### 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Feature Reduction with Support Vector

statistics-lab™ 为您的留学生涯保驾护航 在代写监督学习Supervised and Unsupervised learning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。我们的专家在代写监督学习Supervised and Unsupervised learning代写方面经验极为丰富，各种代写监督学习Supervised and Unsupervised learning相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Machines and Application

Since this chapter is mainly related to feature reduction using SVMs in DNA microarray analysis, it is essential to understand the basic steps involved in a microarray experiment and why this technology has become a major tool for biologists to investigate the function of genes and their relations to a particular disease.

In an organism, proteins are responsible for carrying out many different functions in the life-cycle of the organism. They are the essential part of many biological processes. Each protein consists of chain of amino acids in a specific order and it has unique functions. The order of amino acids is determined by the DNA sequences in the gene which codes for a specific proteins. To produce a specific protein in a cell, the gene is transcribed from DNA into a messenger RNA (mRNA) first, then the mRNA is converted to a protein via translation.
To understand any biological process from a molecular biology perspective, it is essential to know the proteins involved. Currently, unfortunately, it is very difficult to measure the protein level directly because there are simply too many of them in a cell. Therefore, the levels of mRNA are used as a surrogate measure of how much a specific protein is presented in a sample, i.e. it gives an indication of the levels of gene expression. The idea of measuring the level of mRNA as a surrogate measure of the level of gene expression dates back to $1970 \mathrm{~s}[21,99]$, but the methods developed at the time allowed only a few genes to be studied at a time. Microarrays are a recent technology which allows mRNA levels to be measured in thousands of genes in a single experiment.
The microarray is typically a small glass slide or silicon wafer, upon which genes or gene fragment are deposited or synthesized in a high-density manner. To measure thousands of gene expressions in a sample, the first stage in making of a microarray for such an experiment is to determine the genetic materials to be deposited or synthesized on the array. This is the so-called probe selection stage, because the genetic materials deposited on the array are going to serve as probes to detect the level of expressions for various genes in the sample. For a given gene, the probe is generally made up from only part of the DNA sequence of the gene that is unique, i.e. each gene is represented by a single probe. Once the probes are selected, each type of probe will be deposited or synthesized on a predetermined position or “spot” on the array. Each spot will have thousands of probes of the same type, so the level of intensity pick up at each spot can be traced back to the corresponding probe. It is important to note that a probe is normally single stranded (denatured) DNA, so the genetic material from the sample can bind with the probe.

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Some Prior Work

As mentioned in Chap. 2, maximization of a margin has been proven to perform very well in many real world applications and makes SVMs one of the most popular machine learning algorithms at the moment. Since the margin is the criterion for developing one of the best-known classifiers, it is natural to consider using it as a measure of relevancy of genes or features. This idea of using margin for gene selection was first proposed in [61]. It was achieved by coupling recursive features elimination with linear SVMs (RFE-SVMs) in order to find a subset of genes that maximizes the performance of the classifiers. In a linear SVM, the decision function is given as $f(x)=\mathbf{w}^{T} \mathbf{x}+b$ or $f(x)=\sum_{k=1}^{n} w_{k} x_{k}+b$. For a given feature $x_{k}$, the size of the absolute value of its weight $w_{k}$ shows how significantly does $x_{k}$ contributes to the margin of the linear SVMs and to the output of a linear classifier. Hence, $w_{k}$ is used as a feature ranking coefficient in RFE-SVMs. In the original RFE-SVMs, the algorithm first starts constructing a linear SVMs classifier from the microarray data with $n$ number of genes. Then the gene with the smallest $w_{k}^{2}$ is removed and another classifier is trained on the remaining $n-1$ genes. This process is repeated until there is only one gene left. A gene ranking is produced at the end from the order of each gene being removed. The most relevant gene will be the one that is left at the end. However, for computational reasons, the algorithm is often implemented in such a way that several features are reduced at the same time. In such a case, the method produces a feature subset ranking, as opposed to a feature ranking. Therefore, each feature in a subset may not be very relevant individually, and it is the feature subset that is to some extent optimal [61]. The linear RFE-SVMs algorithm is presented in Algorithm $4.1$ and the presentation here follows closely to [61]. Note that in order to simplify the presentation of the Algorithm $4.1$, the standard syntax for manipulating matrices in MATLAB is used.

## 机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Influence of the Penalty Parameter C in RFE-SVMs

As discussed previously, the formulation presented in (2.10) is often referred to as the “hard” margin SVMs, because the solution will not allow any point to be inside, or on the wrong side of the margin and it will not work when classes are overlapped and noisy. This shortcoming led to the introduction of the slack variables $\xi$ and the $C$ parameter to (2.10a) for relaxing the margin by making it ‘soft’ to obtain the formulation in (2.24). In the soft margin SVMs, $C$ parameter is used to enforce the constraints (2.24b). If $C$ is infinitely large, or larger than the biggest $\alpha_{i}$ calculated, the margin is basically ‘hard’. If $C$ is smaller than the biggest original $\alpha_{i}$, the margin is ‘soft’. As seen from $(2.27 \mathrm{~b})$ all the $\alpha_{j}>C$ will be constrained to $\alpha_{j}=C$ and corresponding data points will be inside, or on the wrong side of, the margin. In most of the work related to RFE-SVMs e.g., $[61,119]$, the $C$ parameter is set to a number that is sufficiently larger than the maximal $\alpha_{i}$, i.e. a hard margin SVM is implemented within such an RFE-SVMs model. Consequently, it has been reported that the performance of RFE-SVMs is insensitive to the parameter $C$. However, Fig. $4.3[72]$ shows how $C$ may influence the selection of more relevant features in a toy example where the two classes (stars $*$ and pluses +) can be perfectly separated in a feature 2 direction only. In other words, the feature 1 is irrelevant for a perfect classification here.

As shown in Fig. 4.3, although a hard margin SVMs classifier can make perfect separation, the ranking of the features based on $w_{i}$ can be inaccurate.

The $C$ parameter also affects the performance of the SVMs if the classes overlap each other. In the following section, the gene selection based on an application of the RFE-SVMs having various $C$ parameters in the cases of two medicine data sets is presented.

## 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。