Standardization

Finally, let's start with the analysis of the PCA mathematical model.

First of all, we start by standardizing the data that the algorithm will work with. By standardization is meant the reduction of all continuous variables to a set where the mean will be equal to 0.

This is an important step because PCA cannot work properly if there is a variable in the dataset with a range of values ​​0-20 and 100-10,000, for example. PCA will start to "ignore" the characteristic with a small spread (0-20) and it will not be able to affect the result of the algorithm.

The formula for data standardization is very simple. Subtract the mean from the value of the variable and divide the result by the standard deviation:

The scikit-learn Python library allows us to do this in 1 line:

# Importing libraries
import numpy as np
from sklearn.preprocessing import StandardScaler

# Standardizing
X = np.asarray([[1, 3],[2, 10],[3, 35],[4, 40]], dtype = np.float64)
X_scaled = StandardScaler().fit_transform(X)