What is Standardization in Machine Learning

Last Updated : 11 Jan, 2023

In Machine Learning we train our data to predict or classify things in such a manner that isn't hardcoded in the machine. So for the first, we have the Dataset or the input data to be pre-processed and manipulated for our desired outcomes. Any ML Model to be built follows the following procedure:

Collect Data
Perform Data Munging/Cleaning (Feature Scaling)
Pre-Process Data
Apply Visualizations

Feature Scaling is a method to standardize the features present in the data in a fixed range. It has to perform during the data pre-processing. It has two main ways: Standardization and Normalization.

Standardization

The steps to be followed are :

Data collection

Our data can be in various formats i.e., numbers (integers) & words (strings), for now, we'll consider only the numbers in our Dataset.

Assume our dataset has random numeric values in the range of 1 to 95,000 (in random order). Just for our understanding consider a small Dataset of barely 10 values with numbers in the given range and randomized order.

1) 99 2) 789 3) 1 4) 541 5) 5 6) 6589 7) 94142 8) 7 9) 50826 10) 35464

If we just look at these values, their range is so high, that while training the model with 10,000 such values will take lot of time. That's where the problem arises.

Understanding standardization

We have a solution to solve the problem arisen i.e. Standardization. It helps us solve this by :

Down Scaling the Values to a scale common to all, usually in the range -1 to +1.
And keeping the Range between the values intact.

So, how do we do that? we'll there's a mathematical formula for the same i.e., Z-Score = (Current_value - Mean) / Standard Deviation.

Using this formula we are replacing all the input values by the Z-Score for each and every value. Hence we get values ranging from -1 to +1, keeping the range intact.

Standardization performs the following:

Converts the Mean (μ) to 0
Converts to S.D. (σ) to 1

It's pretty obvious for Mean = 0 and S.D = 1 as all the values will have such less difference and each value will nearly be equal 0, hence Mean = 0 and S.D. = 1.

NOTE : (Just for Better Understanding)

For Mean

When we Subtract a value Smaller than the Mean we get (-ve) Output
When we Subtract a value Larger than the Mean we get (+ve) Output

Hence, when we get (-ve) & (+ve) Values for Subtraction of Value with Mean, while Summation of all these values,
We get the Final Mean as 0.

And when we get the Mean as 0, it means that most or nearly all values are equal to highly close to 0 and have very low variance among them.

Therefore, the S.D also becomes 1 (as good as no difference).

Implementation of Code

Here we are doing the Following:

Calculating the Z-Score
Comparing the Original Values and Standardized Values
Comparing the Range of both using Scatter Plots

Python3

# Importing Libraries import matplotlib import matplotlib.pyplot as plt  # We are just using 10 values # for our Dataset  # Here, dataset_0 will be constant # as it's range is just 1 - 10 # But, dataset_1 will be scaled down # as it's range is 1 - 95,000  global dataset_0, dataset_1 dataset_0 = [10, 5, 6, 1, 3, 7, 9, 4, 8, 2] dataset_1 = [1, 99, 789, 5, 6859, 541,              94142, 7, 50826, 35464]  n = len(dataset_1) mean_ans = 0 ans = 0 j = 0

Now to calculate the summation, run below code :

Python3

# Calculating summation for i in dataset_1:     j = j + i     k = i*i     ans = ans + k  print('n : ', n) print("Summation (X)   : ", j) print("Summation (X^2) : ", ans)

Output :

n :  10 Summation (X)   :  188733 Summation (X^2) :  12751664695

Then Calculate the Standard Deviation

Python3

# Calculating Standard Deviation part_1 = ans/n part_2 = mean_ans*mean_ans standard_deviation = part_1 - part_2 print("Standard Deviation : ", standard_deviation)

Output :

1275166469.5

Then calculate the Mean by using this code

Python3

# Calculating Mean mean = j/n mean

Output :

18873.3

To Calculate the Z-Score for each Value of dataset_1

Python3

# Calculating the Z-Score for each  # Value of dataset_1 final_z_score = [] print("Calculating Z-Score of Each Value in dataset_1")  for i in dataset_1:     z_score = (i-mean)/standard_deviation     final_z_score.append("{:.20f}".format(z_score))

Comparison between the Values of Original Dataset and Scaled Down Dataset

Python3

# Comparing the Values of Original Dataset and Saled Down Dataset print("\nOriginal DataSet   |               Z-Score ") print() for i in range(len(dataset_1)):     print("    ", dataset_1[i], "          |     ", final_z_score[i])

Output :

Original DataSet   |               Z-Score        1           |      -0.00001479987158649171      99          |      -0.00001472301887561513      789         |      -0.00001418191305413712      5           |      -0.00001479673474114981      6859        |      -0.00000942175024780167      541         |      -0.00001437639746533501      94142       |      0.00005902656774649453      7           |      -0.00001479516631847886      50826       |      0.00002505766953904366      35464       |      0.00001301061500347112

Now we will compare and see the graph of the Original Values and the Standardized Values.

Python3

# Here We are checking the Graph # of the Original Values plt.scatter(dataset_0, dataset_1, label="stars",             color="blue", marker="*", s=40) plt.xlabel('x - axis') plt.ylabel('y - axis') plt.legend() plt.show()    # Here we are checking the Graph of # the Standardized Values plt.scatter(dataset_0, final_z_score, label="stars",             color="blue", marker="*", s=30) plt.xlabel('x - axis') plt.ylabel('y - axis') plt.legend() plt.show()

Output :

Python3

final_z_score = []  for i in dataset_1:     z_score = (i-mean)/standard_deviation     final_z_score.append("{:.20f}".format(z_score))

Comparison between the Values of Original Dataset and Scaled Down Dataset.

Python3

print("  Original DataSet   |               Z-Score ") print() for i in range(len(dataset_1)):     print("         ", dataset_1[i], "         |     ", final_z_score[i])

Output :

  Original DataSet   |               Z-Score             1          |      -0.00001479987158649171           99         |      -0.00001472301887561513           789        |      -0.00001418191305413712           5          |      -0.00001479673474114981           6859       |      -0.00000942175024780167           541        |      -0.00001437639746533501           94142      |      0.00005902656774649453           7          |      -0.00001479516631847886           50826      |      0.00002505766953904366           35464      |      0.00001301061500347112

Comparing the Range of Values using Graphs

1) Graph of the Original Values

Python3

# Now we will compare and see the graph  # of the Original Values and the  # Standardized Values import matplotlib import matplotlib.pyplot as plt  # Here We are checking the Graph of the  # Original Values plt.scatter(dataset_0, dataset_1, label="stars",             color="blue", marker="*", s=40)  plt.xlabel('x - axis') plt.ylabel('y - axis')  plt.title('Original Values') plt.legend()  plt.show()

Output :

2) Graph of the Standardized Values

Python3

import matplotlib  import matplotlib.pyplot as plt  plt.scatter(dataset_0, final_z_score, label= "stars",              color= "blue", marker= "*", s=30)    plt.xlabel('x - axis') plt.ylabel('y - axis')  plt.title('Original Values') plt.legend()    plt.show()

Output :

Hence we have Reviewed, Understood the Concept, and Implemented as well the Concept of Standardization in Machine Learning

What is Standardization in Machine Learning

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What is Standardization in Machine Learning

Standardization

Data collection

Understanding standardization

Implementation of Code

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