# Mean Normalization

In addition to scaling the features, some may also consider Mean Normalization.

In this, we replace $$x_i$$ by $$x_i-μ_i$$ so as to make the features have approximately 0 mean.

(**Note**: This is not applied for $$x_0$$ which has a fixed value 1).

In general, we can use the following formula to scale the features using mean normalization:

$$x_i = (x_i-μ_i)/S_i$$

where $$x_i$$ is the $$i^{th}$$ feature, $$μ_i$$ is its mean and $$S_i$$ is its range (i.e. max-min).

If this leads to $$x_i$$ being in the range \[-0.5, 0.5] approximately, the gradient descent will work quickly.
