Normalization

Data transformation is one of the critical steps in Data Mining. Among many data transformation methods, normalization is a most frequently used technique. For example, we can use Z-score normalization to reduce possible noise in sound frequency.

We will introduce three common normalization method, Max-Min Normalization, Z-Score Normalization, Scale multiplication.

• Max-Min Normalization x_normal= (x- min(x))/ (max(x)- min(x))
  *it will scale all the data between 0 and 1. *
  Example: Chinese high schools use 150 point scale, USA high schools use 100 point scale and Russian high schools use 5 point scale.

norm1

• Z-Score Normalization X_z-normal= (X- mean)/ sd
  It will transform the data in units relative to the standard deviation. Example: It is useful when comparing data sets with different units (cm and inch).

norm2

• Scale multiplication
  Z_z-normal =X*10 or Z_z-normal =X/10
  It will transform the data in scales of muliple of 10.
  Example: Some money transactions are too large, we will divide 1000 to make it viewer friendly.

norm3

Happy Studying 🐷!

Source Code

import random
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import colors
from matplotlib.ticker import PercentFormatter
from matplotlib import pylab

y=random.sample(range(0,150),50)
x=list(map(int,y))
x1=np.array(x)
xmin=min(x)
xmax=max(x)

#Max-Min normalization
mmnorm=(x1 - xmin)/(xmax-xmin)
#plot
fig,axs=plt.subplots(1,2,sharey=True)

#Original random number
axs[0].hist(x, bins=10)
axs[0].title.set_text("Random Data")


#Max-Min normalizaed histogram Plot
axs[1].hist(mmnorm, bins=10,color="lightblue")
plt.title("Max-Min Normalized Data")
plt.show()

#Z-score Normalization
y2=random.sample(range(0,150),50)
x2=list(map(int,y3))
x21=np.array(x2)
mean=np.mean(x21)
sd=np.std(x21)

#scale normalization
znorm=(x21-mean)/sd

#plot
fig,axs=plt.subplots(1,2,sharey=True)

#Original random number
axs[0].hist(x2, bins=10, color="green")
axs[0].title.set_text("Random Data")

#scale normalizaed histogram Plot
axs[1].hist(znorm, bins=10,color="lightgreen")
plt.title("Z-score Normalized Data")
plt.show()

#scale
y3=random.sample(range(1000,10000),50)
x3=list(map(int,y3))
x31=np.array(x3)

#scale normalization
snorm=x31/1000

#plot
fig,axs=plt.subplots(1,2,sharey=True)

#Original random number
axs[0].hist(x3, bins=10, color="orange")
axs[0].title.set_text("Random Data")


#scale normalizaed histogram Plot
axs[1].hist(snorm, bins=10,color="yellow")
plt.title("Scale Normalized Data")
plt.show()