Articles
Posts Tags Categories Random
Partners
About
About Author Portfolio Terms of Use Privacy Policy Time Travel Donate
More
Settings Funny Tools Useful Websites Student Works Message Board Recent Comments

Contents

Methods of Normalization

 Included in Machine Learning
 Published   Updated    519 words   3 minutes   views
https://raw.githubusercontent.com/Josh-test-lab/website-assets-repository/refs/heads/main/posts/Methods%20of%20Normalization/cover%20image.png

The cover image was generated by ChatGPT.

Introduction

In statistical analysis, we often encounter various types of data, which may differ in units and value ranges. To eliminate the influence of unit differences and enhance the comparability of data, it is often necessary to apply appropriate scale transformations, known as normalization, to bring all data onto a common scale for analysis. Depending on the application, there are different methods of normalization, each potentially affecting subsequent statistical inferences and model performance.

However, a common question arises: there are many ways to “normalize” data, with “Normalization” and “Standardization” being the most frequently mentioned. But what exactly do these terms mean? What are the differences between them? And which one should you use? The following sections will provide a detailed explanation.

Standardization

Standardization, also known as the standard score or Z-score standardization, involves subtracting the mean from the original data and then dividing by the standard deviation. The formula is as follows:

$$ Z = \frac{X - \mu}{\sigma}, $$

where $Z$ is the standardized value or vector, $X$ is the original value or vector, $\mu$ is the sample or population mean of $X$, and $\sigma$ is the sample or population standard deviation. After standardization, the data will have a mean of 0 and a standard deviation of 1, which means the data will follow a normal (Gaussian) distribution, reducing the impact of outliers on the model during statistical analysis.

$$ Z = \frac{X - \mu}{\sigma} \sim N(0, 1). $$

Normalization

Normalization, also known as min-max scaling or feature scaling, is a method of scaling data to a specified range. The most common technique is Min-Max normalization, which rescales the data to the range $[0, 1]$ using the following formula:

$$ X’ = \frac{X - X_{\min}}{X_{\max} - X_{\min}} \in [0, 1], $$

where $X’$ is the normalized value or vector, $X$ is the original value or vector, $X_{\min}$ is the minimum value of the data, and $X_{\max}$ is the maximum value. This technique does not change the original data distribution, it only rescales the values within the specified range.

Alternatively, data can be scaled to any desired range $[a, b]$ using the formula:

$$ X’ = a + \frac{(X - X_{\min})(b - a)}{X_{\max} - X_{\min}} \in [a, b]. $$

Conclusion

Standardization is suitable for data that follows a normal distribution or when it is necessary to eliminate differences in mean and variance. In contrast, Normalization is more appropriate when data needs to be scaled to a specific range, especially in scenarios where large differences in feature magnitudes may negatively impact the model. Although both terms are often collectively referred to as “standardization” in Chinese, they serve distinct purposes and involve different transformation techniques.

References

Updated on 2025-07-09 16:55 UTC+0800   a997dbfb
Creative Commons License
 Normalization, Standardization, Machine Learning
Back | Home