Normalization is an important part of preparing data for machine learning. It helps make sure that different features, or parts of the data, have the same impact when measuring distances. The choice of normalization method depends on what kind of data you have and what your model needs. Here are some main normalization techniques and when to use them.

1. Min-Max Scaling

• How It Works: For a feature called $x$, Min-Max normalization uses this formula: $$x' = \frac{x - \text{min}(x)}{\text{max}(x) - \text{min}(x)}$$
• When to Use It: This method is great for data that already falls within a certain range. It’s often used with methods like Neural Networks and K-Means clustering. It changes data to be between 0 and 1.
• Things to Note: It can be affected by outliers, which means any extreme values can distort the results.

2. Z-Score Standardization

• How It Works: For each feature, you calculate the Z-score using this formula: $$z = \frac{x - \mu}{\sigma}$$ Here, $\mu$ is the average and $\sigma$ is the standard deviation.
• When to Use It: This is helpful when your data has a bell-shaped (Gaussian) distribution. It centers the data around 0 and adjusts based on how spread out it is. You’ll find it used in logistic regression and SVM.
• Things to Note: If there are outliers, they can skew the mean and standard deviation, making this method less effective.

3. Robust Scaling

• How It Works: This method uses the median and the interquartile range (IQR) with the formula: $$x' = \frac{x - \text{median}(x)}{IQR(x)}$$
• When to Use It: It’s perfect for datasets with outliers or that don’t follow a normal distribution. It focuses on using statistics that can handle outliers well.
• Things to Note: It keeps the data balanced and avoids being affected by outliers, while still centering the values.

4. Logarithmic Transformation

• How It Works: This technique uses the logarithm of the values: $$x' = \log(x + 1)$$
• When to Use It: It's helpful for data that increases quickly or has a wide range of values, like financial data or data that is skewed to the right.
• Things to Note: You need to make sure your data is non-negative to use this method.

5. MaxAbs Scaling

• How It Works: This technique scales the data by dividing by the largest absolute value: $$x' = \frac{x}{\text{max}(|x|)}$$
• When to Use It: It works well when the data is already centered around zero and keeps the matrix from being too crowded, which is good for sparse data like text data in TF-IDF format.
• Things to Note: It allows you to interpret the original data's distribution while scaling it.

Conclusion

Choosing the right normalization method depends on the special traits of your dataset, like how it is distributed and if it has any outliers. If you pick the wrong method, your model may not perform well, which can hurt important measures like accuracy. That's why it’s crucial to understand your data and choose the right normalization technique to train your machine learning model effectively.