Easy Explanation of Normalization with example

by keshav


Data normalization or standardization is defined as the process of rescaling original data without changing its behavior or nature. We define new boundary (most common is (0,1),(-1,1)) and convert data accordingly. Data normalization technique is useful in classification algorithms involving neural network or a distance based algorithm (e.g. KNN, K-means). 

Some data normalization (standardization) techniques are:
a)     Min-Max Normalization/standardization: It performs linear transformation on original data. Let (X1,X2) be min and max boundary of an attribute and (Y1,Y2) be the new scale at which we are normalizing, then for Vi  value of attribute, the normalized value Ui is given as,
min-max normalization

     Min-max normalization preserves the relationship among the original data values. If in future the input values comes to be beyond the limit of normalization, then it will encounter an error known as “out-of-bound error.”

     Let’s see an example: Suppose the minimum and maximum values for price of house be $125,000 and $925,000 respectively. We need to normalize that price range in between 0,1, . We can use min- max normalization to transform any value between them (say, 300,000). In this case we use above formula with,
X1= 125,000
X2= 925,000
Y1= 0
Y2= 1

In python:     

Here is an example to scale a toy data matrix to the [0, 1] range:
from sklearn import preprocessing
import numpy as np

X_train = np.array([[ 1., -1.,  2.],
  [ 2.,  0.,  0.],
  [ 0.,  1., -1.]])
min_max_scaler = preprocessing.MinMaxScaler()
X_train_minmax = min_max_scaler.fit_transform(X_train)
[[0.5        0.         1.        ]
 [1.         0.5        0.33333333]
 [0.         1.         0.        ]]

b)     Z-score Normalization/standardization( Zero mean normalization /standardization) : In this technique, the values are normalized based on the mean and standard deviation of attribute A. For V value of attribute A, normalized value Ui is given as,

Z-score normalization

  where Avg(A) and Std(A) represents the average and standard deviation of values attribute A respectively.

Let’s see an example: Suppose that the mean and standard deviation of values for attribute income $54,000 and $16,000 respectively. With z-score normalization, a value of $73,000 for income is transformed to (73,000-54,000)/16,000=1.225.

In Python:
from sklearn.preprocessing import StandardScaler

print("Before standardisation X values are ", X)
sc_X = StandardScaler()X = sc_X.fit_transform(X)
print("After standardisation X values are ", X)
Before standardization X values are  
[[101, 105, 222, 333, 225, 334, 556],
 [105, 105, 258, 354, 221, 334, 556]]
After standardization X values are
[-1.  0. -1. -1.  1.  0.  0.]
 [ 1.  0.  1.  1. -1.  0.  0.]]
c)     Decimal Normalization/standardization: In this method, we normalize the given value by moving the decimal points of the value. The number of decimal points to move is defined by the maximum absolute value of given data set.If  V value of attribute A, then normalized value Ui is given as, 
decimal normalization
Where, j is the smallest integer such that max|Ui|<1.

     Lets understand it by an example: Suppose we have data set in which the value ranges from -9900 to 9877.  In this case the maximum absolute value is 9900. So to perform decimal normalization, we divide each of values in data set by 10000 i.e j=4.(since it near to 9900).

Why is data normalization important?

Let’s understand it by an example. Suppose we are making a predictive model using dataset that contains the net worth of citizens of a country. For this data set we find that there is large variation in data. If we feed this data to train any model, then it may generate some undesirable results. So, to get rid of that we opt normalization.

I have written this article taking reference of book ‘DATA MINING Concepts and techniques’ by Jiawei Han, Micheline Kamber, and Jian Pei. You can download this book free here

More on Data preprocessing- click here

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