In this article, we are going to discuss how to normalize 1D and 2D arrays in Python using NumPy. Normalization refers to scaling values of an array to the desired range.
Normalization of 1D-Array
Suppose, we have an array = [1,2,3] and to normalize it in range [0,1] means that it will convert array [1,2,3] to [0, 0.5, 1] as 1, 2 and 3 are equidistant.
Array [1,2,4] -> [0, 0.3, 1]
This can also be done in a Range i.e. instead of [0,1], we will use [3,7].
Now,
Array [1,2,3] -> [3,5,7]
and
Array [1,2,4] -> [3,4.3,7]
Let’s see examples with code
Example 1:
Python3
# import moduleimport numpy as np# explicit function to normalize arraydef normalize(arr, t_min, t_max): norm_arr = [] diff = t_max - t_min diff_arr = max(arr) - min(arr) for i in arr: temp = (((i - min(arr))*diff)/diff_arr) + t_min norm_arr.append(temp) return norm_arr# gives range starting from 1 and ending at 3 array_1d = np.arange(1,4)range_to_normalize = (0,1)normalized_array_1d = normalize(array_1d, range_to_normalize[0], range_to_normalize[1])# display original and normalized arrayprint("Original Array = ",array_1d)print("Normalized Array = ",normalized_array_1d) |
Output:
Example 2:
Now, Lets input array is [1,2,4,8,10,15] and range is again [0,1]
Python3
# import moduleimport numpy as np# explicit function to normalize arraydef normalize(arr, t_min, t_max): norm_arr = [] diff = t_max - t_min diff_arr = max(arr) - min(arr) for i in arr: temp = (((i - min(arr))*diff)/diff_arr) + t_min norm_arr.append(temp) return norm_arr# assign array and rangearray_1d = [1, 2, 4, 8, 10, 15]range_to_normalize = (0, 1)normalized_array_1d = normalize( array_1d, range_to_normalize[0], range_to_normalize[1])# display original and normalized arrayprint("Original Array = ", array_1d)print("Normalized Array = ", normalized_array_1d) |
Output:
Normalization of 2D-Array
To normalize a 2D-Array or matrix we need NumPy library. For matrix, general normalization is using The Euclidean norm or Frobenius norm.
The formula for Simple normalization is
Here, v is the matrix and |v| is the determinant or also called The Euclidean norm. v-cap is the normalized matrix.
Below are some examples to implement the above:
Example 1:
Python3
# import moduleimport numpy as np# explicit function to normalize arraydef normalize_2d(matrix): norm = np.linalg.norm(matrix) matrix = matrix/norm # normalized matrix return matrix# gives and array starting from -2# and ending at 13array = np.arange(16) - 2# converts 1d array to a matrixmatrix = array.reshape(4, 4)print("Simple Matrix \n", matrix)normalized_matrix = normalize_2d(matrix)print("\nSimple Matrix \n", normalized_matrix) |
Output:
Example 2:
We can also use other norms like 1-norm or 2-norm
Python3
# import moduleimport numpy as npdef normalize_2d(matrix): # Only this is changed to use 2-norm put 2 instead of 1 norm = np.linalg.norm(matrix, 1) # normalized matrix matrix = matrix/norm return matrix# gives and array starting from -2 and ending at 13array = np.arange(16) - 2 # converts 1d array to a matrixmatrix = array.reshape(4, 4) print("Simple Matrix \n", matrix)normalized_matrix = normalize_2d(matrix)print("\nSimple Matrix \n", normalized_matrix) |
Output:
In this way, we can perform normalization with NumPy in python.
