Clustering method, system and device based on double-layer optimization

Abstract

The invention discloses a clustering method, system and device based on double-layer optimization, and belongs to the technical field of information processing. Comprising the following steps: obtaining product quality data, consumer category data and product promotion cost data in a database; according to the obtained data and based on the position decision variable, obtaining probability data of each product selected by each category of consumers; an upper-layer optimization model and a lower-layer optimization model are constructed to form a double-layer optimization model, an equilibrium strategy set is obtained through the double-layer optimization model, and the double-layer optimization model is linearized to obtain a solved optimal strategy set. Compared with the prior art, the method has the advantages that by comprehensively considering merchant behaviors and applying a game theory method and a mathematical optimization technology, the accuracy of ranking data and results is remarkably improved, meanwhile, the efficiency of a ranking algorithm is greatly improved through algorithm optimization, and the capacity of quickly responding to market changes is achieved.

Description

Technical Field

[0001] The present invention relates to the field of information processing technology, and more specifically, to a clustering method, system and device based on double-layer optimization. Background Art

[0002] The rapid development of mobile Internet is due to the popularity of mobile devices such as smartphones and tablets, as well as the widespread application of high-speed network technology. These technologies allow people to access the Internet through mobile devices anytime and anywhere to conduct information search, social entertainment, online shopping and other activities. This convenience has greatly promoted the onlineization of people's daily lives. With the vigorous development of mobile Internet, people's daily lives have gradually shifted from offline to online. This shift has greatly facilitated people's daily lives, but it has also brought obstacles to online consumption such as network virtuality and product diversity. Network virtuality is one of the main obstacles facing online consumption. Unlike offline shopping, online shopping cannot allow consumers to directly touch and try out products. Online shopping relies on product keyword searches and uses virtual information such as pictures, texts and videos to understand products. This information asymmetry can easily lead consumers to have doubts about the quality and performance of products, thereby affecting their purchasing decisions. In addition, some merchants may also use the virtuality of the Internet to carry out false propaganda and exaggeration, further exacerbating consumers' distrust. Product diversity is a major advantage of online shopping, but it is also an obstacle. Online platforms gather a large amount of product information, and consumers often feel dazzled and at a loss when choosing. In addition, due to the wide variety of products and uneven quality, consumers need to spend more time and energy to screen and compare products. This not only increases consumers' shopping costs, but may also lead to returns, exchanges and other problems due to improper choices.

[0003] In an online shopping environment with a wide variety of products, in order to improve user experience and interface friendliness, platforms usually rank related products and display them in pages, helping consumers quickly filter out high-quality and popular products and improve shopping efficiency. Rankings are usually based on a variety of factors, such as sales, positive reviews, click-through rates, conversion rates, product weights (which may include store weights, product weights, brand weights, etc.), user behavior data (such as browsing time, number of favorites, and number of added purchases), etc. The platform will calculate the comprehensive score of each product based on these indicators through complex algorithms and rank them accordingly. Consumers can view more products by turning pages, but usually only pay attention to the products on the first few pages, because the top-ranked products are more likely to attract attention. This display method allows consumers to find products that may be of interest more quickly, but it also triggers unfair competition by some merchants. For example, merchants artificially increase product sales and positive reviews through false transactions, forged sales and positive reviews, etc. The act of brushing orders seriously disrupts the market order, harms the interests of consumers, and also affects the fairness and credibility of the platform. Another example is that merchants induce consumers to give positive reviews by giving them rewards such as cash or coupons. This behavior undermines the fairness of the evaluation system, makes the evaluation lose its reference value, and misleads other consumers' purchasing decisions. Therefore, in order to maintain market order and consumer rights, the platform usually takes measures to deal with the unfair competition of bad merchants.

[0004] At present, the default ranking method of products on mainstream domestic platforms generally takes into account multiple factors such as sales volume, price, and number of positive reviews. However, this mechanism also faces some challenges and problems, especially the impact of false information and inferior products on the ranking system, and the situation where high-quality products are ranked down due to insufficient advertising investment. Although the platform has made many efforts in the ranking mechanism, it is still difficult to fully identify all false information at this stage. Some merchants of inferior products may use false information to improve their rankings, thereby attracting more consumers' attention and purchases, and thus obtaining more profits; while high-quality products may be ranked down due to the merchants' low advertising investment or lack of sufficient exposure opportunities, resulting in a decline in sales and profits, thus falling into a situation of "inferior products driving out good products", which not only harms the interests of consumers, but also destroys the fair competition environment in the e-commerce market. Therefore, the platform needs to strategically design its processing of product data to balance the interests of multiple parties, achieve a balance between consumer utility, merchant profits and platform revenue, and build a healthier and more sustainable e-commerce ecosystem.

[0005] In the related art, for example, Chinese patent document CN114092172A provides a method, device, equipment and storage medium for ranking products on an e-commerce platform, including a time estimation module, which is used to calculate the estimated browsing time based on the average daily usage time of users; a browsing page estimation module, which is used to obtain the estimated browsing page based on the estimated browsing time; and a heat sorting module to sort the popularity of products based on the sales volume and profit of the products on the e-commerce platform. Although this solution achieves a certain degree of personalized product ranking through the time estimation module, the browsing page estimation module and the heat sorting module, it has defects in the accuracy of the ranking data and results and the efficiency of the ranking algorithm, especially failing to effectively solve the impact of merchants' advertising investment and false information on the unfair evaluation system when processing product data.

[0006] From the above, it can be seen that the relevant technology has not proposed an effective solution to the problem of how to solve the problem of how to solve the problem of the unfair evaluation system caused by merchants' advertising investment and false information when processing product data. Summary of the invention

[0007] 1. Technical issues to be solved

[0008] In response to the problem of how to reduce the impact of false information on the data processing process in the prior art, the present invention provides a clustering method, system and device based on double-layer optimization, which can realize the construction of a double-layer optimization model, and then obtain a clustering method for product data based on double-layer optimization by solving examples, thereby obtaining a globally optimal ranking strategy.

[0009] 2. Technical solution

[0010] The purpose of the present invention is achieved through the following technical solutions.

[0011] The content of this application is used to introduce concepts in a brief form, which will be described in detail in the detailed implementation section below. The content of this application is not intended to identify the key features or essential features of the technical solution claimed for protection, nor is it intended to limit the scope of the technical solution claimed for protection.

[0012] Some embodiments of the present application propose a clustering method, system and device based on double-layer optimization to solve the technical problems mentioned in the above background technology section.

[0013] As a first aspect of the present application, some embodiments of the present application provide a clustering method based on two-layer optimization, including the following steps: acquiring product quality data, consumer category data, and product promotion cost data in a database; obtaining probability data of each category of consumers selecting each product based on the acquired data and based on position decision variables; constructing an upper-layer optimization model and a lower-layer optimization model to form a two-layer optimization model, obtaining a balanced strategy set through the two-layer optimization model, and obtaining the optimal strategy set after solving by linearizing the two-layer optimization model.

[0014] Furthermore, after obtaining the product keyword, the database is traversed to output n product information and its corresponding n display location information, where n is a natural number; the location decision variable X ijl The set X is represented as:

[0015] X={X ijl |i,j∈[n]}∈{0,1} n×n ;

[0016] Among them, i represents the serial number of the product, which is a natural number; j represents the serial number of the display location, which is a natural number; l represents the serial number of the merchant type, which is a natural number.

[0017] Furthermore, when the display position number of product number i = j, the position decision variable X ijl =1; when the display position number of product number i ≠ j, the position decision variable X ijl =0.

[0018] Furthermore, when considering the influence of position effect, the initial utility u ilα lnθ occurs j The initial utility considering the position effect is expressed as: ilα +lnθ j ;

[0019] Among them, u ilα represents the initial utility of type α consumer for product number i, θ j Indicates the visibility of the display position with serial number j; lnθ j Represents the base θ j The natural logarithm of

[0020] The initial utility in the product selection stage when considering the impact of advertising investment It is expressed as:

[0021]

[0022] Among them, r il Indicates the rating of the product with serial number i, s ilrepresents the sales volume of product number i, n il represents the number of product reviews with serial number i, and L represents the total number of merchant types; ∈ i It represents the random utility of consumers affected by the environment during the product selection stage, which has a mean of 0 and a variance of ∈ 2 Normal distribution; P cpc Indicates the CPC price set by the platform, P cpa Indicates the CPA unit price set by the platform. It represents the number of CPC investments made by merchants of type l for product i. It is represented by the number of CPA investments made by merchant type l for product i.

[0023] Furthermore, in the utility evaluation phase, the utility of the product with serial number i is evaluated It is expressed as:

[0024]

[0025] Among them, δ i is the random utility of consumers affected by the environment during the utility evaluation stage, which has a mean of 0 and a variance of δ 2 Normal distribution of il The number of fake comments invested is, represents the probability that a type α consumer recognizes that a type l merchant gives a false positive review to product i;

[0026] When evaluating the utility of all products, the expected utility E of the product ijlα It is expressed as:

[0027]

[0028] Among them, z ilα Indicates that an evaluation cost is paid each time an evaluation is performed.

[0029] Furthermore, we introduce the location decision variable X ijl , the preference weight for product number i It is expressed as:

[0030]

[0031] Where, e represents the base of natural logarithm; represents the probability that type α consumers choose a product under the influence of the location decision variable,

[0032] Based on the position decision variable, the set of combinations of product numbers and their corresponding display position numbers S = {(i, j) | X ijl =1}, when hour,

[0033] make

[0034] The probability of selecting product number i is It is expressed as:

[0035]

[0036] Furthermore, the upper optimization model is used to maximize the expected revenue of the platform, and the lower optimization model is used to maximize the expected profit of the merchants. The objective function max F1 of the upper optimization model is expressed as:

[0037] max F1=E c +E a ;

[0038] max means maximizing the function behind it, F1 means the profit within the platform period, E c Indicates the platform commission income, E a Indicates the platform advertising investment.

[0039] Furthermore, the objective function max F2 of the lower optimization model is expressed as:

[0040] max F2=E s -C c -C a -C m -C r -C f ;

[0041] Among them, F2 represents the profit of the merchant during the cycle, E s represents the income of the merchant from selling products, C c Indicates the commission the platform takes from the merchant’s sales amount, C a represents the advertising cost of the merchant, C m Represents the merchant’s product purchase cost, C r represents the merchant’s product return cost, C f It indicates the cost incurred by merchants in generating false positive reviews.

[0042] As a second aspect of the present application, some embodiments of the present application provide a clustering system based on two-layer optimization, including: a data acquisition module for acquiring product quality data, consumer category data and product promotion cost data in a database; a data processing module for obtaining probability data of each category of consumers selecting each product based on the acquired data and based on position decision variables; a two-layer optimization model is composed of an upper-layer optimization model and a lower-layer optimization model, an equilibrium strategy set is obtained through the two-layer optimization model, and the optimal strategy set after solving is obtained by linearizing the two-layer optimization model.

[0043] As the third aspect of the present application, some embodiments of the present application provide a clustering device based on two-layer optimization, including one or more processors and a memory, wherein the memory stores a program and is configured to execute the following steps by the one or more processors: obtaining product quality data, consumer category data, and product promotion cost data in a database; obtaining probability data of each category of consumers selecting each product based on the acquired data and based on position decision variables; constructing an upper-layer optimization model and a lower-layer optimization model to form a two-layer optimization model, obtaining a balanced strategy set through the two-layer optimization model, and obtaining the optimal strategy set after solving the problem by linearizing the two-layer optimization model.

[0044] 3. Beneficial effects

[0045] Compared with the prior art, the advantages of the present invention are:

[0046] (1) This solution constructs a two-layer optimization dynamic ranking model for e-commerce platforms, expands and enriches ranking optimization applications, and proposes a product ranking method that takes into account the impact of merchants’ advertising investment and false information, balancing the interests of merchants and platforms. By simulating the dynamic interaction process between e-commerce platforms and merchants, it deeply explores the false information and advertising investment levels of different types of merchants, and formulates reasonable promotion plans for merchants. It can design more scientific and reasonable product rankings in situations where it is difficult for the platform to identify all the influence of false information, which is conducive to establishing good stickiness and interaction with consumers and merchants, and maximizing the platform’s profits under the principle of mutual benefit and win-win with merchants.

[0047] (2) This technical solution not only significantly improves the accuracy of ranking data and results by comprehensively considering merchant behavior and applying advanced game theory methods and mathematical optimization techniques, making them closer to the actual market situation, but also greatly improves the efficiency of the ranking algorithm through algorithm optimization, achieving the ability to quickly respond to market changes. Compared with existing technologies, it shows obvious advantages in both accuracy and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the process of a clustering method based on double-layer optimization in one embodiment of the present invention;

[0049] Figure 2 A diagram of a two-stage sequential selection model of consumers in one embodiment of the present invention;

[0050] Figure 3 A logical structure diagram of a product ranking method based on double-layer optimization in one embodiment of the present invention;

[0051] Figure 4 This is a flow chart for solving a two-layer optimization problem based on KKT conditions in one embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0053] according to Figures 1 to 4 As shown, a clustering method based on double-layer optimization of the present invention comprises the following steps:

[0054] Collect product quality data, consumer category data, and product promotion cost data from the database;

[0055] According to the acquired data and based on the position decision variables, the probability data of consumers in each category choosing each product is obtained; a two-layer optimization model is formed by constructing an upper optimization model and a lower optimization model.

[0056] Specifically, this solution performs cluster analysis on user behavior data. This cluster analysis is not only based on static data, but also takes into account dynamic user behavior data; user behavior data includes consumer behavior data and merchant behavior data. In addition, the merchant behavior data is used as one of the important inputs in the two-layer optimization model of this solution. By analyzing this data, the cost-effectiveness of different promotion strategies can be evaluated. Through the two-layer optimization model, this solution comprehensively considers user behavior data, deeply analyzes user behavior data and merchant behavior data, and achieves accurate grasp of user needs and optimization of marketing strategies.

[0057] Among them, the two-level optimization model involves two levels of decision makers, namely merchants and platforms, each of which has independent objective functions and decision variables. In this case, it is very difficult to directly find the global optimal strategy set, because decision makers at different levels may make conflicting decisions in pursuit of their own optimal interests. Therefore, the two-level optimization model adopts a more realistic and feasible approach, namely, finding an equilibrium strategy set. An equilibrium strategy set refers to a mutually coordinated decision-making scheme that is accepted and implemented by decision makers at all levels under given conditions. These schemes may not be globally optimal, but they achieve a certain degree of balance among decision makers, so that there is no motivation to change the strategy because the change will not bring additional benefits. This equilibrium state provides a stable and predictable decision-making framework in a complex decision-making environment, which helps to reduce decision risks and improve decision efficiency.

[0058] In addition, the equilibrium strategy set also takes into account the mutual influence and constraints between decision makers at different levels. In the two-level optimization model, the decisions of upper-level decision makers will affect the behavior and goal achievement of lower-level decision makers, and the reactions of lower-level decision makers will in turn affect the decisions of upper-level decision makers. This mutual influence and constraint relationship makes the equilibrium strategy set more in line with the actual situation, because in the actual decision-making process, each decision maker often needs to consider the reactions and interests of other decision makers.

[0059] Since the game between merchants and platforms is dynamic, there is a certain time difference between the strategies given by both parties. The state where merchants obtain temporary "maximum benefits" (greater than the benefits of the equilibrium strategy) is unstable. Since the platform strategy will change, the merchant's benefits will be affected. When solving the model, this solution considers the final equilibrium strategy. Therefore, the optimal strategy mentioned in this solution is equivalent to the equilibrium strategy.

[0060] In a specific embodiment, the specific steps of the clustering method based on double-layer optimization are as follows:

[0061] S1. Obtain and process data:

[0062] The process of acquiring and processing data is that the platform collects product quality data and consumer category data from the database, and merchants obtain product promotion cost data from the platform, and finally obtain the probability of different categories of consumers choosing each product.

[0063] Specifically, the process of acquiring and processing data focuses on the in-depth description of the interactive behaviors and their mutual relationships between the platform, merchants and consumers during the transaction process, and at the same time, carefully analyzes the two-stage selection behavior pattern of consumers. Given the positional advantage effect inherent in the ranking, consumers' attention is often focused on the top-ranked products. In addition, the limited time and patience resources significantly increase the probability of the top-ranked products being selected. The platform increases its own advertising revenue and the commission income extracted from the merchant's sales by setting the advertising unit price and product ranking mechanism, aiming to optimize the advertising revenue and sales commission structure. In this scheme, the commission income extracted from the merchant's sales is referred to as commission. At the merchant level, based on the platform ranking mechanism, merchants will choose to invest in advertising and false information to improve the product's display position ranking, thereby increasing the product selection rate and sales revenue, that is, strategically investing in advertising or taking information beautification measures based on the platform's ranking mechanism to improve the product's ranking, thereby promoting the growth of the product's selection probability and sales revenue.

[0064] In this game scenario, the platform plays the role of a leader, whose goal is to maximize the expected revenue of the platform; while merchants, as followers, strive to maximize their expected profits. The interaction between the two parties follows the logic of the master-slave game, reflecting the dynamic process of "bargaining". In the process of analyzing the two-stage selection behavior of consumers, it is necessary to recognize the uniqueness of consumer selection behavior in the e-commerce environment. This uniqueness is reflected in two stages: one is the product selection stage, and the other is the utility evaluation stage.

[0065] like Figure 2 As shown in the figure, in the product selection stage, consumers browse products according to the ranking order of platform products. At this time, they only view the basic attributes of the products displayed on the page. This stage is a quick browsing based on the basic attributes of the products. When the product meets the consumer's preferences, it will generate a certain initial utility and be added to the shopping cart. At this stage, consumers need to pay the search cost related to the display position of the product to decide whether to continue browsing the product. Consumers weigh the cost of continuing to browse (related to the display position corresponding to the product) and potential benefits. Once the total utility of the product combination in the shopping cart reaches its expectation, the browsing behavior stops. At this time, all the product sets in the shopping cart constitute a consideration set. It is worth noting that although the platform has the overall distribution of consumer types (affected by factors such as gender, age, and purchase history, which determine the expected utility of consumers for different products), the specific individual type information is unknown. Therefore, the platform needs to design a reasonable product ranking strategy to improve consumers' expected utility and purchase intention, and ultimately promote the joint improvement of merchants and platform benefits.

[0066] In a specific embodiment, the specific process of obtaining and processing data is as follows:

[0067] Assume that after a consumer enters a product keyword, the platform displays a total of n products, that is, there are a total of n display positions corresponding to n products, where n is a natural number;

[0068] Let X ijl is the location decision variable, the location decision variable X ijl Used to indicate whether the product with serial number i of merchant type l is placed in the display position with serial number j, where i represents the serial number of the product, which is a natural number; j represents the serial number of the display position, which is a natural number; and l represents the serial number of the merchant type, which is a natural number.

[0069] At this time, the location decision variable X ijl The set X in which it is located is expressed as:

[0070] X={X ijl |i,j∈[n]}∈{0,1} n×n ;

[0071] According to this expression, the product display position is judged and the value of the position decision variable is obtained:

[0072] When the display position number of the product with serial number i = j, the position decision variable X ijl =1; when the display position number corresponding to the product with serial number i ≠ j, the position decision variable X ijl =0.

[0073] Based on the position decision variable, the set S is used to represent the combination of product numbers and their corresponding display position numbers, that is, the set S contains the ranking method of all products. Among them, each element in the set S is the combination of product numbers and their corresponding display position numbers (i, j), that is, S = {(i, j)|X ijl =1}.

[0074] Since different types of consumers have different preferences for the same product, assume that there are K types of consumers, K is a natural number; β α represents the proportion of consumers of type α, then β α ∈[0,1]; remember u ilα It represents the initial utility of type α consumers for product i. Specifically, initial utility refers to the initial attraction or value that consumers have when they consider adding the product to their shopping cart based on the basic attributes of the product when the product meets their preferences during the product selection stage.

[0075] In a specific embodiment, when it is mentioned that consumers will view products in a given ranking order, this is a specific manifestation of the position effect, which describes the different effects of products or information on consumers due to their different display locations. Since the display location of the product will have a utility on the consumer's choice behavior, this solution uses the degree of difficulty that the product location can be seen by consumers, that is, the position visibility, to represent the position effect, here θ j to represent the viewability of placement j.

[0076] When only the influence of position effect on consumer choice behavior is considered, the initial utility obtained by consumers when they choose product number i of type l merchant at display position number j will be lnθ j The offset of j Represents the base θ j The natural logarithm of , therefore, the initial utility considering the position effect becomes u ilα +lnθ j .

[0077] Position visibility is related to the investment level of merchant advertising and fake positive reviews. When considering the relationship between position visibility and merchant advertising investment, this solution analyzes the CPC and CPA pricing advertising types. CPC (cost per click) refers to charging per click; CPA (cost per action) refers to charging per specified action. CPA is usually the cost that consumers pay after making a purchase.

[0078] In a specific embodiment, when considering the impact of advertising input, at the product selection stage, the initial utility of type α consumers is It can be expressed as:

[0079]

[0080] Among them, r il Indicates the rating of the product with serial number i, s il represents the sales volume of product number i, n il represents the number of product reviews with serial number i, and L represents the total number of merchant types;

[0081] ∈ i It represents the random utility of consumers affected by the environment during the product selection stage, which has a mean of 0 and a variance of ∈ 2 Normal distribution of

[0082] P cpc Indicates the CPC price set by the platform, P cpa Indicates the CPA unit price set by the platform. It represents the number of CPC investments made by merchants of type l for product i. It is represented by the number of CPA investments made by merchant type l for product number i.

[0083] Specifically, since consumers browse products in descending order of product ranking, each browsing requires a certain browsing cost v jα . Browsing cost v jα It is only related to the type of consumer and the placement of the product, and the browsing cost v jα As the visibility of the location decreases, it increases. Consumers usually have a psychological expectation of the product they may buy. α When the difference between the initial utility obtained by consumers from browsing products and the browsing cost they paid exceeds the set threshold τ α, the product is added to a set, which is called a consideration set. If the difference between the total initial utility and the total browsing cost obtained by the consumer from further browsing the product is less than the difference between the total initial utility and the total browsing cost paid by the current browsing product, the consumer stops browsing downwards, and all the products included in the set are constructed into a consideration set.

[0084] In the utility evaluation stage, consumers further evaluate the utility of products by viewing the ratings, sales volume, online reviews and other information of the products in the consideration set, and choose the product with the greatest utility or not choose any product in the consideration set based on the MNL model. The MNL model is a multinomial logit (MNL) model, which is a classic discrete choice model based on consumer utility. In the MNL model, consumers' choices are divided into two categories: buying products and not buying any products. Among them, the consumer's choice behavior of not buying any products is equivalent to choosing to buy product "0", that is, buying a non-existent product.

[0085] In a specific embodiment, consumers' perceived quality of a product is affected by ratings, sales volume, and the number of online reviews. In the utility evaluation stage, consumers' evaluation utility for product number i is It can be expressed as:

[0086]

[0087] Among them, δ i is the random utility of consumers affected by the environment during the utility evaluation stage, which has a mean of 0 and a variance of v 2 Normal distribution of

[0088] Among them, f il The number of fake comments invested is, It represents the probability that a type α consumer identifies that a type l merchant gives a false positive review to product i.

[0089] Since consumers will evaluate the utility of all products under consideration, each evaluation requires a certain evaluation cost z ilα , evaluation cost z ilα It is related to the consumer type, product online reviews, and the size of the consideration set, and the evaluation cost increases with the increase of the consideration set and the number of online reviews. Further, the expected utility E of a type α consumer for a product with serial number i from a type l merchant is ijlα It can be expressed as:

[0090]

[0091] Specifically, the preference weight w of type α consumers for product i of type l merchants is ijlα It can be expressed as:

[0092]

[0093] Introducing the location decision variable X ijl Indicates product ranking, X ijl =1 means that the product with serial number i of type l merchant is in the display position with serial number j, and e represents the base of the natural logarithm. At this time, the preference weight of type α consumer for the product with serial number i of type l merchant is It can be expressed as:

[0094]

[0095] Since there are cases where consumers do not click on any product when browsing products, this solution uses w0 to represent the preference weight in this case. Without loss of generality, assuming that the expected utility of consumers not clicking on any product is 0, then w0 = e 0 =1, indicating that the consumer has the same preference for all products.

[0096] In a specific embodiment, It represents the probability that a type α consumer chooses the product with number i displayed in the display position with number j from a type l merchant under the given product ranking of the platform. like but

[0097] To simplify the formula, let

[0098] Based on the MNL model, the probability that a type α consumer chooses product number i is It can be expressed as:

[0099]

[0100] Through the process of obtaining data in step S1, the probability of different categories of consumers choosing each product can be obtained. Based on the obtained selection probability, the expected income that the merchant will get from consumers purchasing products can be characterized, and the commission income of the platform can be further obtained, thus laying the foundation for the subsequent construction of a two-layer optimization model.

[0101] S2. Construct a two-layer optimization model:

[0102] like Figure 3 As shown in FIG. 1 , this scheme deeply depicts the complex and dynamic game process between the platform and merchants in product ranking by constructing a two-layer optimization model. Constructing a two-layer optimization model includes constructing an upper optimization model and constructing a lower optimization model.

[0103] Among them, the optimization model that describes the expected income of the upper-level platform is realized by constructing an upper-level optimization model, and the optimization model that describes the expected profit of the lower-level merchants is realized by constructing a lower-level optimization model.

[0104] First, from the perspective of the platform, an upper-level optimization model is constructed. The process of constructing the upper-level optimization model includes constructing the upper-level optimization model objective function and constructing the upper-level optimization model constraint conditions.

[0105] In a specific embodiment, the process of constructing the upper layer optimization model is as follows:

[0106] First, construct the objective function of the upper optimization model. The upper optimization model is used to maximize the expected platform revenue, which includes the platform commission income and platform advertising investment. Therefore, the objective function of the upper optimization model is expressed as:

[0107] max F1=E c +E a (7)

[0108] Among them, max means maximizing the function behind it, F1 means the profit within the platform period, E c Indicates the platform commission income, E a Indicates the platform advertising investment.

[0109] Specifically, the platform commission income E c It can be expressed as:

[0110]

[0111] Among them, n ic refers to the total number of consumers on the platform who have demand for the product with serial number i; p il It refers to the price of the product with serial number i of the merchant of type l; il It refers to the proportion of commission that the platform takes from the product with serial number i of the merchant of type l, p il e il It refers to the commission that the platform takes from the transaction amount of each product sold. It is worth noting that if the consumer returns the product, the platform will not refund the commission paid by the merchant.

[0112] Different types of merchants are divided based on the quality of their products. The platform knows the distribution of merchant types, but not the specific types. The probability that a type α consumer chooses a product with serial number i from a type l merchant is

[0113] Specifically, platform advertising revenue E a It can be expressed as:

[0114]

[0115] Advertising investment refers to the advertising fees paid by merchants to the platform. It is a fixed income, which is not affected by whether the product is purchased or not; and, Payment will only be made when the consumer makes an actual purchase.

[0116] Specifically, the constraints of the upper-level optimization model include product position constraints and fact integer constraints. The specific process of constructing the constraints is as follows:

[0117] Construct product position constraints: Product position constraints include that there is at most one product on each placement and each product is placed on at most one placement; the product position constraint that there is at most one product on each placement can be expressed as: The product placement constraint that each product must be placed in at most one placement can be expressed as: Therefore, the product location constraint is expressed as:

[0118]

[0119] Construct fact integer constraints: Fact integer constraints include X ijl is a variable with a value of 0-1; and there are n products and their corresponding ranking positions. ijl is a variable with a value of 0-1, represented here as X ijl ∈{0,1}; there are n products in total, represented by: 1≤i≤n,i∈Z; the corresponding ranking display positions of n products are represented by: 1≤j≤n,j∈Z; therefore, the fact integer constraint is expressed as:

[0120] X ijl ∈{0,1}(12)

[0121] 1≤i≤n,i∈Z(13)

[0122] 1≤j≤n,j∈Z(14)

[0123] Thus, the upper optimization model from the platform perspective in the two-layer optimization model is obtained. The constructed upper optimization model is as follows:

[0124]

[0125] Through the above steps, we obtain the upper optimization model from the platform perspective in the two-layer optimization model, and then build the lower optimization model from the merchant perspective. The process of building the lower optimization model includes building the objective function of the lower optimization model and building the constraints of the lower optimization model.

[0126] In a specific embodiment, the process of constructing the lower layer optimization model is as follows:

[0127] First, construct the objective function of the lower optimization model. The lower optimization model is used to maximize the expected profit of the merchant, which includes the merchant's income and expenditure. The objective function max F2 of the lower optimization model is expressed as:

[0128] max F2=E s -C c -C a -C m -C r -C f (16)

[0129] Among them, F2 represents the profit of the merchant during the cycle, E s represents the income of the merchant from selling products, C c Indicates the commission the platform takes from the merchant’s sales amount, C a represents the advertising cost of the merchant, C m Represents the merchant’s product purchase cost, C r represents the merchant’s product return cost, C f It indicates the cost incurred by merchants in generating false positive reviews.

[0130] Specifically, the merchant's sales revenue E s It is expressed as:

[0131]

[0132] in, It refers to the probability that type α consumer chooses product i from type l merchant.

[0133] Commission C c It is expressed as:

[0134]

[0135] Merchant advertising cost C a It is expressed as:

[0136]

[0137] Among them, CPC type advertising cost Product costs and fake reviews are fixed expenses and are not affected by whether the product is ultimately purchased, while CPA type advertising costs Expenditure occurs when consumers actually make a purchase.

[0138] Product purchase cost C m It is expressed as:

[0139]

[0140] Among them, c il It refers to the cost of product number i of merchant type l.

[0141] Cost of fake positive reviews f It is expressed as:

[0142]

[0143] Among them, F il refers to the number of false positive reviews for the product with serial number i from the merchant of type l, f il It is the cost of a single false positive review for product number i of type l merchant.

[0144] Product return cost C r It is expressed as:

[0145]

[0146] in, It refers to the probability that type α consumer returns product i after purchasing it.

[0147] In a specific embodiment, the constraints of the lower optimization model are constructed including fact constraints, consumer selection constraints and merchant promotion constraints. The specific process of constructing the constraints of the upper optimization model is as follows:

[0148] Specifically, the factual constraints include: the number of times the merchant has invested in advertising for product number i is a non-negative integer; the product rating is based on a 5-point system; the number of false positive reviews for the product is no more than the total number of product reviews; there are n products in total and their corresponding ranking display positions; the merchant's product price is no less than the total cost invested in the product.

[0149] Among them, the number of times the merchant invests in advertising for the product with serial number i is a non-negative integer and is expressed as: as well as The product rating is expressed as 5 points: il ∈[0,5]; the number of false positive reviews of a product is no more than the total number of product reviews, expressed as: F il ≤n il ∈Z; there are n products in total, which is represented by: 1≤i≤n, i∈Z; the ranking display position corresponding to the n products is represented by: 1≤j≤n, j∈Z; the price of the merchant's product is not less than the total cost invested in the product, which is represented by:

[0150] Therefore, the fact constraint is expressed as:

[0151]

[0152] s il ∈[0,5](25)

[0153] F il ≤n il ∈Z (26)

[0154] 1≤i≤n,i∈Z (27)

[0155] 1≤j≤n,j∈Z (28)

[0156]

[0157] Specifically, consumer choice constraints include: threshold conditions for products to be added to the consideration set; and termination conditions for consumer browsing behavior.

[0158] Among them, the threshold condition for products to be added to the consideration set is expressed as: The termination condition of consumer browsing behavior is expressed as:

[0159]

[0160] Therefore, the consumer choice constraint is expressed as:

[0161]

[0162] Specifically, the merchant promotion constraints include: merchants can obtain higher profits through advertising investment and false positive reviews investment, among which, It represents the probability of consumers buying products when the merchant does not invest in any advertising and false positive reviews. The merchant promotion constraints are expressed as:

[0163]

[0164]

[0165] Thus, the lower optimization model in the constructed two-layer optimization model is as follows:

[0166]

[0167] Through the above steps, the lower-level optimization model from the merchant perspective in the two-layer optimization model is constructed, and the upper-level optimization model from the platform perspective and the lower-level optimization model from the merchant perspective together constitute the two-layer optimization model.

[0168] S3. Verify Stackelberg equilibrium

[0169] For the two-layer optimization model constructed in step S2, this step will verify whether there is a Stackelberg equilibrium in the two-layer optimization model. Stackelberg equilibrium means that the merchants and platforms involved in the present invention need to reach a consensus on the decision, and any party will not improve the overall decision-making effect of the game by unilaterally changing the strategy.

[0170] When merchants make the best response based on the product ranking and advertising pricing given by the platform, and the platform also accepts this result, the game reaches the Stackelberg equilibrium. and is the equilibrium solution of the upper and lower level objectives of the master-slave game model proposed in this scheme, then and The following conditions are met:

[0171]

[0172] Before finding the Stackelberg equilibrium solution, we must first verify the existence and uniqueness of the Stackelberg equilibrium solution, which requires satisfying the following three conditions:

[0173] The set of all feasible strategies of the leader and the follower is a non-empty compact convex set, that is, the strategy is a non-empty convex set and a compact set;

[0174] When the leader's strategy is given, the follower has a unique optimal solution;

[0175] When the follower's strategy is given, the leader has a unique optimal solution.

[0176] In this scheme, the platform is the leader and the merchant is the follower. The strategies of the platform and the merchant are the decision variables in the above steps. The decision variable of the platform in the two-level optimization model in this scheme is the position decision variable X ijl , the advertising unit price variable is set to P cpc and P cpa The merchant’s decision variable is the number of false positive reviews variable F il and the number of ad impressions variable and The process of proving that the equilibrium solution exists and is unique is as follows:

[0177] First, the platform decision variables must satisfy the constraints of expressions (10)-(14), and the merchant decision variables must satisfy the constraints of expressions (23)-(33), both of which are non-empty compact convex sets; secondly, the first-order derivatives of the upper optimization model objective function and the lower optimization model objective function are calculated. Since at any time, the platform's location decision variables and the advertising unit price, advertising and false positives are all non-negative integers, the first-order partial derivatives of the upper optimization model objective function and the lower optimization model objective function are always greater than zero and are subject to the strategy interval constraints, so both the upper optimization model and the lower optimization model have a unique optimal solution. Therefore, the two-level optimization model proposed in this scheme has a unique Stackelberg equilibrium solution.

[0178] S4. Transform the linearized model and solve it

[0179] The objective function of the upper optimization model and the objective function of the lower optimization model of the two-layer optimization model established in this scheme are coupled, which makes it difficult to solve them directly. Figure 4 As shown in the figure, through the analysis of the model, it can be known that the upper and lower objective functions of the two-layer optimization model are convex functions, and their respective constraints are convex sets. Therefore, it is considered to transform the lower optimization model into an additional condition of the upper optimization model through KKT condition transformation, so as to transform the model established by this scheme into a single-objective model; in addition, considering the visibility of the display position of the product ranking, the objective function of the upper optimization model and the objective function of the lower optimization model both have nonlinear terms. According to the duality theorem, the nonlinear terms in each objective function can be transformed into linear terms. Among them, KKT) condition (KarushKuhnTucher) is a set of nonlinear equations, which is widely used in solving optimization problems with inequality constraints. The complementary relaxation condition in the KKT condition is a nonlinear constraint. We can introduce a sufficiently large number and a variable with a value of 0-1 to convert it into a linear constraint, and then convert the model into a mixed-integer linear programming MILP (Mixed-integer linear programming) problem. The MILP problem can then be solved in the Python program by calling the Gurobi solver, where the Gurobi solver is a mathematical programming optimizer that can be used to quickly and efficiently solve large-scale optimization problems.

[0180] Existing technologies focus on ranking products through comprehensive indicators, but do not consider the impact of merchant behavior on product rankings. To this end, this solution builds a two-layer optimization model, in which the upper-layer optimization model is to maximize the expected platform revenue, including merchant product commissions and advertising investment amounts; the lower-layer optimization model is to maximize the expected merchant profit. Merchant revenue refers to the price revenue of the sold product, and merchant expenditure includes return costs, advertising investment costs, and false positive investment costs. Both the platform and the merchant pursue the maximization of their own interests, and use the master-slave game to describe the bargaining process between the two parties. It is proved through theoretical derivation that the proposed model has a unique Stackelberg equilibrium solution, and the two-layer model is transformed into a mixed integer quadratic programming problem by applying the KKT optimal condition and the duality theorem; finally, by solving the example, the global optimal product ranking strategy is obtained.

[0181] Combination Figures 1 to 4 , a clustering system based on two-level optimization, comprising:

[0182] A data acquisition module, used to acquire product quality data, consumer category data, and product promotion cost data from a database;

[0183] The data processing module is used to obtain the probability data of consumers of each category choosing each product based on the acquired data and the position decision variable; and to form a double-layer optimization model by constructing an upper-layer optimization model and a lower-layer optimization model.

[0184] The clustering device based on double-layer optimization may be a hardware device, including one or more processors and a memory, wherein the memory stores a program and is configured to execute the following steps by the one or more processors:

[0185] Obtain product quality data, consumer category data, and product promotion cost data from the database;

[0186] According to the acquired data and based on the position decision variables, the probability data of consumers in each category choosing each product is obtained; a two-layer optimization model is formed by constructing an upper optimization model and a lower optimization model.

[0187] While existing technologies mainly rely on comprehensive indicators (such as sales volume, reviews, prices, etc.) to rank products, these indicators often ignore the impact of merchant behavior on the actual value of the product and user satisfaction. For example, some merchants may improve comprehensive indicators in the short term through false positive reviews, excessive marketing, etc., resulting in ranking results that are inconsistent with actual product quality and user feedback. Through a two-layer optimization model, this solution not only considers the direct indicators of the product, but also deeply analyzes the impact of merchant behavior (such as return costs, advertising investment, and false positive investment) on rankings, thereby more accurately reflecting the real market performance and user needs of the product. In addition, theoretical derivation proves that the model has a unique Stackelberg equilibrium solution, which ensures that the strategy choices of the platform and merchants in the game process reach the optimal balance, reducing ranking deviations caused by information asymmetry or strategic misleading.

[0188] The two-layer optimization model of this solution can dynamically adjust the ranking strategy and respond to real-time changes in merchant behavior, making the ranking results closer to market reality and improving the timeliness and accuracy of the data.

[0189] Traditional ranking algorithms are often based on complex rules and a large amount of data processing, with large computational workload and slow response speed, making it difficult to quickly adapt to market changes and the rapid iteration of user needs. The advantage of this solution is that it takes into account mixed integer quadratic programming transformation, global optimal solution solution, modularity and scalability. Specifically, by applying the KKT optimal conditions and duality theorem, this solution successfully transforms the two-layer optimization model into a mixed integer quadratic programming problem. This transformation not only simplifies the computational complexity, but also retains the core optimization objectives of the model, significantly improving the execution efficiency of the algorithm. Moreover, by solving the example, this solution can directly obtain the globally optimal product ranking strategy, avoiding the trap of local optimal solutions and ensuring the effectiveness and efficiency of the algorithm. In addition, the model design of this solution is modular, which is convenient for quickly adjusting algorithm parameters or introducing new variables according to new market trends or regulatory requirements, enhancing the flexibility and scalability of the system, and is conducive to the continuous optimization of the ranking algorithm and maintaining its efficient operation in the long run.

[0190] How to realize the device specifically can be realized in the existing technology, and no further detailed explanation will be given again. The following explains the possibility of corresponding realization in principle.

[0191] In the 1990s, improvements to a technology could be clearly distinguished as hardware improvements (for example, improvements to circuit structures such as diodes, transistors, switches, etc.) or software improvements (improvements to method flows). However, with the development of technology, many improvements to method flows today can be considered direct improvements to hardware circuit structures.

[0192] Designers almost always obtain the corresponding hardware circuit structure by programming the improved method flow into the hardware circuit. Therefore, it cannot be said that the improvement of a method flow cannot be realized by hardware entity modules. For example, a programmable logic device (PLD) (such as a field programmable gate array (FPGA)) is such an integrated circuit, and its logic function is determined by the user's programming of the device. Designers program by themselves to "integrate" a digital system on a PLD, without having to ask chip manufacturers to design and make dedicated integrated circuit chips. Moreover, nowadays, instead of manually making integrated circuit chips, this programming is mostly implemented by "logic compiler" software, which is similar to the software compiler used when writing program development, and the original code before compilation must also be written in a specific programming language, which is called Hardware Description Language (HDL), and there is not only one HDL, but many kinds, such as Verilog. Those skilled in the art should also be aware that it is easy to obtain a hardware circuit that implements the logical method flow by simply performing some logic programming on the method flow using the above-mentioned hardware description languages ​​and programming it into an integrated circuit.

[0193] The controller can be implemented in any appropriate manner, for example, the controller can take the form of a computer-readable medium such as a microprocessor or processor and a computer-readable program code (such as software or firmware) that can be executed by the (micro)processor, a logic gate, a switch, an application-specific integrated circuit (ASIC), a programmable logic controller, and an embedded microcontroller. Examples of controllers include but are not limited to the following microcontrollers: ATMEL AT89S52, microchip pic16c57. The memory controller can also be implemented as part of the control logic of the memory. It is also known to those skilled in the art that in addition to implementing the controller in a purely computer-readable program code manner, the controller can be implemented in the form of a logic gate, a switch, an application-specific integrated circuit, a programmable logic controller, and an embedded microcontroller by logically programming the method steps. Therefore, this controller can be considered as a hardware component, and the devices included therein for implementing various functions can also be considered as structures within the hardware component. Or even, the devices for implementing various functions can be considered as both software modules for implementing the method and structures within the hardware component.

[0194] The systems, devices, modules or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices. For the convenience of description, the above devices are described separately by function into various units. Of course, when implementing this specification, the functions of each unit can be implemented in the same or more software and / or hardware.

[0195] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The present invention is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the functions in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0196] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1The steps of the functions specified in the blocks or multiple blocks. In a typical configuration, the computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory. The memory may include non-permanent memory in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0197] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0198] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0199] Those skilled in the art will appreciate that the embodiments of this specification may be provided as methods, systems or computer program products. Therefore, this specification may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, this specification may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0200] This specification may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. This specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media including storage devices.

Claims

1. A clustering method based on double-layer optimization, comprising the following steps: Obtain product quality data, consumer category data, and product promotion cost data from the database; According to the acquired data and based on the position decision variables, the probability data of consumers in each category choosing each product is obtained; a double-layer optimization model is formed by constructing an upper-layer optimization model and a lower-layer optimization model, and a balanced strategy set is obtained through the double-layer optimization model, and the optimal strategy set after solution is obtained by linearizing the double-layer optimization model.

2. The clustering method based on double-layer optimization according to claim 1, characterized in that: After obtaining the product keyword, traverse the database and output n product information and its corresponding n display location information, where n is a natural number; Location decision variable X ijl The set X is represented as: X={X ijl |i,j∈[n]}∈{0,1} n×n ; Among them, i represents the serial number of the product, which is a natural number; j represents the serial number of the display location, which is a natural number; l represents the serial number of the merchant type, which is a natural number.

3. The clustering method based on double-layer optimization according to claim 2, characterized in that: When the display position number of product number i = j, the position decision variable X ijl =1; when the display position number of product number i ≠ j, the position decision variable X ijl =0.

4. The clustering method based on double-layer optimization according to claim 2, characterized in that: When considering the influence of position effect, the initial utility u ilα lnθ occurs j The initial utility considering the position effect is expressed as: ilα +lnθ j ; Among them, u ilα represents the initial utility of type α consumer for product number i, θ j Indicates the visibility of the display position with serial number j; lnθ j Represents the base θ j The natural logarithm of The initial utility in the product selection stage when considering the impact of advertising investment It is expressed as: Among them, r il Indicates the rating of the product with serial number i, s il Indicates the sales volume of product number i, n il represents the number of product reviews with serial number i, and L represents the total number of merchant types; ∈ i It represents the random utility of consumers affected by the environment during the product selection stage, which has a mean of 0 and a variance of ∈ 2 Normal distribution; P cpc Indicates the CPC price set by the platform, P cpa Indicates the CPA unit price set by the platform. It represents the number of CPC investments made by type l merchants for product i. It is represented by the number of CPA investments made by merchant type l for product i.

5. The clustering method based on double-layer optimization according to claim 4, characterized in that: The utility evaluation phase evaluates the utility of product number i It is expressed as: Among them, δ i is the random utility of consumers affected by the environment during the utility evaluation stage, which has a mean of 0 and a variance of δ 2 Normal distribution of il The number of fake comments invested is, represents the probability that type α consumers recognize that type l merchants give false positive reviews to product i; When evaluating the utility of all products, the expected utility E of the product ijlα It is expressed as: Among them, z ilα Indicates that an evaluation cost is paid each time an evaluation is performed.

6. The clustering method based on double-layer optimization according to claim 5, characterized in that: Introducing the location decision variable X ijl , the preference weight for product number i It is expressed as: Where, e represents the base of natural logarithm; represents the probability that type α consumers choose a product under the influence of the location decision variable, Based on the position decision variable, the set of combinations of product numbers and their corresponding display position numbers S = {(i, j) | X ijl =1}, when hour, make The probability of selecting product number i is It is expressed as:

7. The clustering method based on double-layer optimization according to claim 1, characterized in that: The upper optimization model is used to maximize the expected platform revenue, and the lower optimization model is used to maximize the expected merchant profit. The objective function max F1 of the upper optimization model is expressed as: max F1=E c +E a ; max means maximizing the function behind it, F1 means the profit within the platform period, E c Indicates the platform commission income, E a Indicates the platform advertising investment.

8. The clustering method based on double-layer optimization according to claim 7, characterized in that: The objective function max F2 of the lower optimization model is expressed as: max F2=E s -C c -C a -C m -C r -C f ; Among them, F2 represents the profit of the merchant during the cycle, E s represents the income of the merchant from selling products, C c Indicates the commission the platform takes from the merchant’s sales amount, C a represents the advertising cost of the merchant, C m Represents the merchant’s product purchase cost, C r represents the merchant’s product return cost, C f It indicates the cost incurred by merchants in generating false positive reviews.

9. A clustering system based on double-layer optimization, characterized in that: include, A data acquisition module, used to acquire product quality data, consumer category data, and product promotion cost data in the database; The data processing module is used to obtain the probability data of consumers of each category choosing each product based on the acquired data and the position decision variable; to construct a double-layer optimization model by constructing an upper-layer optimization model and a lower-layer optimization model, to obtain a set of equilibrium strategies through the double-layer optimization model, and to obtain the optimal strategy set after solving by linearizing the double-layer optimization model.

10. A clustering device based on double-layer optimization, characterized in that: The device comprises one or more processors and a memory, wherein the memory stores a program and is configured to execute the following steps by the one or more processors: Obtain product quality data, consumer category data, and product promotion cost data from the database; According to the acquired data and based on the position decision variables, the probability data of consumers in each category choosing each product is obtained; a double-layer optimization model is formed by constructing an upper-layer optimization model and a lower-layer optimization model, and a balanced strategy set is obtained through the double-layer optimization model, and the optimal strategy set after solution is obtained by linearizing the double-layer optimization model.

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