本文選題：復(fù)雜網(wǎng)絡(luò) + 社團(tuán)結(jié)構(gòu)探測(cè)�。� 參考：《中央財(cái)經(jīng)大學(xué)》2016年博士論文

【摘要】：復(fù)雜網(wǎng)絡(luò)理論為各學(xué)科領(lǐng)域中的復(fù)雜系統(tǒng)研究提供了簡(jiǎn)單而有效的研究方法,在近十多年里得到了學(xué)術(shù)界的高度關(guān)注。不同領(lǐng)域中看似迥異的真實(shí)系統(tǒng)在不斷變化發(fā)展中會(huì)自然形成共同的特征,比如節(jié)點(diǎn)度的冪律度分布特征、小世界特征和社團(tuán)結(jié)構(gòu)特征等。由于突破了傳統(tǒng)還原論將對(duì)象孤立研究的局限性,復(fù)雜網(wǎng)絡(luò)能夠準(zhǔn)確刻畫(huà)真實(shí)系統(tǒng)中的關(guān)鍵特征,本文研究的出發(fā)點(diǎn)就是網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)特征。一方面復(fù)雜網(wǎng)絡(luò)中的社團(tuán)結(jié)構(gòu)可以對(duì)應(yīng)于真實(shí)系統(tǒng)中自然形成的子系統(tǒng),比如蛋白質(zhì)合作網(wǎng)絡(luò)會(huì)形成對(duì)應(yīng)不同器官的功能模塊,科學(xué)家合作網(wǎng)絡(luò)會(huì)形成不同學(xué)科的研究群體,社交網(wǎng)絡(luò)會(huì)形成基于不同興趣愛(ài)好的俱樂(lè)部等。另一方面學(xué)術(shù)界對(duì)于復(fù)雜網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)的主流認(rèn)識(shí)只停留在直觀層面,即把社團(tuán)結(jié)構(gòu)看作以更高概率相互連接的節(jié)點(diǎn)的集合,同時(shí)現(xiàn)有的社團(tuán)結(jié)構(gòu)探測(cè)算法也存在很多問(wèn)題亟待解決,因此復(fù)雜網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)研究仍然是一個(gè)開(kāi)放性的課題,研究其探測(cè)算法具有重要的理論意義和現(xiàn)實(shí)意義。類(lèi)似于聚類(lèi)算法,社團(tuán)結(jié)構(gòu)探測(cè)算法也屬于無(wú)監(jiān)督學(xué)習(xí)的范疇,其目標(biāo)在于把網(wǎng)絡(luò)中的節(jié)點(diǎn)賦值到不同的社團(tuán)中,因此基于聚類(lèi)方法的理論框架提出社團(tuán)結(jié)構(gòu)探測(cè)算法是一個(gè)有前景的思路。密度聚類(lèi)相比傳統(tǒng)聚類(lèi)技術(shù)有天然的優(yōu)勢(shì),比如DBSCAN相比K-means來(lái)說(shuō)無(wú)需類(lèi)簇個(gè)數(shù)作為先驗(yàn)參數(shù),不會(huì)落入局部最優(yōu)陷進(jìn),抗噪聲等,然而DBSCAN的聚類(lèi)結(jié)果對(duì)兩個(gè)參數(shù)的取值非常敏感,因此密度聚類(lèi)的參數(shù)選擇問(wèn)題一直是機(jī)器學(xué)習(xí)領(lǐng)域亟待解決的難題。2014年發(fā)表在Science的論文中提出了新的密度聚類(lèi)算法,即快速密度峰值算法(FDP:Fast Density Peak),該算法在保留DBSCAN優(yōu)點(diǎn)的同時(shí)巧妙的克服了其參數(shù)敏感問(wèn)題,為無(wú)監(jiān)督學(xué)習(xí)提供了新的研究思路。受到這樣的啟發(fā),本文擬利用FDP算法探測(cè)復(fù)雜網(wǎng)絡(luò)中的社團(tuán)結(jié)構(gòu)。然而本文通過(guò)理論分析和數(shù)值實(shí)驗(yàn)發(fā)現(xiàn),由于網(wǎng)絡(luò)節(jié)點(diǎn)分布在極端高維空間中,導(dǎo)致FDP算法無(wú)法識(shí)別社團(tuán)核心節(jié)點(diǎn),從而無(wú)法直接應(yīng)用于社團(tuán)結(jié)構(gòu)探測(cè)任務(wù)。除此之外,本文進(jìn)一步發(fā)現(xiàn)當(dāng)網(wǎng)絡(luò)結(jié)構(gòu)變得模糊或社團(tuán)數(shù)量過(guò)多時(shí)FDP算法的決策圖機(jī)制很難通過(guò)人機(jī)交互的方式準(zhǔn)確識(shí)別社團(tuán)個(gè)數(shù)�；谝陨蟽牲c(diǎn)事實(shí),本文提出了基于流形學(xué)習(xí)框架的ISOFDP算法,該算法有效克服了網(wǎng)絡(luò)數(shù)據(jù)維數(shù)災(zāi)難的問(wèn)題從而使得社團(tuán)核心點(diǎn)顯著區(qū)別于其它成員節(jié)點(diǎn),同時(shí)提出了改進(jìn)的分割密度函數(shù)以作為自動(dòng)識(shí)別網(wǎng)絡(luò)社團(tuán)個(gè)數(shù)的依據(jù),最終ISOFDP算法相比經(jīng)典算法取得了更好的社團(tuán)結(jié)構(gòu)探測(cè)結(jié)果。更進(jìn)一步的,本文將ISOFDP算法框架進(jìn)行推廣,分別提出了能夠探測(cè)重疊社團(tuán)結(jié)構(gòu)、有權(quán)有向網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)和動(dòng)態(tài)網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)的算法,并取得了優(yōu)于經(jīng)典算法的實(shí)驗(yàn)結(jié)果。本論文的內(nèi)容包括九章:第1章介紹了本論文的選題背景和研究意義,并說(shuō)明了本論文的研究框架和創(chuàng)新點(diǎn)。第2章介紹了復(fù)雜網(wǎng)絡(luò)的基本理論和相關(guān)概念,然后對(duì)幾類(lèi)社團(tuán)結(jié)構(gòu)探測(cè)算法進(jìn)行了綜述。第3章分析了密度聚類(lèi)算法fdp在探測(cè)社團(tuán)結(jié)構(gòu)時(shí)的缺陷,研究了克服其缺陷的方法之后提出了社團(tuán)結(jié)構(gòu)探測(cè)算法isofdp。第4章基于l-isomap、lle、le和lpp四種局部流形學(xué)習(xí)算法提出了快速社團(tuán)結(jié)構(gòu)探測(cè)算法,克服了isofdp計(jì)算性能低下的缺陷。第5章首先定義了非核心節(jié)點(diǎn)的社團(tuán)隸屬度測(cè)度,根據(jù)節(jié)點(diǎn)隸屬度和閾值η的對(duì)比情況識(shí)別出網(wǎng)絡(luò)的重疊節(jié)點(diǎn),以此提出能夠探測(cè)重疊社團(tuán)結(jié)構(gòu)的isofdpov算法。第6章基于信號(hào)理論的方法計(jì)算網(wǎng)絡(luò)節(jié)點(diǎn)的相似度測(cè)度,該相似度充分利用了網(wǎng)絡(luò)結(jié)構(gòu)中連邊的權(quán)重和方向信息,以此為基礎(chǔ)提出了有權(quán)有向網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)探測(cè)算法isofdpdw。第7章結(jié)合時(shí)間維度的信息利用3-階張量對(duì)所有時(shí)間點(diǎn)上的網(wǎng)絡(luò)序列建模得到鄰接張量,然后利用非負(fù)張量分解模型把鄰接張量分解為節(jié)點(diǎn)社團(tuán)隸屬度矩陣和社團(tuán)動(dòng)態(tài)行為矩陣,以此求得動(dòng)態(tài)社團(tuán)張量,基于其各縱向切片探測(cè)各時(shí)間點(diǎn)上的社團(tuán)結(jié)構(gòu)和社團(tuán)變化規(guī)律,最終提出了動(dòng)態(tài)網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)探測(cè)算法tenfdp。第8章基于2006年6月16日至2014年7月9日中信行業(yè)指數(shù)收盤(pán)價(jià)日數(shù)據(jù),計(jì)算指數(shù)收益率之間的相關(guān)系數(shù)并以此為連邊得到中信行業(yè)指數(shù)的平面最大過(guò)濾圖(pmfg)網(wǎng)絡(luò),利用isofdpdw算法探測(cè)該網(wǎng)絡(luò)金融危機(jī)前中后三個(gè)階段的社團(tuán)結(jié)構(gòu),以揭示金融危機(jī)對(duì)該網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)的影響。第9章對(duì)全文進(jìn)行總結(jié),并給出了本文現(xiàn)階段提出算法的缺點(diǎn)和不足,同時(shí)對(duì)本文算法的進(jìn)一步推廣和改進(jìn)工作進(jìn)行了展望。本文的主要?jiǎng)?chuàng)新點(diǎn)包括以下幾個(gè)方面:第一,提出了一種基于密度聚類(lèi)的社團(tuán)結(jié)構(gòu)探測(cè)算法isofdp。該算法無(wú)需社團(tuán)個(gè)數(shù)作為先驗(yàn)信息,且在準(zhǔn)確度、參數(shù)敏感性和穩(wěn)健性3個(gè)方面都優(yōu)于經(jīng)典算法。isofdp繼承了密度聚類(lèi)算法fdp的優(yōu)點(diǎn)同時(shí)克服了其缺點(diǎn)。首先通過(guò)理論分析和數(shù)值實(shí)驗(yàn)發(fā)現(xiàn)網(wǎng)絡(luò)節(jié)點(diǎn)具備高維數(shù)據(jù)的特點(diǎn),即節(jié)點(diǎn)之間的距離高度同質(zhì)化導(dǎo)致fdp無(wú)法識(shí)別社團(tuán)核心節(jié)點(diǎn),本文假設(shè)存在低維的本征維度可以保存原網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)特征,提出使用經(jīng)典流形學(xué)習(xí)算法isomap推斷出網(wǎng)絡(luò)在其本征維度上的映射,克服同質(zhì)化距離的問(wèn)題。本文進(jìn)一步發(fā)現(xiàn)當(dāng)網(wǎng)絡(luò)結(jié)構(gòu)變得模糊或社團(tuán)數(shù)量太多時(shí),在fdp的決策圖上通過(guò)人機(jī)交互的方法無(wú)法正確識(shí)別社團(tuán)個(gè)數(shù),本文提出了改進(jìn)的分割密度函數(shù)以自動(dòng)識(shí)別社團(tuán)個(gè)數(shù),避免人機(jī)交互的過(guò)程。第二,提出了一種新的重疊社團(tuán)結(jié)構(gòu)探測(cè)算法ISOFDPOV。首先利用ISOFDP算法對(duì)網(wǎng)絡(luò)進(jìn)行硬分割,可以得到社團(tuán)核心節(jié)點(diǎn)以及每個(gè)社團(tuán)的成員節(jié)點(diǎn)。本文定義了成員節(jié)點(diǎn)的社團(tuán)隸屬度測(cè)度,該隸屬度測(cè)度可以衡量節(jié)點(diǎn)歸屬于某社團(tuán)的強(qiáng)度,然后根據(jù)各成員節(jié)點(diǎn)關(guān)于各社團(tuán)的隸屬度與閾值η的對(duì)比判斷成員節(jié)點(diǎn)的社團(tuán)歸屬情況,社團(tuán)歸屬不唯一的節(jié)點(diǎn)為重疊節(jié)點(diǎn),從而找到網(wǎng)絡(luò)中的重疊社團(tuán)結(jié)構(gòu)。ISOFDPOV在人工和真實(shí)網(wǎng)絡(luò)上取得了相比經(jīng)典算法更好的社團(tuán)探測(cè)結(jié)果。第三,提出了有權(quán)有向網(wǎng)絡(luò)上的社團(tuán)結(jié)構(gòu)探測(cè)算法ISOFDPDW。首先分析了結(jié)構(gòu)相似度只能利用二值對(duì)稱(chēng)鄰接矩陣信息描述節(jié)點(diǎn)之間相似度的缺陷,提出使用信號(hào)相似度。信號(hào)相似度可以充分利用有權(quán)有向網(wǎng)絡(luò)中連邊的權(quán)重和方向信息,客觀描述節(jié)點(diǎn)之間的相似度。另外使用有權(quán)有向模塊度函數(shù)作為算法的收斂目標(biāo)。最后在有權(quán)無(wú)向、無(wú)權(quán)有向和有權(quán)有向網(wǎng)絡(luò)上驗(yàn)證了ISOFDPDW算法的有效性。第四,提出了基于非負(fù)張量分解模型的動(dòng)態(tài)網(wǎng)絡(luò)社團(tuán)結(jié)構(gòu)探測(cè)算法TenFDP。該算法假設(shè)每個(gè)時(shí)間片上的社團(tuán)結(jié)構(gòu)不僅與當(dāng)前網(wǎng)絡(luò)結(jié)構(gòu)有關(guān),還與上一時(shí)刻的社團(tuán)結(jié)構(gòu)有關(guān)。因此提出利用3-階張量模型對(duì)每個(gè)時(shí)間點(diǎn)上的網(wǎng)絡(luò)結(jié)構(gòu)進(jìn)行建模,得到領(lǐng)接張量以更好刻畫(huà)網(wǎng)絡(luò)結(jié)構(gòu)隨時(shí)間的變化。利用非負(fù)張量分解模型把領(lǐng)接張量分解為節(jié)點(diǎn)社團(tuán)隸屬度矩陣、社團(tuán)動(dòng)態(tài)行為矩陣,以此求得動(dòng)態(tài)社團(tuán)張量,基于該張量的每個(gè)縱向切片探測(cè)各時(shí)間點(diǎn)上的社團(tuán)結(jié)構(gòu)和社團(tuán)變化規(guī)律。在5種類(lèi)型的動(dòng)態(tài)網(wǎng)絡(luò)上驗(yàn)證了TenFDP算法的有效性。
[Abstract]:Complex network theory provides a simple and effective research method for the research of complex systems in the field of various disciplines. In the last more than 10 years, the academic circle has received high attention. The seemingly disparate real systems in different fields will naturally form the common characteristics in the changing development, such as the distribution of the power law degree of the node degree, the small world Characteristics and community structure characteristics. Because of the limitation of the traditional reductionism, the complex network can accurately depict the key features of the real system. The starting point of this study is the community structure characteristics of the network. On the one hand, the social solidarity structure in the complex network can correspond to the natural formation of the real system. The subsystems, such as the protein cooperation network, will form functional modules for different organs. The cooperative network of scientists will form different subjects, and social networks will form clubs based on different interests. On the other hand, the mainstream understanding of the complex structure of the complex network society is only in the visual level, that is, the society. The group structure is regarded as a set of nodes connected by higher probability, and there are many problems to be solved urgently. Therefore, the study of complex network community structure is still an open issue. It is of great theoretical meaning and practical significance to study its detection algorithm. The method of construction and measurement is also a category of unsupervised learning. Its goal is to assign nodes in the network to different societies. Therefore, it is a promising idea to propose a community structure detection algorithm based on the theoretical framework of clustering method. Density clustering has a natural advantage over traditional clustering techniques, such as DBSCAN compared with K-means. The number of clusters is required as a priori parameters, which will not fall into the local optimal trap and resist noise. However, the clustering results of DBSCAN are very sensitive to the values of the two parameters. Therefore, the parameter selection problem of density clustering has been a difficult problem to be solved in the field of machine learning. A new density clustering algorithm is proposed in the paper published in Science in.2014. The fast density peak algorithm (FDP:Fast Density Peak), which overcomes its parameter sensitivity while preserving the advantages of DBSCAN, provides new research ideas for unsupervised learning. Inspired by this, this paper uses FDP algorithm to detect the community structure in complex networks. However, this paper is based on theoretical analysis and numerical value. It is found that because the network nodes are distributed in extremely high dimensional space, the FDP algorithm can not identify the core nodes of the community, and can not be applied directly to the community structure detection task. In addition, this paper further finds that the decision drawing mechanism of the FDP algorithm is difficult to pass through human-computer interaction when the network structure becomes blurred or the number of societies is too large. Based on the above two facts, the ISOFDP algorithm based on the manifold learning framework is proposed in this paper. The algorithm effectively overcomes the problem of the network data dimension disaster and makes the community core distinctions distinctions from other member nodes. At the same time, the modified segmentation density function is proposed as an automatic identification network. According to the basis of the number of associations, the final ISOFDP algorithm has obtained a better detection result of the community structure compared with the classical algorithm. Further, this paper extends the framework of the ISOFDP algorithm, and puts forward the algorithms that can detect the overlapping community structure, have the right to the network community structure and the dynamic network community structure, and get better than the classic calculation. The contents of this paper include nine chapters: the first chapter introduces the background and significance of this thesis, and explains the research framework and innovation of this paper. The second chapter introduces the basic theory and related concepts of complex networks, and then summarizes several kinds of community structure detection algorithms. The third chapter analyzes density clustering. The defect of algorithm FDP in detecting community structure, and after studying the method to overcome its defects, we put forward the association structure detection algorithm isofdp. fourth chapter based on four local manifold learning algorithms, l-isomap, LLE, le and LPP, put forward the fast community structure detection algorithm, overcome the defects of the low performance of isofdp computing. In the fifth chapter, the non kernel is first defined. The degree of membership degree of the heart node is measured, and the overlapping nodes of the network are identified according to the degree of the node membership and the threshold value. The isofdpov algorithm that can detect the overlapping community structure is proposed. The sixth chapter calculates the similarity measure of the network nodes based on the signal theory. The similarity degree makes full use of the right of the edge of the network structure. Based on the information of weight and direction, this paper proposes a community structure detection algorithm with weighted directed networks isofdpdw. seventh chapter combined with the time dimension information using the 3- order tensor to build the adjacency tensor for the network sequence modeling at all time points, and then decomposes the adjacent tensor into the membership degree matrix of the node community by using the nonnegative tensor decomposition model. The dynamic community behavior matrix is used to obtain the dynamic community tensor. Based on its longitudinal slices, the community structure and the law of community change are detected. Finally, the dynamic network community structure detection algorithm tenfdp. eighth chapter is based on the closing price day data of the CITIC industry index from June 16, 2006 to July 9, 2014, and calculates the index income. The correlation coefficient between the rate and the PMFG network of the CITIC industry index is used to detect the community structure of the three stages of the network before the financial crisis by isofdpdw algorithm to reveal the impact of the financial crisis on the structure of the network community. The ninth chapter summarizes the full text and gives the present stage of this paper. The shortcomings and shortcomings of the algorithm are proposed, and the further promotion and improvement of the algorithm are prospected. The main innovation points of this paper include the following aspects: first, a community structure detection algorithm based on density clustering isofdp. is proposed, which does not need the number of communities as a priori information, and is sensitive to the parameters and is sensitive to parameters. The 3 aspects of nature and robustness are superior to the classical algorithm.Isofdp, which inherit the advantages of the density clustering algorithm FDP and overcome their shortcomings. First, the characteristics of the network nodes with high dimensional data are found through theoretical analysis and numerical experiments, that is, the homogeneity of the distance between nodes leads to the non method recognition of the core nodes of the community by FDP. This paper assumes the existence of the existence of the core nodes of the community. The low dimensional eigendimensions can preserve the community structure characteristics of the original network, and propose the use of the classical manifold learning algorithm Isomap to deduce the mapping of the network on its eigendimensions and overcome the problem of homogeneity distance. This paper further finds that when the network structure becomes blurred or the number of societies is too large, the interaction of human-computer interaction on the FDP's decision map is found. The method can not correctly identify the number of community. In this paper, an improved segmentation density function is proposed to automatically identify the number of communities and avoid the process of human-computer interaction. Second, a new overlapping community structure detection algorithm ISOFDPOV. is proposed, first of all, the ISOFDP algorithm is used to cut the network hard, and the core nodes of the community and each community can be obtained. The membership degree of member nodes is defined in this paper. The membership degree measure can measure the strength of the node belonging to a community. Then, according to the membership degree of each member's Association and the threshold value, the membership node is judged by the comparison of the membership degree. The overlapping community structure in the network.ISOFDPOV has been obtained on the artificial and real network, which is better than the classical algorithm. Third, the community structure detection algorithm on the weighted directed network ISOFDPDW. is proposed. First, the similarity degree of the structure similarity can only be described by the two value pair called adjacency matrix information. The signal similarity is used. The signal similarity can make full use of the weight and direction information of the connected edges in the network, and objectively describe the similarity between the nodes. In addition, the weighted directed modularity function is used as the convergence target of the algorithm. Finally, the ISOFD is proved to be unweighted and unauthorized and entitled to the network. The effectiveness of the PDW algorithm. Fourth, a dynamic network community structure detection algorithm based on the non negative tensor decomposition model TenFDP. is proposed. The algorithm assumes that the community structure on each time slice is not only related to the current network structure, but also is related to the community structure at the last time. Therefore, it is proposed to use the 3- order tensor model to the network at each time point. The network structure is modeled and the collar tensor is obtained to better describe the change of network structure with time. By using the nonnegative tensor decomposition model, the collar tensor is decomposed into the membership degree matrix of the node community, the dynamic behavior matrix of the community is used to obtain the dynamic community tensor, and the community structure on each time point of the tensor is detected based on each longitudinal section of the tensor. The effectiveness of the TenFDP algorithm is verified on 5 types of dynamic networks.

【學(xué)位授予單位】：中央財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O157.5

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