### 计算机代写|神经网络代写neural networks代考|NIT6004

statistics-lab™ 为您的留学生涯保驾护航 在代写神经网络neural networks方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写神经网络neural networks代写方面经验极为丰富，各种代写神经网络neural networks相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

Traditional graph embedding methods are originally studied as dimension reduction techniques. A graph is usually constructed from a feature represented data set, like image data set. As mentioned before, graph embedding usually has two goals, i.e. reconstructing original graph structures and support graph inference. The objective functions of traditional graph embedding methods mainly target the goal of graph reconstruction.

Specifically, Tenenbaum et al (2000) first constructs a neighborhood graph $G$ using connectivity algorithms such as $K$ nearest neighbors (KNN). Then based on $G$, the shortest path between different data can be computed. Consequently, for all the $N$ data entries in the data set, we have the matrix of graph distances. Finally, the classical multidimensional scaling (MDS) method is applied to the matrix to obtain the coordinate vectors. The representations learned by Isomap approximately preserve the geodesic distances of the entry pairs in the low-dimensional space. The key problem of Isomap is its high complexity due to the computing of pair-wise shortest pathes. Locally linear embedding (LLE) (Roweis and Saul, 2000) is proposed to eliminate the need to estimate the pairwise distances between widely separated entries. LLE assumes that each entry and its neighbors lie on or close to a locally linear patch of a mainfold. To characterize the local geometry, each entry can be reconstructed from its neighbors. Finally, in the low-dimensional space, LLE constructs a neighborhood-preserving mapping based on locally linear reconstruction. Laplacian eigenmaps (LE) (Belkin and Niyogi, 2002) also begins with constructing a graph using $\varepsilon$-neighborhoods or $\mathrm{K}$ nearest neighbors. Then the heat kernel (Berline et al, 2003) is utilized to choose the weight of two nodes in the graph. F1nally, the node representations can be obtained by based on the Laplacian matrix regularization. Furthermore, the locality preserving projection (LPP) (Berline et al, 2003), a linear approximation of the nonlinear LE, is proposed.

## 计算机代写|神经网络代写neural networks代考|Structure Preserving Graph Representation Learning

Graph structures can be categorized into different groups that present at different granularities. The commonly exploited graph structures in graph representation learning include neighborhood structure, high-order node proximity and graph communities.

How to define the neighborhood structure in a graph is the first challenge. Based on the discovery that the distribution of nodes appearing in short random walks is similar to the distribution of words in natural language, DeepWalk (Perozzi et al, 2014) employs the random walks to capture the neighborhood structure. Then for each walk sequence generated by random walks, following Skip-Gram, DeepWalk aims to maximize the probability of the neighbors of a node in a walk sequence. Node2vec defines a flexible notion of a node’s graph neighborhood and designs a second order random walks strategy to sample the neighborhood nodes, which can smoothly interpolate between breadth-first sampling (BFS) and depth-first sampling (DFS). Besides the neighborhood structure, LINE (Tang et al, 2015b) is proposed for large scale network embedding. which can preserve the first and second order proximities. The first order proximity is the observed pairwise proximity between two nodes. The second order proximity is determined by the similarity of the “contexts” (neighbors) of two nodes. Both are important in measuring the relationships beetween two nodess. Essentially, LINE is based on the shallow model, consequently, the representation ability is limited. SDNE (Wang et al, 2016) proposes a deep model for network embedding, which also aims at capturing the first and second order proximites. SDNE uses the deep auto-encoder architecture with multiple non-linear layers to preserve the second order proximity. To preserve the first-order proximity, the idea of Laplacian eigenmaps (Belkin and Niyogi, 2002) is adopted. Wang et al (2017g) propose a modularized nonnegative matrix factorization (M-NMF) model for graph representation learning, which aims to preserve both the microscopic structure, i.e., the first-order and second-order proximities of nodes, and the mesoscopic community structure (Girvan and Newman, 2002).

## 有限元方法代写

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## MATLAB代写

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。