### 机器学习代写|流形学习代写manifold data learning代考|EECS559

statistics-lab™ 为您的留学生涯保驾护航 在代写流形学习manifold data 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。我们的专家在代写流形学习manifold data learning代写方面经验极为丰富，各种代写流形学习manifold data 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|流形学习代写manifold data learning代考|Manifold Hypothesis

Each feature of a data point does not carry an equal amount of information. For example, some pixels of an image are background regions with limited information, while other pixels contain important objects that describe the scene in the image. This means that data points can be significantly compressed to preserve the most informative features while eliminating those with limited information. In other words, the $d$-dimensional data points of a dataset usually do not cover the entire $d$ dimensional Euclidean space, but they lie on a specific lower-dimensional structure in the space.

Consider the illustration in Fig. 1.1, where several three-dimensional points exist in $\mathbb{R}^3$. These points can represent any measurement, such as personal health measurements, including blood pressure, blood sugar, and blood fat. As demonstrated in Fig. 1.1, the points of the dataset have a structure in a two-dimensional space. The three-dimensional Euclidean space is called the input space, and the twodimensional space, which has a lower dimensionality than the input space, is called the subspace, the submanifold, or the embedding space. The subspace can be either linear or nonlinear, depending on whether a linear (hyper)plane passes through the points. Usually, subspace and submanifold are used for linear and nonlinear lowerdimensional spaces, respectively. Linear and nonlinear subspaces are depicted in Fig. 1.1a and b, respectively.

Whether the points of a dataset lie on a space is a hypothesis, but this hypothesis is usually true because the data points typically represent a natural signal, such as an image. When the data acquisition process is natural, the data will have a define structure. For example, in the dataset where there are multiple images from different angles depicting the same scene, the objects of the scene remain the same, but the point of view changes (see Fig. 1.2). This hypothesis is called the manifold hypothesis [14]. Its formal definition is as follows. According to the manifold hypothesis, data points of a dataset lie on a submanifold or subspace with lower dimensionality. In other words, the dataset in $\mathbb{R}^d$ lies on an embedded submanifold [38] with local dimensionality less than $d$ [14]. According to this hypothesis, the data points most often lie on a submanifold with high probability [64].

## 机器学习代写|流形学习代写manifold data learning代考|Feature Engineering

Due to the manifold hypothesis, a dataset can be compressed while preserving most of the important information. Therefore, engineering and processing can be applied to the features for the sake of compression [4]. Feature engineering can be seen as a preprocessing stage, where the dimensionality of the data is reduced. Assume $d$ and $p$ denote the dimensionality of the input space and the subspace, respectively, where $p \in(0, d]$. Feature engineering is a map from a $d$-dimensional Euclidean space to a $p$-dimensional Euclidean space, i.e., $\mathbb{R}^d \rightarrow \mathbb{R}^p$. The dimensionality of the subspace is usually much smaller than the dimensionality of the space, i.e. $p \ll d$, because most of the information usually exists in only a few features.

Feature engineering is divided into two broad approaches-feature selection and feature extraction [22]. In feature selection, the $p$ most informative features of the $d$-dimensional data vector are selected so the features of the transformed data points are a subset of the original features. In feature extraction, however, the $d$-dimensional data vector is transformed to a $p$-dimensional data vector, where the $p$ new features are completely different from the original features. In other words, data points are represented in another lower-dimensional space. Both feature selection and feature extraction are used for compression, which results in either the better discrimination of classes or better representation of data. In other words, the compressed data by feature engineering may have a better representation of the data or may separate the classes of data. This book concentrates on feature extraction.

## 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。