketball game data visualization analysis is proposed, namely Voting-TRRF visualization prediction model. The basic structure of this prediction model is shown in Fig. 6.

Fig. 6. Prediction model of TRRF algorithm based on voting ensemble learning.

In Fig. 6, the Voting-TRRF visualization prediction model first inputs the collected game data for visual analysis of basketball game data. The input data is integrated into a training set. Then, the high-precision decision tree of the TRRF algorithm is used to integrate the data into a dataset. The data is then divided into multiple sub forests and combined into a forest set. Finally, the Voting ensemble learning is combined with the TRRF algorithm. The output result is used as the final game data result. To realize the visual prediction of Voting ensemble learning algorithm, Scikit-learn and Plotly in Python ecosystem are used as the core simulation tools. Scikit-learn provides interfaces for VotingClassifiers and VotingRegressor, and supports flexible configuration of hard and soft voting strategies. In the process of visual effect improvement, real-time data flow rendering is implemented through plotly.graph_objects.Fig.Widget to update competition data in real-time. Multi-dimensional overlay analysis uses Scatter3d to simultaneously display player position, movement speed, and tactical path. User interaction enhancement supports user-defined filtering conditions through callback functions, improving the flexibility of data exploration.

4.1. Performance Analysis of Visualization Prediction Model for Basketball Matches

To analyze the performance of the Voting-TRRF visualization prediction model, the study takes data from two regular season teams, A and B, in Anping District from 2010 to 2022 as the experimental dataset. The experimental dataset is derived from Team A and Team B basketball games, covering multiple seasons between 2010 and 2022. Each dataset contains records of different types of game events, including points, shooting efficiency, turnovers, rebounds, assists, etc. A total of about 500 matches from Team A and Team B are recorded in the dataset, involving nearly 50,000 records of match events. The dataset contains sequential data (such as scores, rebounds, etc.), as well as categorical data (such as game results, shooting types, etc.). The experiment is conducted in the following environment to ensure the reproducibility and reliability of the experimental results. Firstly, the experimental equipment is a desktop computer equipped with Intel (R) Core (TM) i7-12700KF processor and NVidia GTX 4070 graphics card. In addition, the operating system takes Windows 10 and the programming language is Python to process and analyze basketball game data. Finally, PyCharm is used as the integrated development environment for the study. The eXtreme Gradient Boosting (XGBoost) model and Light Gradient Boosting Machine (LightGBM) model are introduced. The performance of the prediction model is evaluated using accuracy, Mean Absolute Error (MAE), and precision. Both XGBoost and LightGBM are based on gradient Boosting decision tree, which are typical implementations of boosting strategies in ensemble learning. They can effectively handle the relationship between high-dimensional features and non-linear basketball game data, widely used in structured data classification and regression tasks. In the existing basketball data analysis studies, XGBoost and LightGBM are often selected as the performance baseline, which can ensure the comparability of experimental results with existing work. The experimental dataset is shown in Table 1.

The performance comparison among XGBoost, LightGBM, and Voting-TRRF models is mainly conducted on the dataset shown in Table 1. The model configuration parameters are as follows. The number of decision trees in the RF sub model is set to 200, the maximum depth is 15, and the feature selection strategy based on Gini coefficient is adopted. In the Voting integration part, the soft voting mechanism is adopted, and the weight allocation is based on F1 value of the sub model in the verification set (TRRF sub model weight is 0.6, XGBoost and LightGBM weight is 0.2). In the clustering optimization stage, K-means algorithm is used, the number of clustering centers is K=8, and the threshold of contour coefficient is set to 0.65. To evaluate the visualization performance of different visualization prediction models under different data conditions, the precision and MAE of the three prediction models are compared. The results are shown in Fig. 7.

Fig. 7. The results of the precision and MAE values of the three models.

From Fig. 7(a), among the three models, the Voting-TRRF model was more efficient in visualizing basketball game data, with an average precision of 0.856, significantly higher than the other two models. However, the XGBoost and LightGBM models maintained an average precision of below 0.535 when visualizing game data. The Voting-TRRF model had higher precision than the other two models, verifying its superior performance compared with the other two models. From Fig. 7(b), among the three prediction models, the Voting-TRRF model could accurately analyze the game data. The MAE value of this model always remained within 0.021-0.041, significantly lower than the other two models. However, the MAE of the other two models was significantly higher than those of the Voting-TRRF model, and the curve of the MAE value showed a significant drop. The Voting-TRRF model could accurately analyze basketball game data. Afterwards, to evaluate the proportion of correctly predicted events by the three visualization prediction models in the total number of events under different dataset conditions, the accuracy of the three prediction models is compared, as shown in Fig. 8.

Fig. 8. Accuracy variation results of the three models.

From Fig. 8, the accuracy of the Voting-TRRF model reached 94% when analyzing different event data, significantly higher than the other two models. The accuracy of this model changed slightly, while the accuracy of the XGBoost model remained within 35%-76%, and the accuracy curve showed significant fluctuations. Although the accuracy of the LightGBM model was significantly smaller than that of the XGBoost model when visualizing event data, its average accuracy was significantly lower than that of the Voting-TRRF model. From this, the Voting-TRRF model has significantly higher accuracy than the other two models in visualizing data from multiple events, which verifies its performance advantage.

4.2. Visualization effect of basketball event visualization prediction model

To verify the visualization effect, XGBoost, LightGBM, and Voting-TRRF models are introduced to visualize and analyze data from four basketball games. The actual basketball game data is then compared with the predicted data, and the comparison results are shown in Fig. 9.

Fig. 9. Comparison results of predicted events and actual events for three models.

From Fig. 9(a), the visualization results of Voting-TRRF model for four basketball games were close to the actual game results, with only three errors occurring in the first game. The model could accurately predict actual games when visualizing data from different games. According to Fig. 9(b), the XGBoost model had a significant difference between the visualized results and the actual game results when analyzing basketball games. It made multiple mistakes in different basketball games, with a total of 10 mistakes. This indicates that the model has poor visualization performance when analyzing game data and cannot accurately reflect the actual game. According to Fig. 9(c), the LightGBM model had a significant gap between its visualization effect and the actual event effect when visualizing event data, and the number of errors reached 9 times. From this, when visualizing different event data, the visualization results of the Voting-TRRF model were close to the actual event results. The number of errors occurring was significantly less than that of the other two models, verifying that the visualization effect of this model was significantly better than the other two models. Afterwards, to highlight the superior visualization effect of the Voting-TRRF visualization prediction model compared to other models, the comparison is conducted on basketball games held simultaneously. XGBoost, LightGBM, and Voting-TRRF prediction models are used to visualize and analyze the basketball game data at that time. The analysis results are shown in Fig. 10.

Fig. 10. Visualization effect of three models on the same event data.

From Fig. 10(a), the Voting-TRRF model could analyze the number of successful and failed shots of teams A and B when visualizing the basketball game data. By accurately judging the pitching success rate of teams A and B based on their number of failed and successful shots, the model obtained their scores and rankings, and ultimately obtained the final result of the basketball game. As shown in Fig. 10(b), although the XGBoost model provided a basic understanding of the shooting situation of teams A and B when visualizing basketball game data, it did not accurately obtain the actual number of successful or failed shots, resulting in the inability to obtain the final actual result of the basketball game. From Fig. 10(c), the LightGBM model had a more comprehensive understanding of shooting situations than the XGBoost model when visualizing basketball game data, but did not specifically obtain actual shooting situations. From this, the Voting-TRRF model can accurately visualize and analyze the actual basketball game data based on the actual and failed shooting attempts. The visualized results of the game are the actual game results. In addition, to verify the applicability of the Voting-TRRF prediction model in different user groups, the study compares the statistical results of the three models through different users. In the user group scoring experiment, 210 participants are recruited, with each user group containing 30 subjects. Participants are selected based on their identity characteristics (such as occupation, age, etc.) and stratified random sampling is used to ensure the representativeness of each group of samples. The experiment takes a double-blind design in which participants are not told the specific type of model and are only rated based on the visualization results. The scoring criteria include intuitiveness of the interface, clarity of data presentation and accuracy of results. All scores are independently completed on a unified scale (1-5 points). The objectivity of the scoring results is cross-verified by two researchers to ensure that there is no subjective bias in the experiment. The comparison results are shown in Table 2.

According to Table 2, when different users evaluate the three visualization models, the practicality of the Voting-TRRF model was significantly better than the other two models, and the average evaluation value of this model reached 5.23, which was 1.16 higher than the XGBoost model. However, the applicability of the LightGBM visualization prediction model was the worst among the three models. The visualization effect of the Voting-TRRF model was significantly better than the other two models, and this model has high applicability among different users. To further verify the application effect of the model in actual competition scenarios, this study selects 10 real-time match data in 2023 International Basketball League as the verification set, covering different confrontation intensity scenarios in regular season and postseason. After the model is deployed to the game live analysis system, it receives player position, action sequence, and tactical execution data in real time, and dynamically generates visual analysis results (such as tactical path heat map and real-time win prediction). Compared with the feedback from the field interpretation team and the coaching team, the accuracy of defensive vulnerability identification was 89.7%, and the prediction error of tactical execution efficiency was less than 6.3%. In addition, compared with the traditional manual analysis process, the model reduced the decision response time of key events (such as fast break success rate and zone defense effectiveness) to 0.8 seconds, significantly improving the efficiency of real-time tactical adjustment. The experimental results show that the robustness and practicability of the model can meet the needs of actual competitions.