【摘要】：互聯(lián)網(wǎng)的快速發(fā)展，使得人們面對大量的信息，即信息超載，因此人們很難在如此冗多的信息中挑選出最符合自己要求的信息。為此要進(jìn)行信息過濾，常用方式就是使用搜索引擎，在地址欄中輸入關(guān)鍵字就會(huì)得到相關(guān)的網(wǎng)頁。但是通過使用搜索引擎來過濾信息存在著缺點(diǎn)，截止到現(xiàn)在，最有效的過濾信息超載的方法就是提供個(gè)性化推薦，即根據(jù)用戶的興趣特點(diǎn)和購買行為，向用戶推薦用戶感興趣的信息和商品。通常，一個(gè)完整的推薦系統(tǒng)由三部分組成：收集用戶信息的行為記錄模塊，分析用戶喜好的模型分析模塊和推薦算法模塊。其中，推薦算法是最核心的部分。目前的推薦算法主要包括協(xié)同過濾推薦算法，基于內(nèi)容的推薦算法，基于用戶-產(chǎn)品二部圖關(guān)系的推薦算法及混合推薦算法。然而，目前對于在個(gè)性化推薦系統(tǒng)的推薦算法上結(jié)合特定的背景進(jìn)行用戶-產(chǎn)品之間的動(dòng)力學(xué)研究較少，因此本文做了如下研究： 1.基于用戶-產(chǎn)品二部圖關(guān)系的推薦算法有著與之相對應(yīng)的用戶推薦網(wǎng)絡(luò)，根據(jù)這個(gè)用戶-產(chǎn)品的二部圖，本文主要研究不同品牌產(chǎn)品的用戶數(shù)量的變化情況。本文研究的模型中考慮的產(chǎn)品是快速消費(fèi)品，用戶是普通群體�？焖傧M(fèi)品的三個(gè)基本特點(diǎn)便利性、視覺化產(chǎn)品和品牌忠誠度不高決定了消費(fèi)者對快速消費(fèi)品的購買習(xí)慣是簡單、迅速、沖動(dòng)、感性。根據(jù)這些背景，本文建立了n+1維的關(guān)于產(chǎn)品中不同品牌的用戶數(shù)量變化的動(dòng)力學(xué)模型，分別在用戶選擇一類產(chǎn)品的某種品牌是隨機(jī)連接和優(yōu)先連接時(shí)，對此進(jìn)行了數(shù)值模擬和動(dòng)力學(xué)分析，得到了系統(tǒng)趨于穩(wěn)態(tài)的結(jié)論。 2.當(dāng)用戶選擇一類產(chǎn)品的某種品牌的連接方式是隨機(jī)連接時(shí)，對模型進(jìn)行了數(shù)值模擬，并在特定簡單的情況下，即用戶數(shù)為2，且每一時(shí)間步驟只能有一個(gè)未選擇某種產(chǎn)品的用戶去選擇該產(chǎn)品的條件下，對模型進(jìn)行了理論分析，得到了唯一的平衡點(diǎn)E0，利用Jacobian矩陣證明了E0局部漸近穩(wěn)定，又通過構(gòu)造Dulac函數(shù)證明了無閉軌，，從而得到平衡點(diǎn)E0全局漸近穩(wěn)定，并用數(shù)值模擬對此結(jié)論進(jìn)行了驗(yàn)證。 3.給出了當(dāng)用戶選擇一類產(chǎn)品的某種品牌的連接方式是優(yōu)先連接時(shí)，關(guān)于產(chǎn)品中不同品牌的用戶數(shù)量變化的動(dòng)力學(xué)模型，得到了唯一的平衡點(diǎn)E1，通過構(gòu)造Lyapunov函數(shù)，證明了平衡點(diǎn)E1是全局漸近穩(wěn)定的，并對模型進(jìn)行了數(shù)值模擬。并在同樣特定簡單的情況下，即用戶數(shù)為2，且每一時(shí)間步驟只能有一個(gè)未選擇某種產(chǎn)品的用戶去選擇該產(chǎn)品的條件下，對模型進(jìn)行了理論分析，得到了唯一的平衡點(diǎn)E2，又通過構(gòu)造Lyapunov函數(shù)，證明了平衡點(diǎn)E2是全局漸近穩(wěn)定的，并用數(shù)值模擬對此結(jié)論進(jìn)行了驗(yàn)證。最后，我們可以得到在隨機(jī)連接時(shí)，一類產(chǎn)品中不會(huì)出現(xiàn)品牌壟斷的現(xiàn)象，各個(gè)品牌之間是良性競爭的發(fā)展?fàn)顟B(tài)，結(jié)果是各品牌均勻發(fā)展；在優(yōu)先連接時(shí)，剛開始時(shí)，度越大的品牌占得比例比較高，但是經(jīng)過長時(shí)間的發(fā)展，舊的品牌會(huì)被新的品牌所替代，從而被淘汰。
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：O157.5;TP391.3

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