### 统计代写|主成分分析代写Principal Component Analysis代考|ENVX2001

statistics-lab™ 为您的留学生涯保驾护航 在代写主成分分析Principal Component Analysis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。我们的专家在代写主成分分析Principal Component Analysis代写方面经验极为丰富，各种代写主成分分析Principal Component Analysis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|主成分分析代写Principal Component Analysis代考|Validation

In this section we illustrate our procedure with data from the leukemia data set of Golub et al. (1999) and the lymphoma data set Alizadeh et al. (2000).

In these examples our aim is to validate our procedure for adding input variables information into KPCA representation. We follow the following steps. First, in each data set, we build a list of genes that are differentially expressed. This selection is based in accordance with previous studies such as (Golub et al. (1999), Pittelkow \& Wilson (2003), Reverter et al. (2010)). In addition we compute the expression profile of each gene selected, this profile confirm the evidence of differential expression.

Second, we compute the curves through each sample point associated with each gene in the list. These curves are given by the $\phi$-image of points of the form:
$$\mathbf{y}(s)=\mathbf{x}{i}+s \mathbf{e}{k}$$
where $x_{i}$ is the $1 \times n$ expression vector of the $i$-th sample, $i=1, \ldots, m, k$ denotes the index in the expression matrix of the gene selected to be represented, $\mathbf{e}{k}=(0, \ldots, 1, \ldots, 0)$ is a $1 \times n$ vector with zeros except in the $k$-th. These curves describe locally the change of the sample $x{i}$ induced by the change of the gene expression.

Third, we project the tangent vector of each curve at $s=0$, that is, at the sample points $\mathbf{x}_{i}$, $i=1, \ldots, m$, onto the KPCA subspace spanned by the eigenvectors (9). This representation capture the direction of maximum variation induced in the samples when the expression of gene increases.

By simultaneously displaying both the samples and the gene information on the same plot it is possible both to visually detect genes which have similar profiles and to interpret this pattern by reference to the sample groups.

## 统计代写|主成分分析代写Principal Component Analysis代考|Leukemia data sets

The leukemia data set is composed of 3051 gene expressions in three classes of leukemia: 19 cases of B-cell acute lymphoblastic leukemia (ALL), 8 cases of T-cell ALL and 11 cases of acute myeloid leukemia (AML). Gene expression levels were measured using Affymetrix high-density oligonucleotide arrays.

The data were preprocessed according to the protocol described in Dudoit et al. (2002). In addition, we complete the preprocessing of the gene expression data with a microarray standardization and gene centring.

In this example we perform the KPCA, as detailed in the previous section, we compute the kernel matrix with using the radial basis kernel with $c=0.01$, this value is set heuristically. The resulting plot is given in Figure 1. It shows the projection onto the two leading kernel principal components of microarrays. In this figure we can see that KPCA detect the group structure in reduced dimension. AML, T-cell ALL and B-cell ALL are fully separated by KPCA.

To validate our procedure we select a list of genes differentially expressed proposed by (Golub et al. (1999), Pittelkow \& Wilson (2003), Reverter et al. (2010)) and a list of genes that are not differentially expressed. In particular, in Figures 2, 3,4 and 5 we show the results in the case of genes: X76223_s_at, X82240_rna1_at, Y00787_s_at and D50857_at, respectively. The three first genes belong to the list of genes differentially expressed and the last gene is not differentially expressed.

Figure 2 (top) shows the tangent vectors associated with $\mathrm{X} 76223_{\text {_s_at gene, attached at }}$ each sample point. This vector field reveals upper expression towards T-cell cluster as is expected from references above mentioned. This gene is well represented by the second principal component. The length of the arrows indicate the strength of the gene on the sample position despite the dimension reduction. Figure 2 (bottom) shows the expression profile of X76223_s_at gene. We can observe that X76223_s_at gene is up regulated in T-cell class. This profile is agree with our procedure because the direction in which the expression of the $\mathrm{x} 76223$ _s_at gene increases points to the T-cell cluster.

## 统计代写|主成分分析代写Principal Component Analysis代考|Validation

$$\mathbf{y}(s)=\mathbf{x} i+s \mathbf{e} k$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。