产品销售网络中动力学建模与分析
发布时间：2018-08-29 19:31
【摘要】：互联网的快速发展，使得人们面对大量的信息，即信息超载，因此人们很难在如此冗多的信息中挑选出最符合自己要求的信息。为此要进行信息过滤，常用方式就是使用搜索引擎，在地址栏中输入关键字就会得到相关的网页。但是通过使用搜索引擎来过滤信息存在着缺点，截止到现在，最有效的过滤信息超载的方法就是提供个性化推荐，即根据用户的兴趣特点和购买行为，向用户推荐用户感兴趣的信息和商品。通常，一个完整的推荐系统由三部分组成：收集用户信息的行为记录模块，分析用户喜好的模型分析模块和推荐算法模块。其中，推荐算法是最核心的部分。目前的推荐算法主要包括协同过滤推荐算法，基于内容的推荐算法，基于用户-产品二部图关系的推荐算法及混合推荐算法。然而，目前对于在个性化推荐系统的推荐算法上结合特定的背景进行用户-产品之间的动力学研究较少，因此本文做了如下研究： 1.基于用户-产品二部图关系的推荐算法有着与之相对应的用户推荐网络，根据这个用户-产品的二部图，本文主要研究不同品牌产品的用户数量的变化情况。本文研究的模型中考虑的产品是快速消费品，用户是普通群体。快速消费品的三个基本特点便利性、视觉化产品和品牌忠诚度不高决定了消费者对快速消费品的购买习惯是简单、迅速、冲动、感性。根据这些背景，本文建立了n+1维的关于产品中不同品牌的用户数量变化的动力学模型，分别在用户选择一类产品的某种品牌是随机连接和优先连接时，对此进行了数值模拟和动力学分析，得到了系统趋于稳态的结论。 2.当用户选择一类产品的某种品牌的连接方式是随机连接时，对模型进行了数值模拟，并在特定简单的情况下，即用户数为2，且每一时间步骤只能有一个未选择某种产品的用户去选择该产品的条件下，对模型进行了理论分析，得到了唯一的平衡点E0，利用Jacobian矩阵证明了E0局部渐近稳定，又通过构造Dulac函数证明了无闭轨，，从而得到平衡点E0全局渐近稳定，并用数值模拟对此结论进行了验证。 3.给出了当用户选择一类产品的某种品牌的连接方式是优先连接时，关于产品中不同品牌的用户数量变化的动力学模型，得到了唯一的平衡点E1，通过构造Lyapunov函数，证明了平衡点E1是全局渐近稳定的，并对模型进行了数值模拟。并在同样特定简单的情况下，即用户数为2，且每一时间步骤只能有一个未选择某种产品的用户去选择该产品的条件下，对模型进行了理论分析，得到了唯一的平衡点E2，又通过构造Lyapunov函数，证明了平衡点E2是全局渐近稳定的，并用数值模拟对此结论进行了验证。最后，我们可以得到在随机连接时，一类产品中不会出现品牌垄断的现象，各个品牌之间是良性竞争的发展状态，结果是各品牌均匀发展；在优先连接时，刚开始时，度越大的品牌占得比例比较高，但是经过长时间的发展，旧的品牌会被新的品牌所替代，从而被淘汰。
[Abstract]:With the rapid development of the Internet, people are confronted with a large amount of information, that is, information overload, so it is difficult for people to select the most suitable information from such a large amount of information. The most effective way to filter information overload is to provide personalized recommendation, that is, to recommend the information and goods that users are interested in according to their interests and purchasing behavior. The current recommendation algorithms mainly include collaborative filtering recommendation algorithm, content-based recommendation algorithm, user-product bipartite graph based recommendation algorithm and hybrid recommendation algorithm. In the personalized recommendation system recommendation algorithm combined with specific background for user-product dynamics research is less, so this paper does the following research:
1. The recommendation algorithm based on the user-product bipartite graph has a corresponding user recommendation network. According to the user-product bipartite graph, this paper mainly studies the change of the number of users of different brands of products. Three basic characteristics of convenience, visual products and low brand loyalty determine that the consumer's buying habits of FMCG are simple, rapid, impulsive, and emotional. Based on these background, this paper establishes a n+1-dimensional dynamic model of the number of users of different brands in the product, which is used to select a certain type of product. When the brand is stochastic connection and priority connection, the numerical simulation and dynamic analysis are carried out, and the conclusion that the system tends to be stable is obtained.
2. When the connection mode of a certain brand of a product is random, the model is simulated numerically. Under the specific simple condition, that is, the number of users is 2, and each time step can only have one user who has not selected a certain product to choose the product, the model is analyzed theoretically, and the result is that only one user can choose the product. The Jacobian matrix is used to prove the local asymptotic stability of E0, and the Dulac function is used to prove that there is no closed orbit. Thus the global asymptotic stability of E0 is obtained, which is verified by numerical simulation.
3. The dynamic model of the change of the number of users with different brands in a product is given when the user chooses a certain brand to connect first. The unique equilibrium point E1 is obtained. By constructing Lyapunov function, the equilibrium point E1 is proved to be globally asymptotically stable, and the model is simulated numerically. Under the condition that the number of users is 2 and only one user can choose the product at each time step, the model is theoretically analyzed, and the unique equilibrium point E2 is obtained. By constructing Lyapunov function, it is proved that the equilibrium point E2 is globally asymptotically stable, and the numerical simulation is carried out. Finally, we can conclude that brand monopoly does not occur in a class of products with random connection, and the development of benign competition among brands results in the uniform development of each brand. The old brand will be replaced by the new brand and eliminated.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O157.5;TP391.3
本文编号：2212192
[Abstract]:With the rapid development of the Internet, people are confronted with a large amount of information, that is, information overload, so it is difficult for people to select the most suitable information from such a large amount of information. The most effective way to filter information overload is to provide personalized recommendation, that is, to recommend the information and goods that users are interested in according to their interests and purchasing behavior. The current recommendation algorithms mainly include collaborative filtering recommendation algorithm, content-based recommendation algorithm, user-product bipartite graph based recommendation algorithm and hybrid recommendation algorithm. In the personalized recommendation system recommendation algorithm combined with specific background for user-product dynamics research is less, so this paper does the following research:
1. The recommendation algorithm based on the user-product bipartite graph has a corresponding user recommendation network. According to the user-product bipartite graph, this paper mainly studies the change of the number of users of different brands of products. Three basic characteristics of convenience, visual products and low brand loyalty determine that the consumer's buying habits of FMCG are simple, rapid, impulsive, and emotional. Based on these background, this paper establishes a n+1-dimensional dynamic model of the number of users of different brands in the product, which is used to select a certain type of product. When the brand is stochastic connection and priority connection, the numerical simulation and dynamic analysis are carried out, and the conclusion that the system tends to be stable is obtained.
2. When the connection mode of a certain brand of a product is random, the model is simulated numerically. Under the specific simple condition, that is, the number of users is 2, and each time step can only have one user who has not selected a certain product to choose the product, the model is analyzed theoretically, and the result is that only one user can choose the product. The Jacobian matrix is used to prove the local asymptotic stability of E0, and the Dulac function is used to prove that there is no closed orbit. Thus the global asymptotic stability of E0 is obtained, which is verified by numerical simulation.
3. The dynamic model of the change of the number of users with different brands in a product is given when the user chooses a certain brand to connect first. The unique equilibrium point E1 is obtained. By constructing Lyapunov function, the equilibrium point E1 is proved to be globally asymptotically stable, and the model is simulated numerically. Under the condition that the number of users is 2 and only one user can choose the product at each time step, the model is theoretically analyzed, and the unique equilibrium point E2 is obtained. By constructing Lyapunov function, it is proved that the equilibrium point E2 is globally asymptotically stable, and the numerical simulation is carried out. Finally, we can conclude that brand monopoly does not occur in a class of products with random connection, and the development of benign competition among brands results in the uniform development of each brand. The old brand will be replaced by the new brand and eliminated.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O157.5;TP391.3
【参考文献】
相关期刊论文 前2条
1 刘建国;周涛;郭强;汪秉宏;;个性化推荐系统评价方法综述[J];复杂系统与复杂性科学;2009年03期
2 刘建国;周涛;汪秉宏;;个性化推荐系统的研究进展[J];自然科学进展;2009年01期
本文编号：2212192
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