统计代写|复杂网络代写complex networks代考| Block Modeling

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我们提供的复杂网络complex networks及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
统计代写|复杂网络代写complex networks代考| Block Modeling

统计代写|复杂网络代写complex networks代考|Cohesive Subgroups or Communities as Block

The abundance of diagonal block models or modular structures makes modularity a concept so important that it is often studied outside the general framework of block modeling. One explanation may be that in social networks it may even be the dominant blocking structure. The reason may be that homophily $[16]$, i.e., the tendency to form links with agents similar to oneself, is a dominant mechanism in the genesis of social networks. Recall, however, that the concept of functional roles in networks is much wider than mere cohesiveness as it specifically focuses on the inter-dependencies between groups of nodes. Modularity or community structure, emphasizing the absence of dependencies between groups of nodes is only one special case. It may also be that the concept of modularity appeals particularly to physicists because it is reminiscent of the reductionist approach of taking systems apart into smaller subsystems that has been so successful in the natural sciences.

Nevertheless, in the literature, there is no generally accepted definition of what a community or module actually is. A variety of definitions exist that all imply that members of a community are more densely connected among themselves than to the rest of the network. Two approaches exist to tackle the problem. Either, one starts with a definition of what a community is in the first place and then searches for sets of nodes that match this definition. Or one can use a heuristic approach by designing an algorithm and define a community as whatever this algorithm outputs. Both of these approaches differ in one fundamental way: When starting from a definition of community, it often occurs that some nodes in the network will not be placed into any community. The algorithmic approaches on the other hand will generally partition the set of vertices such that all nodes are found in some community. Whether all nodes need to be assigned into a community needs to be decided by the researcher and may determine which definitions and methods are useful in the analysis of actual data. With these considerations in mind we shall briefly review the approaches taken in the literature.

统计代写|复杂网络代写complex networks代考|Sociological Definitions

The study of community structure has a long tradition in the field of sociology and it comes as no surprise that the example that sparked the interest of physicists in the field was a sociological one $[17,18]$. Alternatively to community, the term cohesive subgroup is often used to subsume a number of definitions

that emphasize different aspects of the problem. These can be grouped into definitions based on reachability, nodal degree or the comparison of within to outside links [11].

Cliques are complete subgraphs, such that every member is connected to every other member in the clique. An $n$-clique is a maximal subgraph, such that the geodesic distance $d(i, j)$ between any two members $i, j$ is smaller or equal to $n$. Naturally, cliques are 1-cliques. Note that the shortest path may also run through nodes not part of the n-clique, such that the diameter of an $\mathrm{n}$-clique may be larger than $n$. An $n$-clan denotes an $\mathrm{n}$-clique with diameter less or equal to $n$. Naturally, all n-clans are also n-cliques. Alternatively, an $n$-club is a maximal subgraph of diameter $n$.

These definitions are problematic in several ways. Cliques can never get larger than the smallest degree among the member nodes which limits these communities to be generally very small in large networks with limited degrees. The other definitions relying on distances are problematic if the network possesses the small world property. The overlap of such communities will generally be as large as a typical group.

Another group of definitions is based on the degree of the members of a community. A $k$-plex is a maximal subgraph of $n$ nodes, such that each member has at least $n-k$ connections to other nodes in the k-plex. This definition is less strict than that of a clique as it allows some links to be missing. At the same time, a k-plex only contains nodes with minimum degree $d \geq(n-k)$. A $k$-core denotes a maximal subgraph, such that each node has at least $k$ connections to other members of the k-core.

Here again, the size of k-plexes is limited by the degrees of the nodes. K-cores are problematic also because they disregard all nodes with degree smaller than $k$ even if they have all their connections to nodes within this core.

While the two former groups of definitions are based primarily on internal connections, a number of definitions of cohesive subgroups exist which compare intra- and inter-group connections. One example are LS sets. A set of $n$ nodes is an LS set, if each of its proper subsets has more ties to its complement than to the rest of the network.

统计代写|复杂网络代写complex networks代考|Definitions from Physicists

The diversity of definitions from sociology already indicates the conceptual difficulties involved and demonstrates that the question of what a community is may not have a simple answer. To make things worse, a number of alternative definitions have been and continue to be contributed by physicists as well $[19,20]$.

Radicchi et al. [21] have introduced the notion of community in a strong sense and in a weak sense. For a subgraph $V$ of $\mathcal{S}$ to be a community in the strong sense, they require
k_{i}^{i n}>k_{i}^{\text {out }} \quad \forall i \in V,
i.e., the number of internal connections $k_{i}^{i n}$ to other members of $V$ shall be larger than the number of external connections $k_{i}^{\text {out }}$ to the rest of the network. Note that $k_{i}^{\text {in }}+k_{i}^{\text {out }}=k_{i}$, the degree of node $i$. Relaxing this condition, for a subgraph $V$ to be a community in a weak sense they require

A paradoxical issue arising from both of these definitions is that communities in the strong or weak sense can be formed of disconnected subgraphs as long as these subgraphs also obey the definition. It should be noted, however, that this definition was initially proposed as a stop criterion for hierarchical agglomerative or divisive clustering algorithms.

Palla et al. $[8,22]$ have given an alternative definition based on reachability, though defined through a clique percolation process and not via paths in the network. Two $k$-cliques are adjacent if they share a (k-1)-clique, i.e., they differ by only one node. Note that the term k-cliques here denotes complete subgraphs with $k$ nodes. As a community or k-clique percolation cluster, they define the set of nodes connected by $(\mathrm{k}-1)$-cliques. An example will clarify these issues. Two vertices connected by an edge form a 2-clique. Two triangles (3-cliques) are adjacent if they share an edge, i.e., a 2-clique. This definition allows nodes to be part of more than one community and hence allows for overlap among communities much like the other definitions based on reachability.

Other approaches given by physicists and computer scientists are algorithmically motivated. The next section will discuss this treatment of the problem.

统计代写|复杂网络代写complex networks代考| Block Modeling


统计代写|复杂网络代写complex networks代考|Cohesive Subgroups or Communities as Block



统计代写|复杂网络代写complex networks代考|Sociological Definitions

社区结构的研究在社会学领域有着悠久的传统,因此引发物理学家对该领域兴趣的例子是社会学的例子也就不足为奇了。[17,18]. 作为社区的替代方案,内聚子组一词通常用于包含许多定义

强调问题的不同方面。这些可以根据可达性、节点程度或内部链接与外部链接的比较进行分组 [11]。

团是完整的子图,因此每个成员都连接到团中的每个其他成员。一个n-clique 是一个最大子图,使得测地线距离d(一世,j)任意两个成员之间一世,j小于或等于n. 自然,派系是1-派系。请注意,最短路径也可能通过不属于 n 团的节点,因此n-clique 可能大于n. 一个n-clan 表示一个n-直径小于或等于的团n. 自然,所有的 n 氏族也是 n 派系。或者,一个n-club 是直径的最大子图n.


另一组定义基于社区成员的程度。一种ķ-plex 是最大子图n节点,使得每个成员至少有n−ķ与 k-plex 中其他节点的连接。这个定义没有一个集团那么严格,因为它允许一些链接丢失。同时,一个 k-plex 只包含度数最小的节点d≥(n−ķ). 一种ķ-core 表示一个最大子图,使得每个节点至少有ķ与 k 核心的其他成员的连接。

同样,k-plex 的大小受节点度数的限制。K-cores 也是有问题的,因为它们忽略了度数小于的所有节点ķ即使它们与该核心内的节点都有所有连接。

虽然前两组定义主要基于内部联系,但存在许多内聚子组的定义,它们比较组内和组间的联系。一个例子是 LS 集。一套n节点是一个 LS 集,如果它的每个真子集与其补集的联系多于与网络的其余部分的联系。

统计代写|复杂网络代写complex networks代考|Definitions from Physicists


拉迪奇等人。[21] 引入了强烈的社区概念和微弱的社区概念。对于子图在的小号要成为一个严格意义上的社区,他们需要
ķ一世一世n>ķ一世出去 ∀一世∈在,
即内部连接数ķ一世一世n对其他成员在应大于外部连接数ķ一世出去 到网络的其余部分。注意ķ一世在 +ķ一世出去 =ķ一世, 节点度一世. 放宽这个条件,对于一个子图在成为他们需要的弱意义上的社区


帕拉等人。[8,22]已经给出了基于可达性的替代定义,尽管是通过集团渗透过程而不是通过网络中的路径来定义的。二ķ如果-cliques 共享(k-1)-clique,则它们是相邻的,即它们仅相差一个节点。请注意,这里的术语 k-cliques 表示完整的子图ķ节点。作为社区或 k-clique 渗透集群,它们定义了通过以下方式连接的节点集(ķ−1)-派系。一个例子将阐明这些问题。由一条边连接的两个顶点形成一个 2-clique。如果两个三角形(3-clique)共享一条边,即 2-clique,则它们是相邻的。该定义允许节点成为多个社区的一部分,因此允许社区之间的重叠,就像基于可达性的其他定义一样。


统计代写|复杂网络代写complex networks代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。统计代写|python代写代考


在概率论概念中,随机过程随机变量的集合。 若一随机系统的样本点是随机函数,则称此函数为样本函数,这一随机系统全部样本函数的集合是一个随机过程。 实际应用中,样本函数的一般定义在时间域或者空间域。 随机过程的实例如股票和汇率的波动、语音信号、视频信号、体温的变化,随机运动如布朗运动、随机徘徊等等。


贝叶斯统计概念及数据分析表示使用概率陈述回答有关未知参数的研究问题以及统计范式。后验分布包括关于参数的先验分布,和基于观测数据提供关于参数的信息似然模型。根据选择的先验分布和似然模型,后验分布可以解析或近似,例如,马尔科夫链蒙特卡罗 (MCMC) 方法之一。贝叶斯统计概念及数据分析使用后验分布来形成模型参数的各种摘要,包括点估计,如后验平均值、中位数、百分位数和称为可信区间的区间估计。此外,所有关于模型参数的统计检验都可以表示为基于估计后验分布的概率报表。





随着AI的大潮到来,Machine Learning逐渐成为一个新的学习热点。同时与传统CS相比,Machine Learning在其他领域也有着广泛的应用,因此这门学科成为不仅折磨CS专业同学的“小恶魔”,也是折磨生物、化学、统计等其他学科留学生的“大魔王”。学习Machine learning的一大绊脚石在于使用语言众多,跨学科范围广,所以学习起来尤其困难。但是不管你在学习Machine Learning时遇到任何难题,StudyGate专业导师团队都能为你轻松解决。


基础数据: $N$ 个样本, $P$ 个变量数的单样本,组成的横列的数据表
变量定性: 分类和顺序;变量定量:数值
数学公式的角度分为: 因变量与自变量


随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。



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