Normalization or standardization

This technique aims to give the dataset the properties of a normal distribution, that is, a mean of 0 and a standard deviation of 1.

The way to obtain these properties is by calculating the so-called z scores, based on the dataset samples, with the following formula:

Let's visualize and practice this new concept with the help of scikit-learn, reading a file from the MPG dataset, which contains city-cycle fuel consumption in miles per gallon, based on the following features: mpg, cylinders, displacement,  horsepower, weight, acceleration, model year, origin, and car name.

from sklearn import preprocessing
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

df=pd.read_csv("data/mpg.csv")
plt.figure(figsize=(10,8))
print df.columns
partialcolumns = df[['acceleration', 'mpg']]
std_scale = preprocessing.StandardScaler().fit(partialcolumns)
df_std = std_scale.transform(partialcolumns)
plt.scatter(partialcolumns['acceleration'], partialcolumns['mpg'], color="grey", marker='^')
plt.scatter(df_std[:,0], df_std[:,1])