What is the formula for min-max normalization?

Conditions

• Applied to a continuous numerical feature.
• Requires knowing the minimum and maximum values of the feature.
• The maximum and minimum values must not be equal (to avoid division by zero).

Reasoning, step by step

1. Identify the raw feature value $x$.
2. Find the minimum value $x_{\min}$ and maximum value $x_{\max}$ of the feature in the dataset.
3. Subtract the minimum value from the raw feature: $x - x_{\min}$.
4. Divide the result by the range of the feature: $x_{\max} - x_{\min}$.
5. The final transformed value is $x' = \frac{x - x_{\min}}{x_{\max} - x_{\min}}$.

Example

The video displays the formula on-screen as "min-max normalization : x' = (x - x_min) / (x_max - x_min)" and shows a pink histogram tightly clustered near zero, demonstrating how this method standardizes the data's range.

Common misconceptions

• Assuming min-max normalization changes the shape of the distribution; it is a linear transformation that only shifts and scales the data.
• Forgetting that the denominator is the range ($x_{\max} - x_{\min}$) rather than just the maximum value.

Watch the explanation

Explore next

• What is the formula for standardization?
• Why is feature scaling important in machine learning?
• How does min-max normalization affect a data distribution?