發(fā)布時(shí)間：2019-03-25 14:10

【摘要】：復(fù)雜網(wǎng)絡(luò)社區(qū)檢測(cè)是復(fù)雜性科學(xué)研究中受到廣泛關(guān)注的方向,在信息科學(xué)、生物學(xué)、數(shù)學(xué)以及社會(huì)學(xué)等鄰域都有著重大貢獻(xiàn)和持續(xù)影響.近年來(lái),針對(duì)不同類(lèi)型的復(fù)雜網(wǎng)絡(luò),人們提出了很多尋找社團(tuán)結(jié)構(gòu)的算法,也稱為社區(qū)檢測(cè)算法.基于復(fù)雜網(wǎng)絡(luò)社區(qū)檢測(cè)在當(dāng)今社會(huì)運(yùn)用的廣泛性,本文以復(fù)雜網(wǎng)絡(luò)中基于相似度的符號(hào)網(wǎng)絡(luò)社區(qū)檢測(cè)以及動(dòng)態(tài)網(wǎng)絡(luò)社區(qū)檢測(cè)作為主要研究?jī)?nèi)容,研究如何根據(jù)符號(hào)網(wǎng)絡(luò)的特點(diǎn)來(lái)定義一個(gè)合理的相似度模型,以及如何將動(dòng)態(tài)網(wǎng)絡(luò)的實(shí)時(shí)信息進(jìn)行數(shù)量化,建立合理的數(shù)學(xué)模型.具體如下:(1)基于離散模型的符號(hào)網(wǎng)絡(luò)社區(qū)檢測(cè).本文首先考慮符號(hào)網(wǎng)絡(luò)中存在正連接和負(fù)連接的特點(diǎn),定義了新的節(jié)點(diǎn)相似度計(jì)算公式.將其加入到動(dòng)力學(xué)演化模型中,使得符號(hào)網(wǎng)絡(luò)中節(jié)點(diǎn)狀態(tài)按照網(wǎng)絡(luò)模型演化,理論證明該模型可以達(dá)到Lyapunov穩(wěn)定.通過(guò)對(duì)真實(shí)網(wǎng)絡(luò)以及人工合成網(wǎng)絡(luò)進(jìn)行仿真,并與已有算法對(duì)比,在時(shí)間和精度上優(yōu)于已有算法.(2)基于離散模型的動(dòng)態(tài)網(wǎng)絡(luò)社區(qū)檢測(cè).本文針對(duì)動(dòng)態(tài)網(wǎng)絡(luò)隨時(shí)間變化的特性,對(duì)不同時(shí)間步的網(wǎng)絡(luò)鄰接矩陣進(jìn)行加權(quán)處理,既考慮上一時(shí)間步的網(wǎng)絡(luò)結(jié)構(gòu),又考慮當(dāng)前時(shí)間步的網(wǎng)絡(luò)結(jié)構(gòu),得到新的鄰接矩陣.通過(guò)時(shí)變的鄰接矩陣并應(yīng)用動(dòng)力學(xué)網(wǎng)絡(luò)模型來(lái)實(shí)現(xiàn)動(dòng)態(tài)符號(hào)網(wǎng)絡(luò)的社區(qū)檢測(cè).經(jīng)實(shí)驗(yàn)仿真得出該算法不僅適用于小規(guī)模動(dòng)態(tài)網(wǎng)絡(luò),還適用于節(jié)點(diǎn)數(shù)目較多且社區(qū)結(jié)構(gòu)不均衡的大規(guī)模動(dòng)態(tài)網(wǎng)絡(luò).
[Abstract]:Community detection based on complex network is the research direction of complexity science, which has great contribution and continuous influence in information science, biology, mathematics and sociology. In recent years, for different types of complex networks, many algorithms for finding community structures, also called community detection algorithms, have been proposed. Based on the extensive application of complex network community detection in today's society, this paper focuses on symbolic network community detection based on similarity and dynamic network community detection in complex network. This paper studies how to define a reasonable similarity model according to the characteristics of symbolic network and how to quantify the real-time information of dynamic network and establish a reasonable mathematical model. The details are as follows: (1) symbolic network community detection based on discrete model. In this paper, we first consider the characteristics of positive and negative connections in symbolic networks, and define a new formula for computing node similarity. It is added to the dynamic evolution model to make the node state in the symbolic network evolve according to the network model. The theory proves that the model can achieve Lyapunov stability. The real network and synthetic network are simulated and compared with the existing algorithms in time and precision. (2) dynamic network community detection based on discrete model. In this paper, according to the characteristic of dynamic network changing with time, the network adjacency matrix with different time steps is weighted to obtain a new adjacency matrix by considering both the network structure of the previous time step and the current time step network structure. Community detection of dynamic symbolic networks is realized by time-varying adjacency matrix and dynamic network model. The simulation results show that the algorithm is suitable not only for small-scale dynamic networks, but also for large-scale dynamic networks with large number of nodes and unbalanced community structure.
【學(xué)位授予單位】：內(nèi)蒙古工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O157.5

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本文編號(hào)：2447045