Input Normalization

Input normalization changes raw input values into a more convenient scale.

For a feature x, a common transformation is:

z = (x - mean) / standard_deviation

This recenters the feature and rescales its spread. The goal is not to erase information. The goal is to stop arbitrary units from dominating optimization.

raw values-1282882normalized values-1.1-0.50.11.5recenter and rescale to make optimization easier
Normalization changes scale while preserving the useful pattern in the values.

Imagine two features:

age: 20 to 80
income: 10,000 to 200,000

Without normalization, the income feature has much larger numerical scale. A model may need awkward weights just to balance units. Normalization makes the optimization problem less distorted.

Exercise: Normalize one value

Let x = 14, mean = 10, and standard_deviation = 2. What is the normalized value?

Compute it first, then check your number.

Exercise: Centered value

If x equals the feature mean, what is (x - mean) / standard_deviation?

Compute it first, then check your number.