### 机器学习代写|自然语言处理代写NLP代考|Scaling Numeric Data via Standardization

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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|自然语言处理代写NLP代考|Scaling Numeric Data via Standardization

The standardization technique involves finding the mean mu and the standard deviation sigma, and then mapping each $x i$ value to (xi-mu)/sigma. Recall the following formulas:
$\mathrm{mu}=[\operatorname{SUM}(\mathrm{x})] / \mathrm{n}$
$\operatorname{variance}(\mathrm{x})=[$ SUM $(\mathrm{x}-\mathrm{xbar}) *(\mathrm{x}-\mathrm{xbar})] / \mathrm{n}$
sigma $=\operatorname{sqrt}($ variance $)$
As a simple illustration of standardization, suppose that the random variable $x$ has the values ${-1,0,1}$. Then $m u$ and sigma are calculated as follows:
mu $\quad=($ SUM $x i) / n=(-1+0+1) / 3=0$
variance $=\left[\mathrm{SUM}(\mathrm{xi}-\mathrm{mu})^{\wedge} 2\right] / \mathrm{n}$
$=\left[(-1-0)^{\wedge} 2+(0-0)^{\wedge} 2+(1-0)^{\wedge} 2\right] / 3$
$=2 / 3$
sigma $=\operatorname{sqrt}(2 / 3)=0.816$ (approximate value)
Hence, the standardization of ${-1,0,1}$ is ${-1 / 0.816,0 / 0.816$,
$1 / 0.816}$, which in turn equals the set of values ${-1.2254,0,1.2254}$.
As another example, suppose that the random variable $x$ has the values
${-6,0,6}$. Then mu and sigma are calculated as follows:
$m u=(\mathrm{SUM} \mathrm{xi}) / \mathrm{n}=(-6+0+6) / 3=0$
variance $=\left[S U M(x i-m u)^{\wedge} 2\right] / \mathrm{n}$
$=\left[(-6-0)^{\wedge} 2+(0-0)^{\wedge} 2+(6-0)^{\wedge} 2\right] / 3$
$=72 / 3$
$=24$
sigma $=\operatorname{sqrt}(24)=4.899$ (approximate value)

Hence, the standardization of ${-6,0,6}$ is ${-6 / 4.899,0 / 4.899$, $6 / 4.899}$, which in turn equals the set of values ${-1.2247,0,1.2247}$.
In the preceding two examples, the mean equals 0 in both cases, but the variance and standard deviation are significantly different. The normalization of a set of values always produces a set of numbers between 0 and 1 .

However, the standardization of a set of values can generate numbers that are less than $-1$ and greater than 1 ; this will occur when sigma is less than the minimum value of every term $|\mathrm{mu}-\mathrm{xi}|$, where the latter is the absolute value of the difference between mu and each xi value. In the preceding example, the minimum difference equals 1 , whereas sigma is $0.816$, and therefore the largest standardized value is greater than $1 .$

## 机器学习代写|自然语言处理代写NLP代考|What to Look for in Categorical Data

This section contains various suggestions for handling inconsistent data values, and you can determine which ones to adopt based on any additional factors that are relevant to your particular task. For example, consider dropping columns that have very low cardinality (equal to or close to 1), as well as numeric columns with zero or very low variance.

Next, check the contents of categorical columns for inconsistent spellings or errors. A good example pertains to the gender category, which can consist of a combination of the following values:
male
Male
female
Female
$\mathrm{m}$
f
$M$
$\mathrm{F}$
The preceding categorical values for gender can be replaced with two categorical values (unless you have a valid reason to retain some of the other values). Moreover, if you are training a model whose analysis involves a single gender, then you need to determine which rows (if any) of a dataset must be excluded. Also check categorical data columns for redundant or missing white spaces.

Check for data values that have multiple data types, such as a numerical column with numbers as numerals and some numbers as strings or objects.

## 机器学习代写|自然语言处理代写NLP代考|Mapping Categorical Data to Numeric Values

Character data is often called categorical data, examples of which include people’s names, home or work addresses, and email addresses. Many types of categorical data involve short lists of values. For example, the days of the week and the months in a year involve seven and twelve distinct values, respectively. Notice that the days of the week have a relationship: For example, each day has a previous day and a next day. However, the colors of an automobile are independent of each other: the color red is not “better” or “worse” than the color blue.

There are several well-known techniques for mapping categorical values to a set of numeric values. A simple example where you need to perform this conversion involves the gender feature in the Titanic dataset. This feature is one of the relevant features for training a machine learning model. The gender feature has ${\mathbf{M}, \mathrm{F}}$ as its set of possible values. As you will see later in this chapter, Pandas makes it very easy to convert the set of values ${M, F}$ to the set of values ${0,1}$.

Another mapping technique involves mapping a set of categorical values to a set of consecutive integer values. For example, the set {Red, Green, Blue} can be mapped to the set of integers $[0,1,2}$. The set ${$ Male, Female $}$ can be mapped to the set of integers ${0,1}$. The days of the week can be mapped to ${0,1,2,3,4,5,6}$. Note that the first day of the week depends on the country: In some cases it’s Sunday, and in other cases it’s Monday.

Another technique is called one-hot encoding, which converts each value to a vector (check Wikipedia if you need a refresher regarding vectors). Thus, {Male, Female} can be represented by the vectors $[1,0]$ and $[0,1]$, and the colors {Red, Green, Blue} can be represented by the vectors $[1,0,0]$, $[0,1,0]$, and $[0,0,1]$. If you vertically “line up” the two vectors for gender, they form a $2 \times 2$ identity matrix, and doing the same for the colors will form a $3 \times 3$ identity matrix.

If you vertically “line up” the two vectors for gender, they form a $2 \times 2$ identity matrix, and doing the same for the colors will form a $3 \times 3$ identity matrix, as shown here:
$$[1,0,0]$$
$[0,1,0]$
$[0,0,1]$

## 机器学习代写|自然语言处理代写NLP代考|Scaling Numeric Data via Standardization

mu=(和X一世)/n=(−1+0+1)/3=0

=[(−1−0)∧2+(0−0)∧2+(1−0)∧2]/3
=2/3

−6,0,6. 然后 mu 和 sigma 计算如下：

=[(−6−0)∧2+(0−0)∧2+(6−0)∧2]/3
=72/3
=24

F

F

[1,0,0]
[0,1,0]
[0,0,1]

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## MATLAB代写

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