### 机器学习代写|聚类分析作业代写clustering analysis代考|Non-hierarchical clustering

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• 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|聚类分析作业代写clustering analysis代考|partitioning clustering

In contrast to hierarchical clustering, which yields a successive level of clusters by iterative fusions or divisions, non-hierarchical or partitioning clustering assigns a set of data points into $c$ clusters without any hierarchical structure. This process usually accompanies the optimization of a criterion function, usually the minimization of a objective function representing the within variability of the clusters (Xu and Wunsch, 2009). One of the best-known and most popular non-hierarchical clustering methods is c-means clustering. Another interesting partitioning method is c-medoids clustering. In the following sections, we briefly present these methods and the cluster validity criteria for determining the optimal number of clusters that have to be pre-specified in these methods.

## 机器学习代写|聚类分析作业代写clustering analysis代考|c-Means clustering method

The c-means clustering method (MacQueen, 1967) which is also known as $\mathrm{k}$ means clustering is one of the best-known and most popular clustering methods. It is also commonly known as k-means clustering. The c-means clustering methods seeks an optimal partition of the data by minimizing the sumof-squared-error criterion shown in Eq. (3.1) with an iterative optimization procedure, which belongs to the category of hill-climbing algorithms (Xu and Wunsch, 2009). The basic clustering procedure of c-means clustering is summarized as follows (Everitt et al., 2011; Xu and Wunsch, 2009):

1. Initialize a c-partition randomly or based on some prior knowledge. Calculate the cluster prototypes (centroids or means) (that is, calculate the mean in each cluster considering only the observations belonging to each cluster).
2. Assign each unit in the data set to the nearest cluster by using a suitable distance measure between each pair of units and centroids.
3. Recalculate the cluster prototypes (centroids or means) based on the current partition.
4. Repeat steps 2 and 3 until there is no change for each cluster.

Mathematically, the c-means clustering method is formalized as follows:
$$\begin{array}{r} \min : \sum_{i=1}^{I} \sum_{c=1}^{C} u_{i c} d_{i c}^{2}=\sum_{i=1}^{I} \sum_{c=1}^{C} u_{i c}\left|\mathbf{x}{i}-\mathbf{h}{c}\right|^{2} \ \sum_{c=1}^{C} u_{i c}=1, u_{i c} \geq 0, u_{i c}={0,1} \end{array}$$
where $u_{i c}$ indicates the membership degree of the $i$-th unit to the $c$-th cluster; $u_{i c}={0,1}$, that is, $u_{i c}=1$ when the $i$-th unit belongs to the $c$-th cluster; $u_{i c}=0$ otherwise; $d_{i c}^{2}=\left|\mathbf{x}{i}-\mathbf{h}{c}\right|^{2}$ indicates the squared Euclidean distance between the $i$-th object and the centroid of the $c$-th cluster.

## 机器学习代写|聚类分析作业代写clustering analysis代考|c-Medoids clustering method

By considering the c-medoids clustering method or partitioning around medoids (PAM) method (Kaufman and Rousseeuw, 1987, 1990), units are classified into clusters represented by one of the data points in the cluster (this method is also often referred to as k-medoids). These data points are the prototypes, the so-called medoids. Each medoid synthesizes the cluster information and represents the prototypal features of the clusters and then synthesizes the characteristics of the units belonging to each cluster. Following the c-medoids clustering method, we minimize the objective function represented by the sum (or mathematically equivalent, average) of the dissimilarity of units to their closest representative units. The c-medoids clustering method first computes a set of representative units, the medoids. After finding the set of medoids, each unit of the data set is assigned to the nearest medoid units. The algorithm suggested by Kaufman and Rousseeuw (1990) for the c-medoids clustering method proceeds in two phases:

Phase $1(B U I L D)$ : This phase sequentially selects $c$ “centrally located” units to be used as initial medoids.

Phase $2(S W A P)$ : If the objective function can be reduced by interchanging (swapping) a selected unit with an unselected unit, then the swap is carried out. This is continued until the objective function can no longer be decreased. Then, by considering a set of $I$ units by X (set of the observations) and a subset of $\mathbf{X}$ with $C$ units by $\tilde{\mathbf{X}}$ (set of the medoids) (where $C<<I$ ), we could formalize the model as follows:
$$\begin{array}{r} \min : \sum_{i=1}^{I} \sum_{c=1}^{C} u_{i c} d_{i c}^{2}=\sum_{i=1}^{I} \sum_{c=1}^{C} u_{i c}\left|\mathbf{x}{i}-\tilde{\mathbf{x}}{c}\right|^{2} \ \sum_{c=1}^{C} u_{i c}=1, u_{i c} \geq 0, u_{i c}={0,1} \end{array}$$ where $u_{i c}$ indicates the membership degree of the $i$-th unit to the $c$-th cluster; $u_{i c}={0,1}$, that is, $u_{i c}=1$ when the $i$-th unit belongs to the $c$-th cluster; $u_{i c}=0$ otherwise; $d_{i c}^{2}=\left|\mathbf{x}{i}-\tilde{\mathbf{x}}{c}\right|^{2}$ indicates the squared Euclidean distance between the $i$-th object and the medoid of the $c$-th cluster.

## 机器学习代写|聚类分析作业代写clustering analysis代考|c-Means clustering method

c-means 聚类方法 (MacQueen, 1967)，也称为ķ意味着聚类是最著名和最流行的聚类方法之一。它也通常称为 k-means 聚类。c-means 聚类方法通过最小化公式中所示的平方和误差标准来寻求数据的最佳划分。（3.1）具有迭代优化过程，属于爬山算法的范畴（Xu and Wunsch，2009）。c-means 聚类的基本聚类过程总结如下（Everitt et al., 2011; Xu and Wunsch, 2009）：

1. 随机或基于一些先验知识初始化一个 c 分区。计算集群原型（质心或均值）（即，仅考虑属于每个集群的观测值来计算每个集群中的平均值）。
2. 通过在每对单位和质心之间使用合适的距离度量，将数据集中的每个单位分配给最近的集群。
3. 根据当前分区重新计算集群原型（质心或均值）。
4. 重复步骤 2 和 3，直到每个集群都没有变化。

## 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。