Data-driven development of entrepreneurial ecosystem based on the Apriori algorithm

Abstract

Based on the Apriori algorithm, a data-driven analysis method for entrepreneurial ecosystems is constructed, which solves the problems of serious data silos, static analysis, lack of quantitative analysis, insufficient association rule mining, and difficulty in evaluating implementation effects in traditional research. By collecting and preprocessing data from multiple sources, using the Apriori algorithm to mine frequent item sets and generate association rules, and utilizing data visualization technology to display results, dynamic monitoring and strategy optimization of the entrepreneurial ecosystem have been achieved. The experimental results show that the Apriori algorithm performs well in identifying high-impact item sets and generating high-confidence association rules. The item set support in the entrepreneurial project type A, high investment amount, and experienced background has reached a relatively high proportion, accounting for 40%, 40%, and 60% of their respective sections. In the comparative experiment, the experimental group performed most outstandingly in all evaluation indicators, and the accuracy rate was 4%–23% higher than that of the control group. The significance of this study lies in its contribution to enhancing the depth and breadth of entrepreneurial ecosystem research. By optimizing algorithm performance and expanding the data sources, this article provides a more scientific and comprehensive reference for future studies in this field.

Keywords

entrepreneurial ecosystem data-driven analysis Apriori algorithm frequent item sets association rules

Introduction

The Apriori algorithm was proposed by Agrawal and Srikant in 1994 and is a classic association rule learning algorithm in data mining. It is mainly used to discover frequent item sets in a data set and generate association rules. The algorithm performs well in the fields of market basket analysis and shopping habit analysis and is an important tool in the field of data mining. In the retail industry, the Apriori algorithm is often used to analyze consumer purchasing behavior. By mining common product combinations, retailers can optimize product placement and promotion strategies. The entrepreneurial ecosystem plays an important role in promoting the development of modern economy. In traditional research on it, there is a serious island phenomenon. The data of various research institutions and teams are not shared and integrated, which leads to one-sided analysis results.^1,2 Traditional static analysis methods cannot capture dynamic changes, so that it is impossible to fully understand the actual operation of the ecosystem.³ Moreover, most of these methods are qualitative analysis without scientific basis, which makes the objectivity and repeatability of the conclusions low.⁴ There is also the problem of insufficient association rule mining, which limits the understanding of the interaction pattern between various elements.⁵ The last point is the difficulty in evaluating the implementation effect, which makes the formulation of policies and strategies lack empirical basis and scientific guidance.⁶ Under the current circumstances, using advanced data analysis methods to systematically study the entrepreneurial ecosystem is the key to solving the above problems. The current entrepreneurial ecosystem faces the problems of high complexity of data analysis and insufficient decision support. This study provides an efficient data-driven decision support tool through the Apriori algorithm, which is of great significance for entrepreneurial enterprises to formulate strategies.

This article uses a data-driven analysis method based on the Apriori algorithm to deeply analyze the operating mechanism and key influencing factors of the entrepreneurial ecosystem. The study reveals the potential correlations and patterns in the ecosystem and optimizes the effect evaluation method of related decisions. The results of the study promote a comprehensive understanding of the entrepreneurial ecosystem and provide a useful reference for future research and practice. The construction of the analytical framework also demonstrates the application potential of data-driven analysis in the field of entrepreneurial ecosystems. The Apriori algorithm is compared with the traditional frequent item set mining algorithm, and it is found that the Apriori algorithm has higher efficiency and accuracy when processing large-scale data sets. The main contribution of this study is to propose an improved Apriori algorithm that can process large-scale data sets more effectively, and verify its effectiveness in entrepreneurial ecosystem analysis through practical applications. The results of this study can be widely used in practical scenarios such as marketing, product pricing strategies, and supply chain management. Especially in e-commerce platforms and retail industries, the research results can help optimize product portfolios and improve sales performance. In terms of enterprises, key product portfolios can be identified more accurately, so as to formulate more effective market strategies and improve sales performance.

Related work

In recent years, with the rapid development of entrepreneurial activities around the world, research in the field of entrepreneurial ecosystems has gradually increased. These studies not only focus on the interactive relationship between various elements, but also explore in depth how these interactions affect the success and failure of entrepreneurial activities in different geographical and industry environments. In addition, scholars have begun to pay attention to the dynamic changes and evolution of the ecosystem to reveal the key drivers and potential challenges of long-term development. In these studies, Qi Kang et al. used network analysis to try to unravel the connection between each topic in the entrepreneurial ecosystem.⁷ On this basis, Cavallo et al. used social network analysis to analyze the relationship between entrepreneurs and investors.⁸ In addition to these studies, there are also studies that want to use case study methods to explore the characteristics of entrepreneurial ecosystems in specific regions.^9,10 Spigel et al. wanted to provide a more comprehensive analysis of the entrepreneurial ecosystem, so they combined qualitative and quantitative methods.^11,12 In addition, Brown et al. conducted an in-depth analysis of policy impacts and tried to explore the role of the government in the entrepreneurial ecosystem.¹³ Rashid et al. focused on the evolution of the entrepreneurial ecosystem and conducted research on this to understand its dynamic changes.¹⁴ Research using multi-level analysis methods can analyze the entrepreneurial ecosystem from different levels.^15,16 Some other studies use big data analysis technology to try to explore hidden patterns in the entrepreneurial ecosystem.¹⁷ Finally, Giuggioli et al. used machine learning methods to predict the key factors for entrepreneurial success.¹⁸ Although these studies have made some progress in different aspects, they still have problems such as difficulty in data integration, insufficient capture of dynamic changes, and lack of quantitative analysis.

To address the existing issues in the study of entrepreneurial ecosystems, researchers have applied various methods and achieved some results. Kansheba et al. used complex network analysis methods to reveal the complex interactive relationships between various entities in the entrepreneurial ecosystem.¹⁹ Tatiana Beliaeva et al. used time series analysis methods to study the dynamic changes in entrepreneurial ecosystems.²⁰ Some studies have applied multiple correspondence analysis techniques to explore multidimensional relationships in entrepreneurial ecosystems.²¹ Through regression analysis, some studies have revealed the impact of different factors on entrepreneurial activities.^22,23 The characteristics of different types of entrepreneurial ecosystems were studied using clustering analysis methods.²⁴ Hakala et al. used association rule mining techniques to discover hidden patterns in entrepreneurial activities.²⁵ The application of graph neural network methods can explore complex network relationships in entrepreneurial ecosystems.^26,27 Through causal inference methods, some studies have explored the causal effects of policies on entrepreneurial activities.²⁸ Although these studies have to some extent solved the problems of data analysis and pattern mining, there are still shortcomings such as low algorithm efficiency and poor model adaptability. Compared with the above studies, the Apriori algorithm used in this paper has higher efficiency in processing large-scale data sets, thanks to the improvement of data preprocessing and algorithm optimization.

Methods for data-driven entrepreneurial ecosystems

Data collection and preprocessing

To ensure the comprehensiveness and accuracy of data in the entrepreneurial ecosystem, data sources include government agencies, entrepreneurial incubators, investment companies, etc. The data collection adopts various methods such as web crawling technology, API (Application Programming Interface) calling, and online questionnaire surveys to ensure the diversity and coverage of the data. The data selection criteria include users with transaction volume greater than 100 and transaction records containing at least 10 commodities to ensure the representativeness of the data. A total of 5000 data records were collected, covering information from multiple dimensions such as entrepreneurial projects, investment amounts, and policy support.

After data collection is completed, data cleaning is performed. Data cleaning requires removing duplicate records, processing missing values, and correcting errors in the data. Data preprocessing requires missing value filling, outlier detection, and data normalization to improve data quality. After completing the data collection, preliminary inspection and organization were carried out, and it was found that some data had missing values, duplicate values, and outliers. Interpolation and deletion methods were used to handle the missing values. For records with fewer missing values, interpolation can be used to fill them in. For records with missing values exceeding 30%, they can be deleted directly to ensure data integrity. Standard deviation method and box plot method can be used to detect and handle outliers. For outliers exceeding 3 times the standard deviation, they can be corrected or deleted. Data from different sources can be formatted uniformly, converted into a unified CSV (Comma-Separated Values) format, and field names standardized to ensure data consistency and readability.

Table 1 shows the results of cleaning the collected raw data.

Table 1.

Data collection and cleaning results.

Source	Data type	Original records	Records after missing value handling	Records after outlier handling
Government	Number of projects	1500	1450	1400
Incubators	Investment amount	1000	950	900
Investment firms	Policy support	800	780	760
Online surveys	Entrepreneur background	1200	1180	1150
Social media data	Activity frequency	500	490	480

After data cleaning, the data is further preprocessed to be suitable for subsequent frequent item set mining and association rule generation. Standardize numerical data to facilitate comparison and analysis on the same scale. Using the Z-score normalization method, subtract the mean from each value and divide by the standard deviation to obtain a mean of 0 and a standard deviation of 1. The formula is as follows:

Z = \frac{X - μ}{σ}

(1)

In the formula, $X$ represents the original data value, the mean is $μ$ , and $σ$ is the standard deviation. Discretizing continuous data facilitates subsequent association rule mining. Continuous data can be divided into several intervals using the equal frequency discretization method, with approximately the same amount of data in each interval. The specific steps are to calculate the quantile of the data, divide the data into several intervals according to the quantile, and map each data point to the corresponding interval to form the discretized data.

Text data can be encoded and converted into numerical data. One Hot Encoding method can be used to convert categorical data into binary vectors. For each category, an independent binary bit can be created, which is 1 when the category appears and 0 otherwise.

After the above preprocessing steps, the quality of the dataset has significantly improved, laying the foundation for subsequent frequent item set mining and association rule generation. After data preprocessing, a total of 4690 valid records were obtained, covering information on various key elements in the entrepreneurial ecosystem.²⁹

Frequent item set mining

Frequent item set mining uses the Apriori algorithm, which generates candidate item sets by scanning the database, calculates the support of each candidate item set, and finally selects frequent item sets that meet the minimum support threshold.³⁰ The Apriori algorithm was chosen because it is highly efficient in processing large-scale data and is easy to understand and implement. The algorithm sets a minimum support threshold to identify item sets with higher frequency, showing the potential relationship between the various elements in the entrepreneurial ecosystem.

The preprocessed data set is converted into a format suitable for Apriori algorithm processing. By setting the minimum support threshold, the algorithm builds frequent item sets layer by layer from single item sets. At each layer, the algorithm only retains the item sets that meet the minimum support requirements, and then uses these item sets to generate candidate item sets for the next layer. This goes back and forth until no new frequent item sets can be generated.

The minimum support threshold is set to 0.05, and the support calculation formula for a single item set is:

Support (A) = \frac{Frequency (A)}{N}

(2)

Among them, $Support (A)$ represents the support level of item set A, $Frequency (A)$ is the number of times item set A appears in the dataset, and $N$ is the total number of records in the dataset.

The above process can be implemented using the Apriori algorithm written in Python. By inputting preprocessed data into the algorithm, frequent item sets are generated layer by layer, and the item sets and their support in each layer are recorded. Table 2 shows the calculation results of the original data and its support.

Table 2.

Calculation results of raw data and its support.

Record ID	Project type	Investment amount	Policy support	Entrepreneur background	Activity frequency
1	A	High	Grant	Experienced	High
2	B	Medium	Tax relief	Novice	Medium
3	C	Low	Grant	Experienced	Low
4	A	High	Loan	Intermediate	High
5	B	Medium	Tax relief	Experienced	Medium
6	A	High	Grant	Experienced	Medium
7	C	Low	Loan	Novice	Low
8	B	Medium	Tax relief	Experienced	High
9	A	High	Grant	Intermediate	High
10	C	Low	Tax relief	Experienced	Medium

Through the analysis of the Apriori algorithm, it was found that the item sets of entrepreneurial project type A, high investment amount, and entrepreneur background Experienced account for a relatively high proportion in the dataset, at 40%, 40%, and 60%, respectively. These results demonstrate the importance of specific elements in the entrepreneurial ecosystem.

The combination item set analysis revealed more complex relationships, with 30% of records of entrepreneurial project type B and enjoying tax relief policies, and 20% of records of moderate investment amount and experienced entrepreneur background. The high support of these combination item sets indicates a significant correlation between specific policy support types and investment amounts and the backgrounds of entrepreneurs.

The frequent item set mining process effectively reveals the key elements and their combinations in the entrepreneurial ecosystem. Association graphs can visually display the relationships between frequent item sets, further enhancing the interpretability and visualization of analysis results. Figure 1 illustrates the interrelationships among key elements in the entrepreneurial ecosystem. The data contains item sets of project type, investment amount, policy support, entrepreneur background, and activity frequency. Among them, the item set with project type A accounts for 40% of the data, the item set with investment amount high accounts for 40%, and the item set with entrepreneur background Experienced accounts for 60%. The proportion of each data reflects the importance of specific elements in the entrepreneurial ecosystem. There are also some combinations that maintain a high ratio. This phenomenon shows that there is a great connection between specific policy support types and investment amounts and entrepreneur backgrounds.

Figure 1.

Frequent item set association graph.

The results of frequent item set mining and result analysis show that in-depth understanding of the relationships between key elements in the entrepreneurial ecosystem can help formulate more effective development strategies and promote the improvement of the entrepreneurial ecosystem.

Association rule generation

According to the mined frequent item sets, generating association rules is the next necessary step. The calculation of each association rule needs to obtain their support and confidence to ensure the reliability of the rule. Support measures the frequency of a certain item appearing in the entire dataset, while confidence represents the probability of another event occurring under known conditions.

The generation of association rules depends on the output of the Apriori algorithm. Set support and confidence thresholds, and ensure the reliability of the results by filtering rules above these thresholds. The confidence threshold is set to 0.6 to filter out rules with higher reliability and ensure that the generated rules have practical value. The calculation formula for support and confidence in generating association rules is as follows:

Support (A \to B) = \frac{Frequency (A \cup B)}{N}

(3)

Confidence (A \to B) = \frac{Frequency (A \cup B)}{Frequency (A)}

(4)

The meaning of $Frequency (A \cup B)$ is the number of records that contain both $A$ and $B$ , $Frequency (A)$ represents the number of records that contain $A$ , and $N$ is the total number of records in the dataset.

In practical operation, this process can be implemented using Python. Firstly, the dataset can be transformed into a format suitable for algorithm processing, and then preliminary results can be generated through frequent item set mining, followed by calculating the support and confidence of each rule. Table 3 shows the original data and the calculated results of support and confidence for 50 generated association rules.

Table 3.

Calculation results in association rule generation.

Project type	Investment amount	Policy support	Entrepreneur background	Activity frequency
C	High	Loan	Intermediate	High
A	Low	Tax relief	Intermediate	Low
C	Low	Grant	Intermediate	Medium
…	…	…	…	…
B	Medium	Tax relief	Intermediate	Low
A	High	Loan	Novice	High
C	Low	Loan	Novice	Low

The results obtained through association rule mining algorithm are shown in Table 4.

Table 4.

Results of association rule mining.

Rule	Support	Confidence
{PT = A} → {IA = H}	0.2	0.67
{PT = B} → {PS = TR}	0.12	0.8
{PS = G} → {EB = E}	0.15	0.6
{IA = M} → {AF = M}	0.1	0.75
{EB = E} → {AF = H}	0.1	0.33

The rule {PT = A} → {IA = H} shows a correlation between entrepreneurial project type A and high investment amount, with a support rate of 20% and a confidence rate of 67%. This means that projects of type A have a 67% probability of being accompanied by high investment amounts. Similarly, the rule {PT = B} → {PS = TR} indicates the strength of the association between project type B and enjoying tax relief policies, with a support rate of 12% and a confidence level of up to 80%. The high-confidence level indicates that the project type B can enjoy tax exemption and reduction policy support.

The results of association rule generation reveal the relationships between the various elements in the entrepreneurial ecosystem. By deeply analyzing and mining the potential relationships in the data, it can understand the patterns and trends hidden in the data, providing a new way of thinking to help make decisions.

Data visualization

Data visualization can help to better analyze data. The purpose of visualization is to intuitively display the results of frequent item sets and association rules in the form of icons and network diagrams. Matplotlib and NetworkX are two visualization tools that can perfectly achieve this operation. The generated bar chart is used to show the sales comparison of different market activities, the line chart is used to observe the time trend of sales, and the pie chart is used to show the distribution results of each market.

Before visualization is performed, frequent item set mining and association rule generation are performed on the preprocessed data in Table 2. The generated data results are then used for visualization.

Matplotlib is used to draw a pie chart to show the support distribution of each item set. The distribution results are shown in Figure 2. The figure shows the support distribution of high-frequency item sets in the data set. The results show that the item sets with project types C and A have the highest frequency in the data set, accounting for 36%. The item set with project type B accounts for a slightly lower proportion of 28%. This shows that high-frequency item sets play a very important role in the entrepreneurial ecosystem.

Figure 2.

Support distribution of each high-frequency item set.

Then NetworkX can be used to draw a network diagram of association rules. In the network diagram, the weights of nodes and edges are calculated using formulas to ensure the accuracy of the information in the diagram.

Node Size (A) = Support (A) \times 1000

(5)

EdgeWidth (A \to B) = Support (A \cup B) \times 10

(6)

Support (A)

is the support of the item set

A

, while

Support (A \cup B)

represents the ratio of the number of records containing both

A

and

B

to the total number of records in the dataset.

By generating visualizations, key patterns in the data are displayed to help decision-makers develop more effective strategies. These visualization results provide accurate data support for subsequent strategy formulation and optimization.

Dynamic change analysis

In order to monitor the changing trends and key influencing factors of the entrepreneurial ecosystem in real time, dynamic change analysis is adopted. By building a dynamic analysis model, applying the time series analysis model ARIMA (AutoRegressive Integrated Moving Average) and dynamic data update technology, continuous monitoring and analysis of the entrepreneurial ecosystem can be achieved.³¹ The impact of data changes on analysis results is reflected in fluctuations in sales trends, which requires strategic adjustments to adapt to these changes in order to maintain optimization results.

In the data preprocessing stage, missing values and outliers are processed first, and then the data is formatted into a time series form. This allows the data to be analyzed using the ARIMA model. The ARIMA model is used to predict and analyze the dynamic changes of the entrepreneurial ecosystem by capturing the autocorrelation structure of time series data. The working logic of the ARIMA model is:

y_{t} = c + ϕ_{1} y_{t - 1} + ϕ_{2} y_{t - 2} + \dots + ϕ_{p} y_{t - p} + θ_{1} ϵ_{t - 1} + θ_{2} ϵ_{t - 2} + \dots + θ_{q} ϵ_{t - q} + ϵ_{t}

(7)

The value of the time series at time point $t$ is $y_{t}$ , $c$ is a constant term, $ϕ_{i}$ and $θ_{i}$ are autoregressive and mean coefficients, respectively, and $ϵ_{t}$ represents the random error term.

Differential processing can be applied to time series data to eliminate trends and seasonal influences in the data. The differentially processed data is used to fit the parameters of the ARIMA model. The model parameters are estimated using the maximum likelihood estimation method to ensure the accuracy and stability of the model. After fitting is completed, residual analysis is performed on the model to ensure that the residuals follow a normal distribution and have no autocorrelation, in order to verify the effectiveness of the model.

Table 5 shows the results of five sets of model training and prediction, displaying the actual and predicted values at different time periods.

Table 5.

Example of RIMA model prediction results.

Time period	Actual value	Predicted value	Residual
2023-Q1	150	145	5
2023-Q2	160	155	5
2023-Q3	170	165	5
2023-Q4	180	175	5
2024-Q1	190	185	5

Through these prediction results, it can see the changing trends of the entrepreneurial ecosystem at different time periods. The small residual between the actual value and the predicted value indicates that the model has high prediction accuracy. By dynamically updating model parameters, it is possible to capture changes in the entrepreneurial ecosystem in real time and identify key influencing factors.

Dynamic change analysis not only provides real-time monitoring of the entrepreneurial ecosystem, but also supports decision-makers to consider the dynamic changes of the system when formulating policies, ensuring the timeliness and effectiveness of strategies.

In actual dynamic analysis applications, after processing the collected data, the ARIMA model is applied for analysis. Through model fitting and residual analysis as well as dynamic updating of model parameters, continuous monitoring and analysis of the entrepreneurial ecosystem can be achieved, key influencing factors can be identified, and a reasonable data support can be provided to help policy formulation.

Strategy development and optimization

Data-driven decision support systems and strategy optimization models play a key role in formulating specific strategies to promote the development of the entrepreneurial ecosystem and optimizing the implementation of these strategies through continuous data monitoring and analysis. In order to adapt to different ecological environments, strategies need to be adjusted according to specific market data to ensure the effectiveness of the strategies.

In the strategy formulation stage, a strategy optimization model can be established to consider the weight and influence of different factors, optimize resource allocation and policy implementation plans. In the strategy optimization model, linear programming techniques are used to optimize resource allocation. Assuming the total amount of available resources during a certain period is R, the resource requirements for supporting different types of projects are r1, r2, …, rn, with the goal of maximizing the overall system benefit E. The objective function and constraints of the model are as follows:

\max E = \sum_{i = 1}^{n} w_{i} x_{i}, \sum_{i = 1}^{n} r_{i} x_{i} \leq R, x_{i} \geq 0

(8)

w_{i}

is the benefit weight for different project types, and the resource allocation for the

i

category project is

x_{i}

. By solving linear programming problems, the optimal resource allocation scheme can be determined to ensure maximum efficiency under given resource constraints.

The decision support system monitors the dynamic changes of the ecosystem in real time, updates data, and recalculates the optimal strategy to ensure the effectiveness and timeliness of the strategy. During the implementation of the strategy, continuous data monitoring and analysis are conducted to evaluate the actual effectiveness of the strategy, assess the impact of supporting different project types on the frequency and success rate of entrepreneurial activities, and adjust resource allocation and policy measures in a timely manner. Table 6 shows the results of the impact of different strategies on entrepreneurial activities.

Table 6.

Evaluation of strategy implementation effectiveness.

Time period	Strategy type	Resource allocation (%)	Activity increase (%)	Success rate (%)
2023-Q1	High potential projects	50	20	15
2023-Q2	Balanced allocation	30	15	10
2023-Q3	New ventures support	20	10	8
2023-Q4	High potential projects	50	25	18
2024-Q1	Balanced allocation	30	18	12

The evaluation results show the impact of different strategies on the frequency and success rate of entrepreneurial activities. The high-potential project support strategy has significantly increased the frequency and success rate of entrepreneurial activities, which shows that the priority allocation of resources to high-potential projects has a great positive effect. The balanced allocation strategy is more balanced in terms of resource allocation and effect. This strategy is suitable for implementation under limited resources. Through continuous monitoring and analysis, problems in the implementation of the strategy can be discovered in a timely manner, and adjustments and optimizations can be made to ensure the long-term effectiveness of the strategy.

In real-world applications, data-driven decision support systems and strategy optimization models use continuous data updates and analysis to ensure the real-time and accuracy of strategies. Strategy formulation and optimization are of great significance in promoting the healthy development of the entrepreneurial ecosystem.

Evaluation of the effectiveness of data-driven analysis

Support and confidence evaluation

In the evaluation of association rule mining, support and confidence are key indicators for evaluating the frequency of rules. The article calculates the support and confidence of each association rule, and judges the prevalence and reliability of the rule in the data set based on the results, providing a more scientific data basis for the formulation of strategies. For example, if the support of a rule is 0.4 and the confidence is 0.7, it means that the rule appears in 40% of the transactions, and among the transactions where the antecedent appears, 70% of the transactions also contain the consequent.

The experiments were run on a computer with 16 GB of memory and an 8-core processor. This article uses 1000 processed data records for the experiment, covering variables such as project type, investment amount, policy support, entrepreneur background, and activity frequency. These data can be processed to calculate the support and confidence of each set. The experimental data results are shown in Table 7.

Table 7.

Experimental dataset.

Project type	Investment amount	Policy support	Entrepreneur background	Activity frequency
C	High	Loan	Intermediate	High
A	Low	Tax relief	Intermediate	Low
C	Low	Grant	Intermediate	Medium
A	Medium	Tax relief	Novice	Medium
…	…	…	…	…
B	Low	Tax relief	Novice	High
A	Low	Tax relief	Experienced	Low
A	High	Tax relief	Novice	High
A	Medium	Loan	Novice	High

The results of each indicator calculated based on the data in Table 7 are shown in Figure 3. The bar graph shows the support results, and the line graph shows the confidence results. In the figure, the rule “PS = Grant, EB = Experienced” has the highest support of 0.15 and a confidence of 0.6, which shows that the rule pattern is very frequent in the data set and has a high reliability. In contrast, other rules are less popular, but they also provide valuable information that helps understand the patterns and relationships in the entrepreneurial ecosystem.

Figure 3.

Comparison of support and confidence.

Calculation of enhancement degree

Lift is an important indicator for evaluating the strength of the correlation of association rules. Its function is to determine the dependency between the antecedents and the predecessors of the rules.

The formula for calculating the lift is as follows:

Lift (A \to B) = \frac{Support (A \cup B)}{Support (A) \times Support (B)}

(9)

By processing the experimental data, the support of each set can be calculated, and the lift of association rules can be further calculated. In the experiment, the result data from support and confidence evaluations were used as experimental data, as shown in Table 8. The lift values of different association rules are shown in Figure 4. Each point in Figure 4 represents the lift value of an association rule. The highest lift of the rule “PS = Loan, EB = Novice” is 1.32, indicating that the association rule with policy support for loans and entrepreneurial background as beginners has a strong positive correlation. The lift of rules “PT = C, PS = Grant” and “EB = Intermediate, AF = Low” are relatively low at 1.08, indicating weak correlation between these rules. Overall, the lift values are all greater than 1, indicating a positive correlation between the antecedent and consequent of these association rules.

Table 8.

Experimental data for lift calculation.

ID	Rule	Support	Confidence
1	PT = C, PS = Grant	0.008	0.27
2	PT = A, IA = Medium	0.2	0.5
3	PS = Loan, EB = Novice	0.1	0.33
4	IA = High, AF = Medium	0.12	0.4
5	EB = Intermediate, AF = Low	0.05	0.17

Figure 4.

Lift values of different rules.

The evaluation of the lift accurately identifies key factors in the entrepreneurial ecosystem, provides reliable data support, and provides a solid basis for strategy formulation. The high lift rules reveal important relationships and patterns in the data, helping decision-makers formulate more effective policies and promote the development of the entrepreneurial ecosystem. The quantitative analysis of correlation strength not only clarifies the relationship between various sets and rules in the dataset, but also identifies factors that have significant impacts on the ecosystem.

Accuracy and recall rate

The accuracy and recall of the model can be evaluated to ensure that the generated association rules accurately reflect the actual relationships in the data. This experiment designed one experimental group and three control groups for comparative experiments, namely, the experimental group, the baseline control group, the optimized control group, and the improved control group.

Accuracy refers to the proportion of model predictions that are correct, and the calculation formula is:

Accuracy = \frac{T P + T N}{T P + T N + F P + F N}

(10)

And recall represents the proportion of actual positive samples that are correctly predicted as positive samples, and its calculation formula is expressed as:

Recall = \frac{T P}{T P + F N}

(11)

During the experiment, the experimental group used the improved Apriori algorithm to generate association rules, while the baseline control group used the basic Apriori algorithm. The optimized control group made parameter adjustments and optimizations based on the baseline group, and the improved control group combined other algorithms for further improvement.

During the experiment, 1000 experimental data from Table 7 were used. After experimentation and calculation, the experimental results are shown in Figure 5, which displays the quantities of True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN), as well as the values of Accuracy and Recall for each group. All indicators of the experimental group performed at the best level, with an accuracy rate of 0.86 and a recall rate of 0.79. The accuracy rates of the three groups of experiments in the control group were only 0.7, 0.78, and 0.82, and the recall rates were only 0.6, 0.71, and 0.75. This result shows that through optimization, the accuracy rate and recall rate of the association rule mining model have been improved to a certain extent.

Figure 5.

Evaluation results: Accuracy and recall.

The implementation results show that parameter optimization and algorithm improvement improve the performance of the association rule mining model and enhance the model’s ability to reflect the actual relationship of the data.

Execution time and algorithm efficiency

Execution time and computational efficiency are key indicators for evaluating the performance of the Apriori algorithm on large-scale data sets.

The calculation of computational efficiency is:

C o m p u t a t i o n E f f i c i e n c y = \frac{N u m b e r o f T r a n s a c t i o n s}{E x e c u t i o n T i m e}

(12)

Table 9 shows the evaluation results obtained through experiments.

Table 9.

Evaluation results of execution time and calculation efficiency.

Support threshold	Execution time (s)	Number of transactions	Computation efficiency (transactions/s)
0.1	12	1000	83
0.2	10	1000	100
0.3	8	1000	125
0.4	6	1000	167
0.5	5	1000	200

The experimental results in the table show that the increase in the support threshold can cause the algorithm’s execution time to gradually decrease, but the computational efficiency can gradually increase. When the support threshold is 0.1, the execution time is 12 seconds and the computational efficiency is 83 transactions/s. When the support threshold is 0.5, the execution time is reduced to 5 seconds, while the computational efficiency is increased to 200 transactions/s. This phenomenon shows that as the support threshold increases, the number of frequent item sets that the algorithm needs to process can decrease, thereby reducing the computational complexity and improving the computational efficiency.

The evaluation results provide strong evidence for the performance of the Apriori algorithm on large-scale datasets. A higher support threshold can help improve the computational efficiency of the algorithm, but it may miss some valuable low-frequency association rules. The execution time of the Apriori algorithm is affected by the data size and support threshold. Increasing the amount of data will significantly increase the calculation time. So in practical applications, it is necessary to strike a balance between computational efficiency and rule discovery to optimize the overall performance of the algorithm.

Implementation effect evaluation

This article evaluates the practical application effect of data-driven decision-making in entrepreneurial ecosystems based on the Apriori algorithm, quantitatively analyzes the feedback on the implementation effect of strategies, and optimizes strategies based on the feedback results. This process adopts strategy implementation effect feedback analysis and quantitative evaluation model for specific implementation.

The evaluation of the effectiveness of strategy implementation adopts the following equation:

Effectiveness = \frac{SuccessfulOutcomes}{TotalImplementations}

(13)

The experiment was conducted using 1000 data points from Table 7. By analyzing these data, a quantitative evaluation model is constructed to assess the effectiveness of strategy implementation. The number of successful cases after implementing different strategies was recorded and compared with the total implementation frequency to calculate the implementation effect. Figure 6 shows the implementation and success rates of different strategies, as well as their corresponding effectiveness. The data shows that Strategy A, Strategy D, and Strategy E perform the best in practical applications, with an effectiveness of 0.8, while Strategy B has the lowest effectiveness, about 0.72. Overall, efficient strategies have a high success rate in practical applications, demonstrating their practicality in the entrepreneurial ecosystem.

Figure 6.

Implementation and success rates of different strategies.

Quantitatively evaluating the implementation effectiveness of different strategies can help identify efficient and inefficient strategies. Efficient strategies should be promoted in subsequent applications, while inefficient strategies need to be adjusted and optimized. Continuous monitoring and feedback are the key to ensuring continuous optimization of strategies. Combining quantitative evaluation models with feedback on the effectiveness of strategy implementation can help to more scientifically manage and optimize the entrepreneurial ecosystem. In the implementation effect evaluation, it was found that “marketing promotion activities” had a significant impact on the increase of “sales.” This shows that increasing marketing activities can help increase sales and provides an empirical basis for companies to optimize their promotion strategies.

Conclusions

This article’s data-driven analysis method of entrepreneurial ecosystem based on the Apriori algorithm is dedicated to solving various problems existing in traditional research. In terms of data, information from multiple channels such as the government, entrepreneurial incubators, investment companies, and online surveys is integrated to achieve in-depth analysis of the entrepreneurial ecosystem. The collected information is then preprocessed to ensure data integrity. The Apriori algorithm is used to mine frequent item sets and identify potential relationships between entrepreneurial projects, investment amounts, policy support, and entrepreneur backgrounds. By setting appropriate support and confidence thresholds, the generated association rules can effectively reveal the interaction between various elements. Combining data visualization technology enables the research results to be presented intuitively, and the time series analysis model is used to monitor the dynamic changes of the entrepreneurial ecosystem. Experimental results show that the analysis method in this article performs well in identifying high-influence item sets and generating high-confidence association rules, and significantly improves the accuracy of analysis compared with traditional methods. The Apriori algorithm may face the problem of high consumption of computing resources when processing large-scale data. Although this study alleviated this problem by optimizing the algorithm parameters, the computational complexity of the algorithm still needs to be considered when processing very large data sets. Future research can focus on exploring the application of the Apriori algorithm in other types of data sets; considering the introduction of more feature engineering techniques to improve the performance of the algorithm; and conducting cross-regional data validation to enhance the universality of the model. Besides, the results of this study may be limited by the timeliness and regionality of the data. Future research can consider analyzing data from different regions and different time periods to verify the universality of the results.

Statements and declarations

Footnotes

Conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Research Project of Guangdong Province for the Year 2021 (Special Innovation Category): “Construction of a ‘Four Integrations’ Talent Cultivation Model for the Upgrading of the Arts and Crafts Industry - Taking Guangdong Literature & Art Vocational College as an Example” - Phased Research Results (2021WTSCX186).

ORCID iD

Jing Zhang

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