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

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
• (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|Feature Reduction with Support Vector Machines

Recently, more and more instances have occurred in which the learning problems are characterized by the presence of a small number of the highdimensional training data points, i.e. $n$ is small and $m$ is large. This often occurs in the bioinformatics area where obtaining training data is an expensive and time-consuming process. As mentioned previously, recent advances in the DNA microarray technology allow biologists to measure several thousands of genes’ expressions in a single experiment. However, there are three basic reasons why it is not possible to collect many DNA microarrays and why we have to work with sparse data sets. First, for a given type of cancer it is not simple to have thousands of patients in a given time frame. Second, for many cancer studies, each tissue sample used in an experiment needs to be obtained by surgically removing cancerous tissues and this is an expensive and time consuming procedure. Finally, obtaining the DNA microarrays is still expensive technology. As a result, it is not possible to have a relatively large quantity of training examples available. Generally, most of the microarray studies have a few dozen of samples, but the dimensionality of the feature spaces (i.e. space of input vector $\mathbf{x}$ ) can be as high as several thousand. In such cases, it is difficult to produce a classifier that can generalize well on the unseen data, because the amount of training data available is insufficient to cover the high dimensional feature space. It is like trying to identify objects in a big dark room with only a few lights turned on. The fact that $n$ is much smaller than $m$ makes this problem one of the most challenging tasks in the areas of machine learning, statistics and bioinformatics.

The problem of having high-dimensional feature space led to the idea of selecting the most relevant set of genes or features first, and only then the classifier is constructed from these selected and “important”‘ features by the learning algorithms. More precisely, the classifier is constructed over a reduced space (and, in the comparative example above, this corresponds to an object identification in a smaller room with the same number of lights). As a result such a classifier is more likely to generalize well on the unseen data. In the book, a feature reduction technique based on SVMs (dubbed Recursive Feature Elimination with Support Vector Machines (RFE-SVMs)) developed in [61], is implemented and improved. In particular, the focus is on gene selection for cancer diagnosis using RFE-SVMs. RFE-SVM is included in the book because it is the most natural way to harvest the discriminative power of SVMs for microarray analysis. At the same time, it is also a natural extension of the work on solving SVMs efficiently. The original contributions presented in the book in this particular area are as follows:

机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Graph-Based Semi-supervised Learning Algorithms

As mentioned previously, semi-supervised learning (SSL) is the latest development in the field of machine learning. It is driven by the fact that in many real-world problems the cost of labeling data can be quite high and there is an abundance of unlabeled data. The original goal of this book was to develop large-scale solvers for SVMs and apply SVMs to real-world problems only. However, it was found that some of the techniques developed in SVMs can be extended naturally to the graph-based semi-supervised learning, because the optimization problems associated with both learning techniques are identical (more details shortly).

In the book, two very popular graph-based semi-supervised learning algorithms, namely, the Gaussian random fields model (GRFM) introduced in $[160]$ and $[159]$, and the consistency method (CM) for semi-supervised learning proposed in [155] were improved. The original contributions to the field of SSL presented in this book are as follows:

1. An introduction of the novel normalization step into both CM and GRFM. This additional step improves the performance of both algorithms significantly in the cases where labeled data are unbalanced. The labeled data are regarded as unbalanced when each class has a different number of labeled data in the training set. This contribution is presented in Sect. $5.3$ and 5.4.
2. The world first large-scale graph-based semi-supervised learning software SemiL is developed as part of this book. The software is based on a Conjugate Gradient (CG) method which can take box-constraints into account and it is used as a backbone for all the simulation results in Chap. $5 .$ Furthermore, SemiL has become a very popular tool in this area at the time of writing this book, with approximately 100 downloads per month. The details of this contribution are given in Sect. $5.6$.

机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Unsupervised Learning Based on Principle

SVMs as the latest supervised learning technique from the statistical learning theory as well as any other supervised learning method require labeled data in

order to train the learning machine. As already mentioned, in many real world problems the cost of labeling data can be quite high. This presented motivation for most recent development of the semi-supervised learning where only small amount of data is assumed to be labeled. However, there exist classification problems where accurate labeling of the data is sometime even impossible. One such application is classification of remotely sensed multispectral and hyperspectral images $[46,47]$. Recall that typical family RGB color image (photo) contains three spectral bands. In other words we can say that family photo is a three-spectral image. A typical hyperspectral image would contain more than one hundred spectral bands. As remote sensing and its applications receive lots of interests recently, many algorithms in remotely sensed image analysis have been proposed [152]. While they have achieved a certain level of success, most of them are supervised methods, i.e., the information of the objects to be detected and classified is assumed to be known a priori. If such information is unknown, the task will be much more challenging. Since the area covered by a single pixel is very large, the reflectance of a pixel can be considered as the mixture of all the materials resident in the area covered by the pixel. Therefore, we have to deal with mixed pixels instead of pure pixels as in conventional digital image processing. Linear spectral unmixing analysis is a popular approach used to uncover material distribution in an image scene $[127,2,125,3]$. Formally, the problem is stated as:
$$\mathbf{r}=\mathbf{M} \alpha+\mathbf{n}$$
where $\mathbf{r}$ is a reflectance column pixel vector with dimension $L$ in a hyperspectral image with $L$ spectral bands. An element $r_{i}$ in the $\mathbf{r}$ is the reflectance collected in the $i^{\text {th }}$ wavelength band. $\mathbf{M}$ denotes a matrix containing $p$ independent material spectral signatures (referred to as endmembers in linear mixture model), i.e., $\mathbf{M}=\left[\mathbf{m}{1}, \mathbf{m}{2}, \ldots, \mathbf{m}{p}\right], \boldsymbol{\alpha}$ represents the unknown abundance column vector of size $p \times 1$ associated with $\mathbf{M}$, which is to be estimated and $\mathbf{n}$ is the noise term. The $i^{t h}$ item $\alpha{i}$ in $\boldsymbol{\alpha}$ represents the abundance fraction of $\mathbf{m}_{i}$ in pixel $\mathbf{r}$. When $\mathbf{M}$ is known, the estimation of $\boldsymbol{\alpha}$ can be accomplished by least squares approach. In practice, it may be difficult to have prior information about the image scene and endmember signatures. Moreover, in-field spectral signatures may be different from those in spectral libraries due to atmospheric and environmental effects. So an unsupervised classification approach is preferred. However, when $\mathbf{M}$ is also unknown, i.e., in unsupervised analysis, the task is much more challenging since both $\mathbf{M}$ and $\boldsymbol{\alpha}$ need to be estimated [47]. Under stated conditions the problem represented by linear mixture model (1.3) can be interpreted as a linear instantaneous blind source separation (BSS) problem [76] mathematically described as:
$$\mathbf{x}=\mathbf{A s}+\mathbf{n}$$
where x represents data vector, $\mathbf{A}$ is unknown mixing matrix, $\mathbf{s}$ is vector of source signals or classes to be found by an unsupervised method and $\mathbf{n}$ is again additive noise term.

机器学习代写|监督学习代考Supervised and Unsupervised learning代写|Graph-Based Semi-supervised Learning Algorithms

1. 将新的标准化步骤引入 CM 和 GRFM。在标记数据不平衡的情况下，这一额外步骤显着提高了两种算法的性能。当每个类别在训练集中具有不同数量的标记数据时，标记数据被认为是不平衡的。这一贡献在第 3 节中介绍。5.3和 5.4。
2. 世界上第一个大规模的基于图的半监督学习软件 SemiL 是本书的一部分。该软件基于共轭梯度 (CG) 方法，该方法可以考虑框约束，并用作第 1 章中所有模拟结果的主干。5.此外，在编写本书时，SemiL 已成为该领域非常流行的工具，每月下载量约为 100 次。该贡献的详细信息在第 3 节中给出。5.6.

r=米一种+n

X=一种s+n

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。