Network payment rights and interests promotion method based on big data

Abstract

The invention relates to the technical field of network payment rights and interests promotion based on big data, and discloses a network payment rights and interests promotion method based on big data. Firstly, through original data record set definition, operation data of user login, transaction, interaction and the like are structured, and the problems of disordered data sources and non-uniform formats are solved. Secondly, all records are converted into numerical values between 0 and 1 through data normalization processing, and the situation that the stability of the algorithm is affected by dimensional differences of different operation numerical values is avoided; de-duplication and abnormal record removal are performed repeatedly at the same moment, only a larger normalized value is reserved, and a threshold value is set to remove abnormal data, so that redundancy and noise are reduced. Finally, the cleaned high-quality data set provides a standardized data source for links such as user layering, excitation design and A / B testing, and it is ensured that follow-up analysis is accurate and effective. The whole process optimizes the network payment rights and interests promotion method through data standardization, cleaning and quality improvement.

Description

Technical Field

[0001] The present invention relates to the technical field of network payment right promotion, and particularly to a method for promoting network payment rights based on big data. Background Art

[0002] In the current network payment ecosystem, promoting user rights has become an important strategy to improve user activity and payment conversion rate. With the rapid development of big data technology, the right promotion method based on data analysis has gradually replaced the traditional static right allocation mode. However, there are still many problems in the existing promotion methods, mainly reflected in the insufficient utilization efficiency of user data, the inaccurate user stratification strategy, the lag in the adjustment of the incentive plan, the imperfect monitoring and feedback mechanism, etc., resulting in an unsatisfactory overall promotion effect.

[0003] The existing network payment right promotion methods mainly rely on preset rules for user right allocation. For example, based on static indicators such as user registration time and transaction times, user levels are divided, and fixed right plans are provided for users at different levels. However, this method fails to fully consider the changes in user behavior characteristics, resulting in the promotion plan being difficult to match the real needs of users. In terms of data processing, the existing methods usually adopt simple data collection and cleaning strategies, such as directly removing abnormal data or performing normalization processing based on fixed thresholds. However, this method has a high noise interference when facing a large amount of user data and fails to fully utilize the correlation between data. In terms of user stratification and life cycle management, the existing technologies usually use a fixed cycle to count the activity of users. For example, user types are divided based on 30-day transaction data. However, this method is difficult to adapt dynamically to the changes in user behavior. For the design of the right incentive plan, the existing methods mainly set fixed incentive amounts based on the results of user stratification. For example, cashback is provided for new users' first payment, and additional points are provided for active users. This incentive strategy based on static rules is difficult to cope with the personalized differences in user needs and may result in poor incentive effects for some users. In terms of real-time monitoring and A / B testing, the existing methods randomly divide users into two groups and compare the effects of different right plans to adjust the experimental strategy. However, this method is difficult to adjust the experimental strategy in real time in the case of changing user behavior characteristics. In terms of promotion effect evaluation, the existing methods mainly rely on a single revenue calculation formula, such as calculating the promotion return rate through the ratio of incentive cost to transaction revenue. However, this calculation method fails to fully consider the long-term value of users. In addition, in terms of model optimization, the existing methods usually adopt a fixed parameter adjustment strategy, such as optimizing incentive parameters based on the gradient descent method. However, this method may have a problem of too high computational overhead when facing a large amount of user data and lacks an adaptive adjustment mechanism in the process of parameter update.

[0004] In summary, there are still many deficiencies in the existing network payment rights and interests promotion methods in aspects such as data processing, user stratification, rights and interests incentive, effect evaluation, and parameter optimization. In response to these problems, this case aims to propose a more accurate, efficient, and dynamically adjustable rights and interests promotion method based on big data to improve the effectiveness of user rights and interests promotion, optimize the promotion cost, and enhance the user experience of the overall payment ecosystem. Summary of the Invention

[0005] The present invention provides a network payment rights and interests promotion method based on big data, which helps to solve the problems mentioned in the above background technology.

[0006] The present invention provides the following technical solution: A network payment rights and interests promotion method based on big data, including:

[0007] S1. Data collection and preprocessing:

[0008] S11. Definition of the original data record set:

[0009] Let the user set ;

[0010] Among them, is the unique identifier of user ; is the total number of users;

[0011] Set the original record set as: ;

[0012] Among them, is the record of user at the th operation; is the total number of operations of user ;

[0013] Each record is the detailed data of user in one operation, and the specific form is:

[0014] ;

[0015] Among them, is the timestamp when the record is generated; is the operation type code, specifically:

[0016] When , it represents a login operation; when , it represents a transaction operation; when , it represents an interaction operation;

[0017] is the original value corresponding to the record, specifically:

[0018] When then ; When obtain the transaction amount of the user in the th transaction, denoted as , ; When obtain the interaction count generated by the user in this interaction, denoted as , ;

[0019] S12. Data normalization:

[0020] Normalize the original values of all records:

[0021] Let ; ;

[0022] wherein, is the minimum value of the original value of the record; is the maximum value of the original value of the record;

[0023] For each record calculate the normalized value: ; wherein, is the normalized value;

[0024] The updated record is denoted as: ;

[0025] S13. Duplicate removal and abnormal record elimination;

[0026] S14. Output the cleaned data set:

[0027] Finally, generate the cleaned data set:

[0028] ;

[0029] S2. User stratification and life cycle stage division;

[0030] S3. Design of customized rights and interests incentive plan;

[0031] S4. Real-time monitoring, A / B testing and dynamic adjustment;

[0032] S5. Effect evaluation and continuous optimization.

[0033] Optionally, the duplicate removal and abnormal record elimination specifically include:

[0034] S131. Duplicate removal processing:

[0035] For the same user of any two records and if they satisfy: and , set the selection function:

[0036] ;

[0037] wherein, is the th record of user ; and are the timestamp and operation type in the th record of user ;

[0038] S132. Eliminate abnormal records:

[0039] Set the abnormal threshold, denoted as ;

[0040] For each record if it satisfies: , then delete the record .

[0041] Optionally, the user stratification and life cycle stage division specifically include:

[0042] Set the statistical period to 30 days, denoted as ;

[0043] For each user , within the statistical period , calculate the following metrics:

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] ;

[0049] wherein, is the current time, in days; is the number of logins of user ; is the number of transactions of user ; is the number of interactions of user ; is the user The most recent login interval; For the user The number of days since registration; For the user The registration time;

[0050] Through the active scoring algorithm, calculate the active score of the user Active score:

[0051] ;

[0052] Among them, For the user Active score;

[0053] According to the number of days since the user's registration And the active score Set the life cycle stage of the user As: For:

[0054] ;

[0055] Among them, Is a new user; Is an active user; Is a dormant user; Is a churned user.

[0056] Optionally, the design of the customized rights and interests incentive plan specifically includes:

[0057] For each user According to the life cycle stage Calculate the incentive value And set the incentive cost ; Let ;

[0058] If Set the new user incentive algorithm, and calculate the incentive value according to the new user incentive algorithm Specifically: ;

[0059] If Set the active user incentive algorithm, and calculate the incentive value according to the active user incentive algorithm Specifically: ;

[0060] If Set the dormant user incentive algorithm, and calculate the incentive value according to the dormant user incentive algorithm Specifically: ;

[0061] If , set the churn user incentive algorithm and calculate the incentive value according to the churn user incentive algorithm , specifically: ;

[0062] Send the incentive value to the user terminal and record the incentive log.

[0063] Optionally, the real-time monitoring, A / B testing, and dynamic adjustment specifically include:

[0064] For the user set in the same life cycle stage , randomly divide it into two groups: namely, group and group ; where the total number of users in group is denoted as , and the total number of users in group is denoted as ;

[0065] Set incentive plans respectively;

[0066] Use the incentive plan for group ;

[0067] Use the incentive plan for group ;

[0068] Record the users with successful transactions as converted users;

[0069] Set a time window, denoted as ;

[0070] Within , obtain the total number of converted users in group , denoted as ;

[0071] Within , obtain the total number of converted users in group , denoted as ;

[0072] Calculate the conversion rate of group , specifically: , specifically: ;

[0073] Calculate the conversion rate of group , specifically: , specifically: ;

[0074] Set the difference index algorithm and calculate the difference index according to the difference index algorithm , specifically:

[0075] ;

[0076] If , then select the incentive plan for group ;

[0077] If , then select the incentive plan for group ;

[0078] If , then maintain the current incentive plan.

[0079] Optionally, the effect evaluation and continuous optimization specifically include:

[0080] During the statistical period, record the incentive cost and generate revenue for all users ;

[0081] Among them, the generated revenue is the revenue value generated by the user conversion behavior;

[0082] Calculate the overall rate of return, denoted as , specifically as:

[0083] ;

[0084] Set the user conversion prediction algorithm, specifically as:

[0085] ;

[0086] Among them, is the predicted probability of user conversion under the incentive ; is the parameter vector, among which, represents the incentive sensitivity coefficient, represents the incentive smoothing parameter;

[0087] Calculate the average predicted conversion rate of all users, specifically as:

[0088] ;

[0089] Set the evaluation function as: ;

[0090] Among them, is the conversion rate weight; is the incentive cost weight;

[0091] Update each parameter in the parameter vector;

[0092] Output And ;

[0093] Wherein is the updated parameter vector.

[0094] Optionally, each parameter in the updated parameter vector specifically includes:

[0095] S51. Take the partial derivative of , specifically:

[0096] ;

[0097] S52. Take the partial derivative of , specifically:

[0098] ;

[0099] Let the learning rate be ;

[0100] S53. The update formula is:

[0101] ;

[0102] ;

[0103] Wherein, is the original value of the excitation sensitivity parameter at the start of the current iteration step. It is the value determined at the end of the previous iteration or the initial value set in the first iteration value; represents the new value of the excitation sensitivity parameter after being updated in the current iteration step; is the original value of the excitation smoothing parameter at the start of the current iteration step. It is the value at the end of the previous iteration or the initial value set value; is the new value of the excitation smoothing parameter after being updated in the current iteration step;

[0104] Set the convergence threshold, denoted as ;

[0105] If , return to step S51, repeat steps S51 to S53, and perform iterative updates until the convergence condition is met .

[0106] The present invention has the following beneficial effects:

[0107] 1. Through the original data record set definition step, the system structurally defines various types of operation data of users, including logins, transactions, and interactions. Each record contains a unique user ID, a timestamp when the record was generated, an operation type code, and the original value. This solves the problems of messy original data sources and inconsistent formats, laying a standardized foundation for subsequent data processing and analysis. By clearly distinguishing different operation types, with logins fixed at 1.0, transactions obtaining specific amounts, and interactions obtaining specific counts, it ensures the accuracy and consistency in the data collection stage, thus improving the usability of the data. Through the data normalization step, the original values of all records are unified into the same value range, that is, by calculating the minimum and maximum values, the value of each record is converted into a normalized value between 0 and 1. This solves the problem that subsequent algorithms cannot be compatible due to the huge differences in the dimensions of the original values of different operation types, such as transaction amounts and fixed login values or interaction counts, making different data comparable and reducing the impact of extreme values on the stability of the algorithm, thereby enhancing the accuracy of subsequent data mining and analysis. Through the duplicate removal and abnormal record elimination step, the system screens duplicate records of the same user performing the same operation at the same time, retains the record with the larger normalized value, and uses a preset threshold to eliminate abnormal data below the threshold. This not only effectively removes data redundancy and reduces the interference of noise on subsequent analysis, but also ensures the integrity and accuracy of the data. Through these steps, the system can ensure that the input data is of high quality, without duplicates, and without abnormalities, providing a solid data foundation for subsequent user stratification, rights and interests incentives, and effect evaluation. Through the output of the cleaned data set step, the data set after normalization, duplicate removal, and abnormal elimination is output, providing a standardized and high-quality data source for subsequent user stratification and life cycle stage division. Overall, this data collection and preprocessing process solves the problems of messy original data, high data noise, and inconsistent formats, realizes data standardization, cleaning, and quality improvement, thus ensuring that subsequent links can perform efficient operations and make accurate decisions based on accurate and unified data, ultimately enhancing the efficiency and user experience of the entire network payment rights and interests promotion method.

[0108] 2. Through the deduplication process, the system filters out duplicate records of the same user, solving the data redundancy problem caused by the fact that a user may generate multiple data records of the same type at the same time. During this process, the system compares the normalized values of any two records and uses a selection function to retain only the record with the larger value, thus avoiding the situation of duplicate data statistics or abnormally high data caused by multiple repeated records. In this way, only one valid record is retained for the same user at each moment in the dataset, ensuring the uniqueness and accuracy of the data and providing clean and accurate input data for subsequent data analysis and algorithm calculations. At the same time, through the abnormal record elimination step, the system sets an abnormal threshold. The smaller the threshold, the more accurate the record, and the larger the threshold, the rougher the record. For each record, if its normalized value is lower than the preset threshold, the record is considered abnormal data or noise and is deleted. This measure effectively solves the problem of low-quality records in the data and avoids the interference of abnormal data on overall data statistics and model training. Abnormal elimination ensures the stability and consistency of the data, enabling subsequent data mining, user behavior analysis, and prediction model calculations to be carried out on a high-quality and reliable dataset.

[0109] 3. By setting the statistical period to 30 days and calculating multiple key indicators for each user during this period, this step solves the problem of incomplete user behavior information caused by inconsistent time spans or incomplete data collection in traditional user stratification. Specifically, by counting data such as the number of logins, transactions, interactions, the most recent login interval, and the number of registration days of users within 30 days, the system can comprehensively and dynamically capture the behavior characteristics of users and accurately calculate the user's lifecycle information by comparing the current moment with the registration moment. In addition, an active score algorithm is used to score users. By adding 1 in the formula to ensure that the denominator is not zero, the score of users who have not logged in for a long time is effectively reduced, solving the problem of abnormally high or low scores caused by long-term inactivity. Based on the user registration days and active scores, the system further divides users into four distinct lifecycle stages: new users, active users, dormant users, and churned users. This step not only eliminates the drawback of unclear user categories in traditional stratification methods but also makes the user groups in each stage have clear behavior characteristics and value manifestations. In this way, marketing and rights and interests promotion strategies can formulate differentiated incentive measures for users in different lifecycle stages, thereby improving the accuracy and conversion rate of promotion. Generally speaking, this step solves problems such as incomplete user information, strong data heterogeneity, and unclear stratification through a complete set of processes including data collection, indicator statistics, active scoring, and stratification division, and finally achieves the accurate capture and scientific management of user behavior, providing a solid data foundation for the optimization of subsequent personalized rights and interests incentives and promotion strategies.

[0110] 4. Through the overall step of designing a customized rights and interests incentive plan, the system calculates the incentive value for each user according to their life cycle stage respectively and sets the corresponding incentive cost, thus effectively solving the problems of single and lack of pertinence in incentive measures in traditional rights and interests promotion. Specifically, the system first stratifies users, clearly divides new users, active users, dormant users and lost users, and then designs specialized incentive algorithms for each type of user: The new user incentive algorithm encourages new users to complete transactions as soon as possible when they first experience the online payment service by setting a relatively high initial incentive value, thus improving the initial conversion rate of users. This step solves the problem that new users are difficult to complete the first transaction due to insufficient trust in the platform, ensuring that the platform can quickly accumulate an active user base. The active user incentive algorithm designs an incentive growth mechanism for active users, dynamically adjusting the incentive value according to the active score of users, making the incentive closely linked to the recent behavior of users. This step solves the problems of insufficient or excessive incentive for active users, ensuring that the incentive can not only keep users continuously participating but also avoid waste of resources, thus effectively enhancing the long-term user stickiness and repurchase rate. The dormant user incentive algorithm reactivates dormant users by giving them certain incentive compensation through compensatory incentives. This step solves the problem that dormant users cannot return to the platform due to lack of timely incentives, helping to improve the overall user retention rate. The lost user incentive algorithm designs a retention incentive strategy for lost users, providing a higher incentive amount to attract them to reuse the platform service, thus solving the risk of complete loss of lost users due to insufficient incentives. Finally, the system sends the calculated incentive value to the user terminal and records the incentive log, realizing real-time tracking of rights and interests distribution and effect monitoring. Through this series of steps, the system not only solves the problems of mismatched user incentives at each stage, out-of-control incentive costs and low user conversion rates, but also significantly improves the overall user participation and payment conversion rate of the platform. At the same time, it provides detailed basis for subsequent data analysis and promotion effect evaluation, ultimately enhancing the competitiveness and operation efficiency of the entire online payment ecosystem.

[0111] 5. Through real-time monitoring, A / B testing, and dynamic adjustment steps, the system first randomly divides the user set in the same life cycle stage into two groups, namely Group A and Group B, thus solving the problem that it is impossible to directly compare the effects of different incentive schemes when user characteristics are similar. This step ensures an equal number of users in each group through random grouping, making subsequent comparative analysis statistically significant and able to reflect the differences between the two incentive schemes in actual applications. Then, the system sets two different incentive schemes for the two groups of users respectively, and within a preset time window, which can be flexibly set according to the actual test duration, counts the number of users who complete transactions and successfully convert in each group, and then calculates the conversion rate of each group. In this way, the system can dynamically capture the real responses of users under different incentive schemes, thus solving the problem that traditional incentive measures are fixed and lack real-time feedback. After calculating the conversion rates of each group, the system further uses the difference index algorithm to calculate the conversion rate difference between the two groups, and this difference index reflects the effect gap between the two incentive schemes in the same user group. According to the preset positive and negative thresholds, the system can automatically determine which incentive scheme is better: if the difference index is greater than the positive threshold, it means that the incentive effect of the Group A scheme is significantly better than that of Group B, and at this time the system selects the incentive scheme of Group A; if the difference index is less than the negative threshold, the scheme of Group B is selected; if the difference index is in the middle range, the current scheme remains unchanged. Such a dynamic adjustment mechanism solves the problem that the incentive scheme cannot be optimized and switched in a timely manner during the traditional promotion process, ensuring that the system can quickly adjust the strategy according to real-time data feedback, thereby continuously improving the user conversion rate and platform operation efficiency. Overall, through a series of steps such as random grouping, conversion rate statistics, difference index calculation, and automatically selecting the optimal incentive scheme according to the preset threshold, the system not only solves the problems of inaccurate evaluation of the incentive scheme effect, lagging feedback, and fixed strategy, but also realizes the dynamic optimization of the incentive scheme. This method enables the system to continuously monitor the performance of each incentive scheme and automatically adjust the promotion strategy according to real-time data, thereby effectively improving the overall user conversion rate and the effect of rights and interests promotion.

[0112] 6. Through the effect evaluation and continuous optimization steps, the system first records the incentive cost and generated revenue of each user within a statistical period, where the generated revenue is the actual revenue generated by users through conversion behaviors. In this way, the system can accurately calculate the overall return rate, that is, the proportional relationship between the incentive cost and the generated revenue, solving the problem of difficult quantification of the promotion investment effect in traditional methods and making the overall promotion effect visually presented. Next, the system sets up a user conversion prediction algorithm, and calculates the predicted probability of each user's conversion under incentives according to this algorithm, thus quantifying the user's conversion behavior into specific values. This move solves the problem that relying solely on historical data cannot accurately predict future conversion trends, providing a scientific basis for the adjustment of subsequent promotion strategies. The system further calculates the average predicted conversion rate of all users and constructs an evaluation function based on this. This function comprehensively considers the conversion rate weight and the incentive cost weight, which can not only reflect the importance of high conversion rates but also the negative effects of incentive costs, and then realizes the balance between the economy and effectiveness of the incentive plan. By setting such an evaluation function, the system solves the problem that traditional promotion strategies fail to consider both user conversion effects and cost control at the same time, and can provide real-time feedback on the actual benefits of the promotion plan. Finally, the system continuously optimizes the user conversion prediction model and the evaluation function by updating each parameter in the parameter vector and using self-created algorithms such as gradient optimization to achieve the purpose of continuously optimizing the promotion strategy. Overall, through data recording, prediction model construction, evaluation function setting, and dynamic parameter update, this step effectively solves problems such as inaccurate promotion effect evaluation, lagging feedback, and rigid strategies, and finally realizes the real-time monitoring and continuous improvement of the online payment rights promotion plan, thereby improving the promotion benefits and user conversion rates.

[0113] 7. Through the three steps of S51 to S53, the system realizes the automatic update and optimization of each parameter in the parameter vector, thus solving the problem of fixed parameter settings and lack of dynamic adaptive adjustment in traditional methods. First, in step S51, by taking the partial derivative of the evaluation function, the system can quantify the sensitivity of each parameter to the overall objective function, such as the comprehensive index of conversion prediction and cost control, and solve the problem of mismatch between parameters and system performance. Then, in step S52, taking the partial derivative of the parameter again further refines the contribution of the parameter to different parts, ensuring that the comprehensive impact of each variable on the system effect can be fully considered when updating the parameter. Then, set the learning rate. Through the update formula in S53, after multiplying the previously calculated gradient information by the learning rate, the parameter value is gradually adjusted to achieve the dynamic update of the parameter. By setting the convergence threshold, the system can determine whether the current parameter update has reached the optimal point, solving the problem of possible oscillation or slow convergence during the parameter iteration process. If the convergence condition is not met, return to S51 and repeat the entire gradient solution and parameter update process until the convergence condition is satisfied, and finally output the updated parameter vector. This updated parameter vector can more accurately reflect the optimal combination of excitation sensitivity and excitation smoothness, so that the user conversion prediction model and evaluation function can more accurately predict the user conversion probability and control the excitation cost. Therefore, the problem of unclear mapping relationship between parameters and the evaluation function is solved through the partial derivative calculation step of S51; through the further partial derivative of S52, the problems of local extreme values and error accumulation during parameter update are solved; through the update formula and convergence judgment in S53, the system realizes the dynamic optimization of parameters, enabling the entire incentive strategy to continuously self-adjust, and finally achieving the effect of optimizing the user conversion rate and reducing the incentive cost. Overall, this parameter update mechanism enables the network payment rights promotion method to have the ability of adaptive learning and continuous optimization, greatly improving the flexibility of the system to respond to market changes and user behaviors, and ensuring the real-time effectiveness of the promotion plan and the optimization of resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 It is a schematic flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0115] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0116] Example, referring to Figure 1 , a network payment rights promotion method based on big data, including:

[0117] S1. Data collection and preprocessing:

[0118] S11. Definition of the original data record set:

[0119] Let the user set be ;

[0120] where is the unique number of user ; is the total number of users;

[0121] Set the original record set as: ;

[0122] where is the record of user at the th operation; is the total number of operations of user ;

[0123] Each record is the detailed data of user in one operation, and the specific form is:

[0124] ;

[0125] where is the timestamp when the record is generated; is the operation type code, specifically:

[0126] When , it represents a login operation; when , it represents a transaction operation; when , it represents an interaction operation;

[0127] is the original value corresponding to the record, specifically:

[0128] When , ; when , obtain the transaction amount of user in the th transaction, denoted as , ; when , obtain the interaction count generated by user in this interaction, denoted as , ; for example, when user clicks 3 times, it means 3 interactions, ;

[0129] S12. Data normalization:

[0130] Normalize the original values of all records:

[0131] Let ; ;

[0132] where is the minimum value of the original value of the record; is the maximum value of the original value of the record;

[0133] For each record Calculate the normalized value: ; where is the value after normalization; eliminate the dimensional influence between different operation types (such as transaction amount and click count) for convenient unified processing;

[0134] The updated record is denoted as: ;

[0135] S13. Remove duplicates and eliminate abnormal records;

[0136] S14. Output the cleaned data set:

[0137] Finally, generate the cleaned data set:

[0138] ;

[0139] S2. User stratification and life cycle stage division;

[0140] S3. Design of customized rights and interests incentive plan;

[0141] S4. Real-time monitoring, A / B testing and dynamic adjustment;

[0142] S5. Effect evaluation and continuous optimization.

[0143] Through the step of defining the original data record set, the system structurally defines various types of operation data of the user, including logins, transactions, and interactions. Each record contains a unique user identifier, a timestamp when the record was generated, an operation type code, and the original value. This solves the problems of messy original data sources and inconsistent formats, laying a standardized foundation for subsequent data processing and analysis. By clearly distinguishing different operation types, the accuracy and consistency in the data collection phase are ensured, thereby improving the usability of the data. Through the data normalization step, the original values of all records are unified into the same numerical range, that is, by calculating the minimum and maximum values, the value of each record is converted into a normalized value between 0 and 1. This solves the problem that subsequent algorithms cannot be compatible due to the huge differences in the dimensions of the original values of different operation types, such as transaction amounts and fixed login values or interaction counts, making different data comparable and reducing the impact of extreme values on the stability of the algorithm, thereby enhancing the accuracy of subsequent data mining and analysis. Through the duplicate removal and abnormal record elimination step, the system screens duplicate records of the same user performing the same operation at the same time, retains the record with the larger normalized value, and uses a preset threshold to eliminate abnormal data below the threshold. This not only effectively removes data redundancy, reduces the interference of noise on subsequent analysis, but also ensures the integrity and accuracy of the data. Through these steps, the system can ensure that the input data is of high quality, without duplicates, and without anomalies, providing a solid data foundation for subsequent user stratification, rights and interests incentives, and effect evaluation. Through the step of outputting the cleaned data set, the data set processed by normalization, duplicate removal, and abnormal elimination is output, providing a standardized and high-quality data source for subsequent user stratification and life cycle stage division. Overall, this data collection and preprocessing process solves problems such as messy original data, high data noise, and inconsistent formats, realizes data standardization, cleaning, and quality improvement, thereby ensuring that subsequent links can perform efficient operations and accurate decision-making based on accurate and unified data, ultimately enhancing the efficiency and user experience of the entire network payment rights and interests promotion method.

[0144] The duplicate removal and abnormal record elimination specifically include:

[0145] S131. Duplicate removal processing:

[0146] For the same user for any two records and If the following conditions are met: and , set the selection function:

[0147] ;

[0148] Wherein, For the user of the th record; and For the user of the timestamp and operation type in the th record;

[0149] Only keep the record with the larger normalized value at that moment;

[0150] S132. Eliminate abnormal records:

[0151] Set the abnormal threshold, denoted as ; The smaller the abnormal threshold, the more accurate the record, and vice versa;

[0152] For each record If it satisfies: , then delete the record .

[0153] Through the deduplication process, the system screens the duplicate records of the same user, solving the data redundancy problem caused by the possible generation of multiple identical type data records by the user at the same moment. In this process, the system compares the normalized values of any two records and uses a selection function to only keep the record with the larger value, thus avoiding the situation of repeated data statistics or abnormally high data caused by multiple repeated records. In this way, only one valid record is retained for the same user at each moment in the dataset, ensuring the uniqueness and accuracy of the data, and providing clean and accurate input data for subsequent data analysis and algorithm calculation. At the same time, through the step of eliminating abnormal records, the system sets an abnormal threshold. The smaller the threshold, the more accurate the record, and the larger the threshold, the rougher the record. For each record, if its normalized value is lower than the preset threshold, then the record is considered as abnormal data or noise and is deleted. This measure effectively solves the problem of low-quality records in the data and avoids the interference of abnormal data on the overall data statistics and model training. Abnormal elimination ensures the stability and consistency of the data, enabling subsequent data mining, user behavior analysis, and prediction model calculation to be carried out on a high-quality and reliable dataset.

[0154] The user stratification and life cycle stage division mentioned above specifically include:

[0155] Set the statistical period to 30 days, denoted as ;

[0156] For each user , within the statistical period , calculate the following indicators:

[0157] ;

[0158] ;

[0159] ;

[0160] ;

[0161] ;

[0162] wherein, is the current time, with the unit of days; is the login times of the user; is the transaction times of the user; is the interaction times of the user; is the recent login interval of the user; is the registration days of the user; is the registration time of the user;

[0163] Calculate the activity score of the user through the activity scoring algorithm:

[0164] ;

[0165] Here, 0.33 represents the contribution degree of the login times to the activity score. Although the login behavior is the most basic action of the user, its guiding role for subsequent transactions and interactions is relatively indirect. Therefore, a medium-level weight is given; 0.44 represents the direct contribution of the transaction behavior to the user activity. The transaction behavior is directly related to income and user stickiness. Therefore, the highest weight is given in the scoring; 0.23 represents the influence of the interaction behavior on the score. Although the interaction can reflect the user participation degree, its influence is relatively indirect. Therefore, a lower value is taken.

[0166] wherein, is the activity score of the user; is used to reduce the score of the user who has not logged in for a long time, and +1 ensures that the denominator is not zero;

[0167] According to the user registration days and the activity score , set the life cycle stage of the user as:

[0168] ;

[0169] wherein, For new users; For active users; For dormant users; For lost users.

[0170] By setting the statistical cycle to 30 days and calculating multiple key indicators for each user during this period, this step solves the problem of incomplete user behavior information caused by inconsistent time spans or incomplete data collection in traditional user stratification. Specifically, by counting the number of logins, transactions, interactions, the interval between the last login, and the number of days registered within 30 days, the system can comprehensively and dynamically capture the user's behavioral characteristics, and accurately calculate the user's life cycle information by comparing the current time with the registration time. In addition, the active scoring algorithm is used to score users, and the method of adding 1 to the formula to ensure that the denominator is not zero effectively reduces the score of users who have not logged in for a long time, solving the problem of high or low scores due to long-term inactivity. Based on the number of days registered by users and the active score, the system further divides users into four clear life cycle stages: new users, active users, dormant users, and lost users. This step not only eliminates the drawback of unclear user categories in traditional stratification methods, but also enables user groups in each stage to have clear behavioral characteristics and value performance. In this way, marketing and equity promotion strategies can formulate differentiated incentives for users at different life cycle stages, thereby improving the accuracy and conversion rate of promotion. In general, this step solves problems such as incomplete user information, strong data heterogeneity, and unclear stratification through a complete set of processes including data collection, indicator statistics, active scoring, and stratification. It ultimately achieves accurate capture and scientific management of user behavior, and provides a solid data foundation for subsequent optimization of personalized equity incentives and promotion strategies.

[0171] The customized equity incentive plan design specifically includes:

[0172] For each user , according to the life cycle stage Calculate incentive value , and set incentive costs ;make ;

[0173] like , set the new user incentive algorithm, and calculate the incentive value according to the new user incentive algorithm , specifically: ;

[0174] here The initial incentive benchmark for new users is 10 points, which means that newly registered users receive higher rewards to lower the threshold for initial use. 1.17 means that the daily attenuation rate of the incentive is 1.17 points.

[0175] If , set the active user incentive algorithm and calculate the incentive value according to the active user incentive algorithm , specifically: ;

[0176] Here, 5 represents that the basic incentive for active users is 5 points, reflecting that users already have a certain behavior basis at this stage and do not require excessive initial rewards. 0.81 means that for every 5 points exceeding the benchmark active score, the incentive increases by 0.81 points; 15 represents the incentive ceiling of 15 points to prevent out-of-control costs caused by excessive incentives;

[0177] If , set the dormant user incentive algorithm and calculate the incentive value according to the dormant user incentive algorithm , specifically: ;

[0178] Here, 8 represents that the basic incentive for dormant users is 8 points, giving a slightly higher benchmark than active users to attract reactivation; 1.52 means that for every 5 points the active score is lower than the benchmark, the compensatory incentive increases by 1.52 points. The higher coefficient reflects the greater difficulty in converting dormant users and requires stronger incentives. 20 represents the incentive ceiling of 20 points;

[0179] If , set the churned user incentive algorithm and calculate the incentive value according to the churned user incentive algorithm , specifically: ;

[0180] Here, 12 represents that the basic incentive for churned users is 12 points, giving a higher initial reward to retain long-term inactive users. 2.03 represents the incentive retention coefficient of 2.03, indicating that a greater compensation is required for the incentive effect of churned users to achieve a stronger retention effect. 2 is the active score limit for determining churned users, and 25 represents the incentive ceiling for churned users of 25 points;

[0181] Send the incentive value to the user terminal and record the incentive log.

[0182] Through the overall step of designing a customized rights and interests incentive plan, the system calculates the incentive value for each user according to their life cycle stage respectively, and sets the corresponding incentive cost, thus effectively solving the problems of single incentive measures and lack of pertinence in traditional rights and interests promotion. Specifically, the system first stratifies users, clearly divides new users, active users, dormant users and lost users, and then designs special incentive algorithms for each type of user: The new user incentive algorithm encourages new users to complete transactions as soon as possible when they first experience the online payment service by setting a relatively high initial incentive value, thereby improving the initial conversion rate of users. This step solves the problem that new users are difficult to complete the first transaction due to insufficient trust in the platform, ensuring that the platform can quickly accumulate an active user base. The active user incentive algorithm designs an incentive growth mechanism for active users, dynamically adjusts the incentive value according to the active score of users, making the incentive closely linked to the recent behavior of users. This step solves the problems of insufficient incentive or over-incentive for active users, ensuring that the incentive can not only keep users continuously participating, but also avoid waste of resources, thus effectively improving the long-term user stickiness and repurchase rate. The dormant user incentive algorithm gives certain incentive compensation to dormant users through compensatory incentives, enabling these users to be reactivated. This step solves the problem that dormant users cannot return to the platform due to lack of timely incentives, helping to improve the overall user retention rate. The lost user incentive algorithm designs a retention incentive strategy for lost users, provides a higher incentive amount to attract them to reuse the platform service, thereby solving the risk of complete loss of lost users due to insufficient incentives. Finally, the system sends the calculated incentive value to the user terminal and records the incentive log, realizing real-time tracking of rights and interests distribution and effect monitoring. Through this series of steps, the system not only solves the problems of mismatched user incentives in each stage, out-of-control incentive costs and low user conversion rate, but also significantly improves the overall user participation and payment conversion rate of the platform, and at the same time provides detailed basis for subsequent data analysis and promotion effect evaluation, ultimately enhancing the competitiveness and operation efficiency of the entire online payment ecosystem.

[0183] The real-time monitoring, A / B testing and dynamic adjustment specifically include:

[0184] For the user set in the same life cycle stage , for all users who meet the same , randomly divide them into two groups: namely group and group ; where the total number of users in group is denoted as , and the total number of users in group is denoted as ; and it satisfies , where is the total number of users in the set ;

[0185] Set separately Incentive plan; The incentive plans can all be set by the actual users, and only the number of converted users of these two incentive plans is used here;

[0186] For the grouping Use Incentive plan;

[0187] For the grouping Use Incentive plan;

[0188] Record the users with successful transactions as converted users;

[0189] Set a time window, denoted as ; The time window Can be set according to the specific duration of the A / B test by the user;

[0190] Within Obtain the total number of converted users in the grouping , denoted as ;

[0191] Within Obtain the total number of converted users in the grouping , denoted as ;

[0192] Calculate the conversion rate of the grouping , specifically: ; ;

[0193] Calculate the conversion rate of the grouping , specifically: , specifically: ;

[0194] Set the difference index algorithm, and calculate the difference index according to the difference index algorithm , specifically:

[0195] ;

[0196] If , then select the incentive plan of the grouping ;

[0197] If , then select the incentive plan of the grouping ;

[0198] If , then maintain the current incentive plan; if the current is the incentive plan of the grouping , then continue to use the grouping 's incentive plan; if it is currently grouped 's incentive plan, then continue to use the grouped 's incentive plan.

[0199] Through real-time monitoring, A / B testing, and dynamic adjustment steps, the system first randomly divides the set of users in the same life cycle stage into two groups, namely Group A and Group B, thus solving the problem that it is impossible to directly compare the effects of different incentive plans when user characteristics are similar. This step ensures an even number of users in each group through random grouping, making subsequent comparative analysis statistically significant and able to reflect the differences between the two incentive plans in actual applications. Then, the system sets two different incentive plans for the two groups of users respectively, and within a preset time window, which can be flexibly set according to the actual test duration, counts the number of users who complete transactions and successfully convert in each group, and then calculates the conversion rate of each group. In this way, the system can dynamically capture the real reactions of users under different incentive plans, thus solving the problem that traditional incentive measures are fixed and lack real-time feedback. After calculating the conversion rates of each group, the system further uses the difference index algorithm to calculate the conversion rate difference between the two groups, and this difference index reflects the effect gap produced by the two incentive plans in the same user group. According to the preset positive and negative thresholds, the system can automatically judge which incentive plan is better: if the difference index is greater than the positive threshold, it means that the incentive effect of the Group A plan is significantly better than that of Group B, and at this time the system selects the incentive plan of Group A; if the difference index is less than the negative threshold, the plan of Group B is selected; if the difference index is in the middle range, the current plan remains unchanged. Such a dynamic adjustment mechanism solves the problem that the incentive plan cannot be optimized and switched in a timely manner during the traditional promotion process, ensuring that the system can quickly adjust the strategy according to real-time data feedback, thereby continuously improving the user conversion rate and platform operation efficiency. Overall, through a series of steps such as random grouping, conversion rate statistics, difference index calculation, and automatically selecting the optimal incentive plan according to the preset threshold, the system not only solves the problems of inaccurate evaluation of the incentive plan effect, lagging feedback, and fixed strategy, but also realizes the dynamic optimization of the incentive plan. This method enables the system to continuously monitor the performance of each incentive plan and automatically adjust the promotion strategy according to real-time data, thereby effectively improving the overall user conversion rate and the effect of rights and interests promotion.

[0200] The said effect evaluation and continuous optimization specifically include:

[0201] During the statistical period, for all users Record the incentive cost and generate revenue ;

[0202] Among them, the generated revenue is the revenue value generated by the user conversion behavior;

[0203] Calculate the overall return rate, denoted as , specifically as follows:

[0204] ;

[0205] Set the user conversion prediction algorithm, specifically as follows:

[0206] ;

[0207] Among them, is the predicted probability of user converting under the incentive ; is the parameter vector, among which, represents the incentive sensitivity coefficient, represents the incentive smoothing parameter;

[0208] Calculate the average predicted conversion rate of all users , specifically as follows:

[0209] ;

[0210] Set the evaluation function as: ;

[0211] Among them, is the conversion rate weight, reflecting the importance of the conversion rate; is the incentive cost weight, reflecting the negative effect of the incentive cost; and can be obtained through historical data fitting, cost-profit analysis, and management strategy formulation;

[0212] Update each parameter in the parameter vector.

[0213] For example, suppose there are two users, namely and , the user incentive costs are and , the user-generated revenues are yuan and yuan; calculate the overall ; assume the initial parameter is ; calculate the predicted conversion rate of each user. For , ; for , ; calculate the average predicted conversion rate, ; assume the weights , , .

[0214] Through the effect evaluation and continuous optimization steps, the system first records the incentive cost and generated revenue of each user within a statistical period, where the generated revenue is the actual revenue generated by users through conversion behaviors. In this way, the system can accurately calculate the overall return rate, that is, the proportional relationship between the incentive cost and the generated revenue, solving the problem of difficult quantification of the promotion investment effect in traditional methods and making the overall promotion effect visually presented. Next, the system sets up a user conversion prediction algorithm, and calculates the predicted probability of each user's conversion under incentives according to this algorithm, thus quantifying the user's conversion behavior into specific values. This move solves the problem that simply relying on historical data cannot accurately predict future conversion trends and provides a scientific basis for the adjustment of subsequent promotion strategies. The system further calculates the average predicted conversion rate of all users and constructs an evaluation function based on this. This function comprehensively considers the conversion rate weight and the incentive cost weight, which can not only reflect the importance of high conversion rates but also the negative effects of incentive costs, and then achieves the balance between the economy and effectiveness of the incentive plan. By setting such an evaluation function, the system solves the problem that traditional promotion strategies fail to take into account both user conversion effects and cost control, and can provide real-time feedback on the actual benefits of the promotion plan. Finally, the system continuously optimizes the user conversion prediction model and the evaluation function by updating each parameter in the parameter vector and using self-created algorithms such as gradient optimization to achieve the purpose of continuously optimizing the promotion strategy. Overall, through data recording, prediction model construction, evaluation function setting, and dynamic parameter update, this step effectively solves problems such as inaccurate promotion effect evaluation, lagged feedback, and rigid strategies, and finally realizes the real-time monitoring and continuous improvement of the network payment rights promotion plan, thereby improving the promotion efficiency and user conversion rate.

[0215] Updating each parameter in the said parameter vector specifically includes:

[0216] S51. Take the partial derivative of , specifically as follows:

[0217] ;

[0218] S52. Take the partial derivative of , specifically as follows:

[0219] ;

[0220] Let the learning rate be ;

[0221] S53. The update formula is:

[0222] ;

[0223] ;

[0224] Where, At the start of the current iteration step, the original value of the excitation sensitivity parameter , which is the value determined at the end of the previous iteration or the initially set value in the first iteration ; denotes the new value of the excitation sensitivity parameter after being updated in the current iteration step, which reflects the result after adjustment along the gradient direction in the current iteration ; At the start of the current iteration step, the original value of the excitation smoothing parameter , which is the value at the end of the previous iteration or the initially set value; is the new value of the excitation smoothing parameter after being updated in the current iteration step, indicating the value after being adjusted by the gradient in this iteration ;

[0225] Set the convergence threshold, denoted as ;

[0226] If , return to step S51, repeat steps S51 to S53 for iterative update until the convergence condition is met ;

[0227] Output and ;

[0228] where is the updated parameter vector.

[0229] For example, calculate the gradient, for , ; for , ; set the learning rate , then update, ; ; if the convergence condition is satisfied, stop the iteration and finally output the optimal parameter vector .

[0230] Through these three steps S51 to S53, the system realizes the automatic update and optimization of each parameter in the parameter vector, thus solving the problem of fixed parameter settings and lack of dynamic adaptive adjustment in traditional methods. First, in step S51, by taking the partial derivative of the evaluation function, the system can quantify the sensitivity of each parameter to the overall objective function, such as the comprehensive index of conversion prediction and cost control, and solve the problem of mismatch between parameters and system performance. Then, in step S52, taking the partial derivative of the parameters again further refines the contribution of the parameters to different parts, ensuring that the comprehensive impact of each variable on the system effect can be fully considered when updating the parameters. Then, set the learning rate. Through the update formula in S53, after multiplying the previously calculated gradient information by the learning rate, the parameter values are gradually adjusted to achieve the dynamic update of the parameters. By setting the convergence threshold, the system can judge whether the current parameter update has reached the optimal point, and solve the problem of possible oscillation or slow convergence during the parameter iteration process. If the convergence condition is not met, return to S51 and repeat the entire gradient solution and parameter update process until the convergence condition is satisfied, and finally output the updated parameter vector. This updated parameter vector can more accurately reflect the optimal combination of incentive sensitivity and incentive smoothness, so that the user conversion prediction model and evaluation function can more accurately predict the user conversion probability and control the incentive cost. Therefore, the problem of unclear mapping relationship between parameters and the evaluation function is solved through the partial derivative calculation step in S51; through the further partial derivative in S52, the problems of local extreme values and error accumulation during parameter update are solved; through the update formula and convergence judgment in S53, the system realizes the dynamic optimization of the parameters, enabling the entire incentive strategy to continuously self-adjust and finally achieve the effect of optimizing the user conversion rate and reducing the incentive cost. Overall, this parameter update mechanism enables the network payment rights and interests promotion method to have the ability of adaptive learning and continuous optimization, greatly improving the flexibility of the system to respond to market changes and user behaviors, and ensuring the real-time effectiveness of the promotion plan and the optimization of resource utilization.

[0231] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device.

[0232] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for promoting network payment rights based on big data, characterized in that: include: S1. Data collection and preprocessing: S11. Original data record set definition: Set user ; in, For users unique number of is the total number of users; Set the original record collection to: ; in, For users In the Records of the first operation; For users The total number of operations; Each record For users Detailed data in one operation, in the form of: ； in, The timestamp when the record was generated; is the operation type code, which is: when When , it indicates a login operation; when When , it indicates a transaction operation; when , it indicates interactive operation; To record the corresponding original values, specifically: when hour, ;when When getting the user In the The transaction amount in the transaction is recorded as , ;when When getting the user The interaction count generated in this interaction is recorded as , ; S12. Data normalization: Normalize the raw values ​​of all records: make, ; ; in, is the minimum value of the original value recorded; is the maximum value of the original value recorded; For each record Calculate the normalized value: ;in, is the normalized value; The updated record is recorded as: ; S13, remove duplicates and eliminate abnormal records; S14. Output the cleaned data set: Finally, the cleaned data set is generated: ； S2, user stratification and life cycle stage division; S3. Design of customized equity incentive plan; S4, real-time monitoring, A / B testing and dynamic adjustment; S5. Effect evaluation and continuous optimization.

2. According to the big data-based online payment rights promotion method of claim 1, it is characterized in that: The deduplication and removal of abnormal records specifically include: S131, deduplication processing: For the same user Any two records of and If satisfied: and , set the selection function: ； in, For users No. records; and For users No. The timestamp and operation type in the record; S132, remove abnormal records: Set the abnormal threshold, denoted as ; For each record If satisfied: , then delete the record .

3. According to the big data-based online payment rights promotion method of claim 1, it is characterized in that: The user stratification and life cycle stage division specifically include: Set the statistical period to 30 days, recorded as ; For each user , in the statistical period The following indicators are calculated: ； ； ； ； ； in, is the current time, in days; For users Number of logins; For users Number of transactions; For users Number of interactions; For users The last login interval of For users Number of days of registration; For users The time of registration; Calculate the user through the active scoring algorithm Activity rating: ； in, For users Activity score of Based on the number of days the user has registered With active score , set user Life cycle stage for: ； in, For new users; For active users; For dormant users; For lost users.

4. According to the big data-based online payment rights promotion method of claim 3, it is characterized in that: The customized equity incentive plan design specifically includes: For each user , according to the life cycle stage Calculate incentive value , and set incentive costs ;make ; like , set the new user incentive algorithm, and calculate the incentive value according to the new user incentive algorithm , specifically: ; like , set the active user incentive algorithm, and calculate the incentive value based on the active user incentive algorithm , specifically: ; like , set the dormant user incentive algorithm, and calculate the incentive value based on the dormant user incentive algorithm , specifically: ; like , set the lost user incentive algorithm, and calculate the incentive value based on the lost user incentive algorithm , specifically: ; Send the incentive value to the user terminal and record the incentive log.

5. According to the big data-based online payment rights promotion method of claim 4, it is characterized in that: The real-time monitoring, A / B testing and dynamic adjustment specifically include: For a collection of users in the same life cycle stage , and randomly divided them into two groups: and grouping ; Group The total number of users in , grouping The total number of users in ; Set separately Incentive schemes; Group use Incentive schemes; Group use Incentive schemes; Record users who successfully completed transactions as converted users; Set the time window, denoted as ; exist Get grouping within The total number of converted users is recorded as ; exist Get grouping within The total number of converted users is recorded as ; Calculation Grouping Conversion rate , specifically: ; Calculation Grouping Conversion rate , specifically: ; Set the difference indicator algorithm and calculate the difference indicator according to the difference indicator algorithm , specifically: ； like , then select Group incentive schemes; like , then select Group incentive schemes; like , then maintain the current incentive plan.

6. A method for promoting network payment rights and interests based on big data according to claim 5, characterized in that: The effect evaluation and continuous optimization specifically include: During the statistical period, for all users Recording incentive costs and generate income ; Which generates income The revenue value generated by user conversion behavior; Calculate the overall rate of return, denoted as , specifically: ； Set the user conversion prediction algorithm, specifically: ； in, For users In Motivation The predicted probability of conversion. is a parameter vector, where represents the excitation sensitivity coefficient, represents the excitation smoothing parameter; Calculate the average predicted conversion rate for all users , specifically: ； Set the evaluation function to: ; in, is the conversion rate weight; is the incentive cost weight; Update each parameter in the parameter vector; Output and ; in is the updated parameter vector.

7. The method for promoting network payment rights and interests based on big data according to claim 1, characterized in that: Each parameter in the update parameter vector specifically includes: S51, yes Find the partial derivative, specifically: ； S52, yes Find the partial derivative, specifically: ； Set the learning rate ; S53, the update formula is: ； ； in, is the excitation sensitivity parameter at the beginning of the current iteration step The original value of , which is the value determined at the end of the previous iteration, or the value initially set in the first iteration value; Indicates that after the current iteration step is updated, the excitation sensitivity parameter The new value of is the excitation smoothing parameter at the beginning of the current iteration step The original value of value; is the excitation smoothing parameter after updating in the current iteration step The new value of Set the convergence threshold, denoted as ; like , return to step S51, repeat steps S51 to S53, iteratively update until the convergence condition is met .

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