### 统计代写|机器学习作业代写machine learning代考| Nearest-Neighbor Classifiers

statistics-lab™ 为您的留学生涯保驾护航 在代写机器学习machine 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。我们的专家在代写机器学习machine learning方面经验极为丰富，各种代写机器学习machine 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

## 统计代写|机器学习作业代写machine learning代考|The k-Nearest-Neighbor Rule

How do we establish that a certain object is more similar to $\mathbf{x}$ than to $\mathbf{y}$ ? Some may doubt that this is at all possible. Is giraffe more similar to horse than to zebra? Questions of this kind raise suspicion. Too many arbitrary and subjective factors have to be considered when looking for an answer.

Similarity of Attribute Vectors The machine-learning task formulated in the previous chapters keeps the situation relatively simple. Rather than real objects, the classifier compares their attribute-based descriptions. Thus in the toy domain from Chap. 1, the similarity of two pies can be established by counting the attributes in

which they differ: the fewer the differences, the greater the similarity. The first row in Table $3.1$ gives the attribute values of object $\mathbf{x}$. For each of the twelve training examples that follow, the right-most column specifies the number of differences in the attribute values of the given example and $\mathbf{x}$. The smallest value being found in the case of ex $\mathrm{x}_{5}$, we conclude that this is the training example most similar to $\mathbf{x}$, and $\mathbf{x}$ should thus be labeled with pos, the class of ex 5 .

In Table 3.1, all attributes are discrete, but dealing with continuous attributes is just as easy. Since each example can be represented by a point in an $n$ dimensional space, we can use the Euclidean distance or some other geometric formula (Section $3.2$ will have more to say on this topic); and again, the smaller the distance, the greater the similarity. This, by the way, is how the nearest-neighbor classifier got its name: the training example with the smallest distance from $\mathbf{x}$ in the instance space is, geometrically speaking, $\mathbf{x}$ ‘s nearest neighbor.

## 统计代写|机器学习作业代写machine learning代考|Measuring Similarity

As mentioned earlier, a natural way to identify the nearest neighbor of some $\mathbf{x}$ is to use the geometrical distances of $\mathbf{x}$ from the training examples. Figure $3.1$ shows a two-dimensional domain where the distances can easily be measured by a rulerbut the ruler surely cannot be used if there are more than three attributes. In that event, we need a mathematical formula.

Euclidean Distance In a two-dimensional space, a plane, the geometric distance between two points, $\mathbf{x}=\left(x_{1}, x_{2}\right)$ and $\mathbf{y}=\left(y_{1}, y_{2}\right)$, is measured by the Pythagorean theorem as illustrated in Fig. 3.2: $d(\mathbf{A}, \mathbf{B})=\sqrt{\left(a_{1}-b_{1}\right)^{2}+\left(a_{2}-b_{2}\right)^{2}}$. The following formula generalizes this to $n$-dimensional domains: the Euclidean distance between $\mathbf{x}=\left(x_{1}, \ldots, x_{n}\right)$ and $\mathbf{y}=\left(y_{1}, \ldots, y_{n}\right)$ :
$$d_{E}(\mathbf{x}, \mathbf{y})=\sqrt{\sum_{i=1}^{n}\left(x_{i}-y_{i}\right)^{2}}$$
The use of this metric in $k$-NN classifiers is illustrated in Table $3.3$ where the training set consists of four examples described by three numeric attributes.

More General Formulation The reader has noticed that the term under the square root symbol is the sum of the squared distances along the individual attributes. ${ }^{1}$ Mathematically, this is expressed as follows:
$$d_{M}(\mathbf{x}, \mathbf{y})=\sqrt{\sum_{i=1}^{n} d\left(x_{i}, y_{i}\right)}$$

## 统计代写|机器学习作业代写machine learning代考|Irrelevant Attributes and Scaling Problems

The reader now understands the principles of the $k$-NN classifier well enough to be able to write a computer program that implements it. Caution is called for, though. When applied mechanically, the tool may disappoint, and we have to understand why this may happen.

The philosophy underlying this paradigm is telling us that “objects are similar if the geometric distance between the vectors describing them is small.” This said we know that the geometric distance is sometimes misleading. The following two cases are typical.

Irrelevant Attributes It is not true that all attributes are created equal. From the perspective of machine learning, some are irrelevant in the sense that their values have nothing to do with the example’s class-and yet they affect the geometric distance between vectors.

A simple illustration will clarify the point. In the training set from Fig. 3.3, the examples are characterized by two numeric attributes: body-temperature (horizontal axis) and shoe-size (vertical axis). Suppose the $k$-NN classifier is to classify object 1 as healthy (pos) or sick (neg).

All positive examples find themselves in the shaded area delimited by two critical points along the “horizontal” attribute: temperatures exceeding the maximum indicate fever, and those below the minimum indicate hypothermia. As for the “vertical” attribute, though, we see that the positive and negative examples alike are distributed along its entire domain, show-size not being able to affect a person’s health. The object we want to classify is in the highlighted region, and by common sense it should be labeled as positive-despite the fact that its nearest neighbor happens to be negative.

## 统计代写|机器学习作业代写machine learning代考|Measuring Similarity

d和(X,是)=∑一世=1n(X一世−是一世)2

d米(X,是)=∑一世=1nd(X一世,是一世)

## 广义线性模型代考

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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。