### 统计代写|数据科学代写data science代考|Analysis of Existing Work

statistics-lab™ 为您的留学生涯保驾护航 在代写数据科学data science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。我们的专家在代写数据科学data science方面经验极为丰富，各种代写数据科学data science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

## 统计代写|数据科学代写data science代考|Principal curve and manifold approaches

Resulting from the fact that the nearest projection coordinate of each sample in the curve is searched along the whole line segments, the computational complexity of the HSPCs algorithm is of order $O\left(n^{2}\right)[25]$ which is dominated by the projection step. The HSPCs algorithm, as well as other algorithms proposed by $[4,18,19,69]$, may therefore be computationally expensive for large data sets.

For addressing the computational issue, several strategies are proposed in subsequently refinements. In reference [8], the $\mathrm{PPS}$ algorithm supposes that the data are generated from a collection of latent nodes in low-dimensional

space, and the computation to determine the projections is achieved by comparing the distances among data and the high-dimensional counterparts in the latent nodes. This results in a considerable reduction in the computational complexity if the number of the latent nodes is less than that number of observations. However, the PPS algorithm requires additional $O\left(N^{2} n\right)$ operations (Where $n$ is the dimension of latent space) to compute an orthonormalization. Hence, this algorithm is difficult to generalize in high-dimensional spaces.
In [73], local principal component analysis in each neighborhood is employed for searching a local segment. Therefore, the computational complexity is closely relate to the number of local PCA models. However, it is difficulty for general data to combine the segments into a principal curve because a large number of computational steps are involved in this combination.

For the work by Kégl $[34,35]$, the KPCs algorithm is proposed by combining the vector quantization with principal curves. Under the assumption that data have finite second moment, the computational complexity of the KPCs algorithm is $O\left(n^{5 / 3}\right)$ which is slightly less than that of the HSPCs algorithm. When allowing to add more than one vertex at a time, the complexity can be significantly decreased. Furthermore, a speed-up strategy discussed by Kégl [33] is employed for the assignments of projection indices for the data during the iterative projection procedure of the ACKPCs algorithms. If $\delta v^{(j)}$ is the maximum shift of a vertex $v_{j}$ in the $j$ th optimization step defined by:
$$\delta v^{(j)}=\max {i=1, \cdots, k+1}\left|v{i}^{(j)}-v_{i}^{(j+1)}\right|,$$
then after the $\left(j+j_{1}\right)$ optimization step, $s_{i_{1}}$ is still the nearest line segment to $x$ if
$$d\left(x, s_{i_{1}}^{(j)}\right) \leq d\left(x, s_{i_{2}}^{(j)}\right)-2 \sum_{l=j}^{j+j_{1}} \delta v^{(l)}$$
Further reference to this issue may be found in [33], pp. 66-68. Also, the stability of the algorithm is enhanced while the complexity is the equivalent to that of the KPCs algorithm.

## 统计代写|数据科学代写data science代考|Neural network approaches

The discussion in Subsect. $4.2$ highlighted that neural network approaches to determine a NLPCA model are difficult to train, particulary the 5 layer network by Kramer [37]. More precisely, the network complexity increases considerably if the number of original variables z,$N$, rises. On the other hand, an increasing number of observations also contribute to a drastic increase in the computational cost. Since most of the training algorithms are iterative in nature and employ techniques based on the backpropagation principle, for example the Levenberg-Marquardt algorithm for which the Jacobian matrix is updated using backpropagation, the performance of the identified network depends on the initial selection for the network weights. More precisely, it may

be difficult to determine a minimum for the associated cost function, that is the sum of the minimum distances between the original observations and the reconstructed ones.

The use of the IT network [68] and the approach by Dong and McAvoy [16] however, provide considerably simpler network topologies that are accordingly easier to train. Jia et al. [31] argued that the IT network can generically rep. resent smooth nonlinear functions and raised concern about the techniqu by Dong and McAvoy in terms of its flexibility in providing generic nonlin. ear functions. This concern related to to concept of incorporating a linea combinátion of nonlinear function to éstimate the nonlinear interrelationshipx between the recorded observations. It should be noted, however, that the IT network structure relies on the condition that an functional injective rela tionship exit bétween thé scorré variảblés and the original variảblés, that a unique mapping between the scores and the observations exist. Otherwise the optimization step to determine the scores from the observations using the identified IT network may converge to different sets of score values depending on the initial guess, which is undesirable. In contrast, the technique by Dong and McAvoy does not suffer from this problem.

## 统计代写|数据科学代写data science代考|Kernel PCA

In comparison to neural network approaches, the computational demand for a KPCA insignificantly increase for larger values of $N$, size of the original variables set $\mathbf{z}$, which follows from (1.59). In contrast, the size of the Gram matrix increases quadratically with a rise in the number of analyzed observations, $K$. However, the application of the numerically stable singular value decomposition to obtain the eigenvalues and eigenvectors of the Gram matrix does not present the same computational problems as those reported for the neural network approaches above.

## 统计代写|数据科学代写data science代考|Principal curve and manifold approaches

d在(j)=最大限度一世=1,⋯,ķ+1|在一世(j)−在一世(j+1)|,

d(X,s一世1(j))≤d(X,s一世2(j))−2∑l=jj+j1d在(l)

## 广义线性模型代考

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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。