## 计算机代写|机器学习代写machine learning代考|COMP4702

2023年2月6日

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## 计算机代写|机器学习代写machine learning代考|Large item sets

To introduce how association rules are generated from a given database, we first introduce some basic concepts. Denote a set of $N$ items by $I=\left{i_1, \ldots, i_N\right}$. An item set is a subset of $I$, and an item set containing $n^{\prime}$ items (where $n^{\prime} \in[1, \ldots, N]$ ) is also called an $n^{\prime}$ item set and is denoted by $I_{n^{\prime}}$. A database consisting of $M$ records, where each record is an item set, is denoted by $D=\left{t_1, \ldots, t_M\right}$. Define the event of observing the occurrence of a particular item set $I_{n^{\prime}}$ by $E\left(I_{n^{\prime}}\right)$, which means that all the items in $I_{n^{\prime}}$ are observed in one record. We further define $P\left(E\left(I_{n^{\prime}}\right)\right)$ as the proportion of the $M$ records that have all the items in $I_{n^{\prime}}$, which can also be interpreted as the probability of the occurrence of event $E\left(I_{n^{\prime}}\right)$. It should also be noted that a record that includes all the items in item set $I_{n^{\prime}}$ can also include items not in $I_{n^{\prime}}$ but in $I$. The probability of $E\left(I_{n^{\prime}}\right)$ is also called the Support of item set $I_{n^{\prime}}$, that is, $P\left(E\left(I_{n^{\prime}}\right)\right)=\operatorname{Sup}\left(I_{n^{\prime}}\right)$, and $P\left(E\left(I_{n^{\prime}}\right)\right) \in[0,1]$. A larger value of $P\left(E\left(I_{n^{\prime}}\right)\right)$ indicates that the more frequently item set $I_{n^{\prime}}$ occurs in $D$. In order to define a large item set denoted by $I_{n^{\prime}}^$ which frequently occurs in the database, we define the minimum threshold of Support for an item set to be a large item set by min_Sup. That is, if and only if $I_{n^{\prime}}^ \subseteq I$ and $I_{n^{\prime}}^* \neq \emptyset$ is a large item set, we have Sup $\left(I_{n^{\prime}}^*\right) \geq$ min_Sup.

A rule is generated by dividing a large $n^{\prime}$ item set, i.e., $I_{n^{\prime}}^$ and $n^{\prime} \geq 2$, into two mutually exclusive and non-empty item sets $I_j$ and $I_k$, with $I_j \cup I_k=I_{n^{\prime}}^$. A rule can be generated from $I_j$ to $I_k$ in form $I_j \rightarrow I_k$. To determine whether rule $I_j \rightarrow I_k$ is an association rule denoted by $I_j \Rightarrow I_k$, two indicators are further introduced: Confidence and Lift of $I_j \rightarrow I_k$ is calculated by
$$\operatorname{Conf}\left(I_j \rightarrow I_k\right)=\frac{P\left(E\left(I_j\right) \cap E\left(I_k\right)\right)}{P\left(E\left(I_j\right)\right)}=P\left(E\left(I_k\right) \mid E\left(I_j\right)\right),$$
and $\operatorname{Conf}\left(I_j \rightarrow I_k\right) \in[0,1]$. The larger value Confidence is, the more likely that the items in $I_k$ appear given that the items in item set $I_j$ appear. Lift of $I_j \rightarrow I_k$ is calculated by
$$L i f t\left(I_j \rightarrow I_k\right)=\frac{P\left(E\left(I_j\right) \cap E\left(I_k\right)\right)}{P\left(E\left(I_j\right)\right) \times P\left(E\left(I_k\right)\right)}=\frac{P\left(E\left(I_k\right) \mid E\left(I_j\right)\right)}{P\left(E\left(I_k\right)\right)},$$
and $\operatorname{Lift}\left(I_j \rightarrow I_k\right) \in[0,+\infty)$ presents the influence of the occurrence of event $E\left(I_j\right)$ on event $E\left(I_k\right)$, which is the ratio of the probability of the occurrence of event $E\left(I_k\right)$ under the condition that event $E\left(I_j\right)$ occurs and the probability that event $E\left(I_k\right)$ occurs unconditionally in the database. This can be interpreted as how the occurrence of event $E\left(I_j\right)$ can increase/decrease (i.e., lift) the occurrence of $E\left(I_k\right)$. To be more specific, if lift $\left.I_j \rightarrow I_k\right) \in[0,1)$, the occurrence of $E\left(I_j\right)$ decreases the probability of the occurrence of $E\left(I_k\right)$. If $L i f t\left(I_j \rightarrow I_k\right) \in(1,+\infty)$, the occurrence of $E\left(I_j\right)$ increases the probability of the occurrence of $E\left(I_k\right)$. If $\operatorname{Lift}\left(I_j \rightarrow I_k\right)=1$, the occurrence of $E\left(I_j\right)$ has no influence on the occurrence of $E\left(I_k\right)$, that is, $E\left(I_j\right)$ and $E\left(I_k\right)$ are independent. It is also interesting to find that as event $E\left(I_k\right)$ acts as the denominator to calculate Lift of rule $I_j \rightarrow I_k$, if $P\left(E\left(I_k\right)\right)$ is large, meaning that the occurrence probability of event $E\left(I_k\right)$ is high, the value of $L i f t\left(I_j \rightarrow I_k\right)$ would be reduced. This shows that a frequently occurring event would have less contribution to generating association rules compared to rare events.

## 计算机代写|机器学习代写machine learning代考|Distance measure in clustering

The key point in cluster analysis is how to measure the “similarity” between two examples in the data set, and this is usually achieved by the calculation of “distance”

of these two examples. Distance measure is an objective score used to measure the relative difference/dissimilarity between two examples in the problem of concern. The distance between two examples $\mathbf{x}_i$ and $\mathbf{x}_j$ is denoted by $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right)$, which satisfies the following properties:

1. non-negativity: $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right) \geq 0$;
2. identity: If and only if $\mathbf{x}_i=\mathbf{x}_j$, $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right)=0$;
3. symmetry: $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right)=\operatorname{dist}\left(\mathbf{x}_j, \mathbf{x}_i\right)$; and
4. triangle inequality: $\operatorname{dist}\left(\mathbf{x}i, \mathbf{x}_j\right) \leq \operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_k\right)+\operatorname{dist}\left(\mathbf{x}_k, \mathbf{x}_j\right)$. Features of an example can be numerical and categorical. Numerical features are ordinal, where the relative feature values are comparable. For example, ship age is a numerical feature, where a ship of age 5 is younger than a ship of age 10 by 5 years. Categorical features can be either ordinal, where the relative feature values are comparable like numerical features (e.g., low, medium, and high for ship company performance, where a ship company with high performance is better than a ship company with medium performance, and is much better than a ship company with low performance), or nominal, where the feature values only indicate the categories and cannot be compared (e.g., container ship, bulk carrier, and passenger ship belonging to the feature of ship type, and they cannot be compared directly with each other). As feature values are comparable in ordinal features and noncomparable in nominal features, different means of distance measure should be used in these two types of features. For data set $D$ with $m$ features, denote the number of its ordinal features by $m_1$ and the number of its nominal features by $m_2$, where $m=m_1+m_2$. For ordinal features, Minkowski distance taking the following form is the most popular one: $$\operatorname{dist}{m k k}\left(\mathbf{x}i, \mathbf{x}_j\right)=\left(\sum{m^{\prime}=1}^{m_1}\left|x_{i m^{\prime}}-x_{j m^{\prime}}\right|^p\right)^{\frac{1}{p}},$$
where the subscript is $m k$ short for Minkowski, and $p$ should be no less than 1, such that the properties of distance measure can be satisfied. Common values of $p$ are 1 and 2. When $p=1$, Equation (11.1) is also called Manhattan distance, and can be written as
$$\operatorname{dist}{\operatorname{man}}\left(\mathbf{x}_i, \mathbf{x}_j\right)=\left|\mathbf{x}_i-\mathbf{x}_j\right|_1=\sum{m^{\prime}=1}^{m_1}\left|x_{i m^{\prime}}-x_{j m^{\prime}}\right| .$$

# 机器学习代考

## 计算机代写|机器学习代写machine learning代考|Large item sets

$\mathrm{l}=$ lleft{i_1，Vldots, i_Nlright $}$.一个项目集是一个子集 $I$, 以 及包含的项集 $n^{\prime}$ 项目 (其中 $n^{\prime} \in[1, \ldots, N]$ ) 也被称为 $n^{\prime}$ 项集并表示为 $I_{n^{\prime}}$.一个数据库包括 $M$ 记录，其中每条 记录是一个项目集，表示为 $D=\backslash$ lleft{t_1，\dots, t_M Mright . 定义观察特定项集出现的事件 $I_{n^{\prime}}$ 经过 $E\left(I_{n^{\prime}}\right)$ ，这意味 看所有项目在 $I_{n^{\prime}}$ 在一个记录中观察到。我们进一步定义 $P\left(E\left(I_{n^{\prime}}\right)\right)$ 作为比例 $M$ 包含所有项目的记录 $I_{n^{\prime}}$ ，也可 以解释为事件发生的概率 $E\left(I_{n^{\prime}}\right)$. 还应该注意的是，包 含项目集中所有项目的记录 $I_{n^{\prime}}$ 也可以包括不在 $I_{n^{\prime}}$ 但在 $I$ . 的概率 $E\left(I_{n^{\prime}}\right)$ 也称为项集的支持度 $I_{n^{\prime}}$ ，那是， $P\left(E\left(I_{n^{\prime}}\right)\right)=\operatorname{Sup}\left(I_{n^{\prime}}\right) ， \quad$ 和 $P\left(E\left(I_{n^{\prime}}\right)\right) \in[0,1]$. 较大的值 $P\left(E\left(I_{n^{\prime}}\right)\right)$ 表示更频繁的项集 $I_{n^{\prime}}$ 发生在 $D$. 为了定义一个大项目集，表示为我{n^{1prime}}^ 对于数 据库中频繁出现的项集，我们定义一个项集为大项集的 最小支持度阈值min_Sup。也就是说，当且仅当 $I{n^{\prime}}^{\subseteq} I$ 和 $I_{n^{\prime}}^* \neq \emptyset$ 是一个大项目集，我们有 $\operatorname{Sup}\left(I_{n^{\prime}}^*\right) \geq$ min_Sup。

$$\operatorname{Conf}\left(I_j \rightarrow I_k\right)=\frac{P\left(E\left(I_j\right) \cap E\left(I_k\right)\right)}{P\left(E\left(I_j\right)\right)}=P(E$$

$$\operatorname{Lift}\left(I_j \rightarrow I_k\right)=\frac{P\left(E\left(I_j\right) \cap E\left(I_k\right)\right)}{P\left(E\left(I_j\right)\right) \times P\left(E\left(I_k\right)\right)}=$$

## 计算机代写|机器学习代写machine learning代考|Distance measure in clustering

1. 非负性: $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right) \geq 0$;
2. 恒等式: 当且仅当 $\mathbf{x}_i=\mathbf{x}_j, \operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right)=0$;
3. 对称: $\operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_j\right)=\operatorname{dist}\left(\mathbf{x}_j, \mathbf{x}_i\right)$; 和
4. 三角不等式:
$\operatorname{dist}\left(\mathbf{x} i, \mathbf{x}j\right) \leq \operatorname{dist}\left(\mathbf{x}_i, \mathbf{x}_k\right)+\operatorname{dist}\left(\mathbf{x}_k, \mathbf{x}_j\right)$. 示例的特征可以是数字的和分类的。数值特征是 有序的，其中相对特征值是可比较的。例如，船 龄是一个数字特征，船龄为 5 的船比船龄为 10 的 船年轻 5 年。分类特征可以是有序的，其中相对 特征值与数值特征具有可比性 (例如，船舶公司 绩效的低、中和高，其中绩效较高的船舶公司优 于绩效中等的船舶公司，并且是比低绩效的船公 司好很多)，或者nominal，特征值只表示类 别，不能比较 (如集装箱船、散货船、客船属于 船型特征，不能比较) 直接比较)。由于特征值 在有序特征上具有可比性，而在名义特征上具有 不可比性，因此对这两类特征应采用不同的距离度量方式。对于数据集 $D$ 和 $m$ 特征，表示其序数 特征的数量 $m_1$ 及其标称特征的数量 $m_2$ ，在哪里 $m=m_1+m_2$. 对于序数特征，采用以下形式 的 Minkowski 距离是最流行的一种: $$\operatorname{dist} m k k\left(\mathbf{x} i, \mathbf{x}_j\right)=\left(\sum m^{\prime}=1^{m_1}\left|x{i m^{\prime}}-x_{j m^{\prime}}\right|^{\mid}\right.$$
下标在哪里 $m k$ 闵可夫斯基的缩写，和 $p$ 应该不小 于1，这样才能满足距离度量的性质。的共同价值 观 $p$ 是 1 和 2。当 $p=1$ ，式(11.1)也称为曼哈顿 距离，可写为
$$\operatorname{dist} \operatorname{man}\left(\mathbf{x}_i, \mathbf{x}_j\right)=\left|\mathbf{x}_i-\mathbf{x}_j\right|_1=\sum m^{\prime}=1^{m_1}$$

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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。