如何在Python的NumPy中对数组进行标准化

在这篇文章中，我们将讨论如何在Python中使用NumPy对一维和二维数组进行归一化。归一化是指将一个数组的值缩放到所需的范围。

一维阵列的规范化

假设我们有一个数组=[1,2,3]，在[0,1]范围内进行归一化，意味着将数组[1,2,3]转换为[0, 0.5, 1]，因为1，2和3是等距的。

Array [1,2,4] -> [0, 0.3, 1]

这也可以在一个范围内进行，即用[0,1]来代替[3,7]。

现在,

Array [1,2,3] -> [3,5,7]

和

Array [1,2,4] -> [3,4.3,7]

让我们看看有代码的例子

示例 1:

# import module
import numpy as np
  
# explicit function to normalize array
def 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 staring 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 array
print("Original Array = ",array_1d)
print("Normalized Array = ",normalized_array_1d)

输出:

如何在Python的NumPy中对数组进行标准化？

示例 2:

现在，Lets的输入数组是[1,2,4,8,10,15]，范围也是[0,1] 。

# import module
import numpy as np
  
# explicit function to normalize array
def 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 range
array_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 array
print("Original Array = ", array_1d)
print("Normalized Array = ", normalized_array_1d)

输出:

如何在Python的NumPy中对数组进行标准化？

二维阵列的归一化

为了使二维数组或矩阵正常化，我们需要NumPy库。对于矩阵来说，一般的归一化是使用欧氏规范或弗罗比纽斯规范。

简单归一化的公式是

如何在Python的NumPy中对数组进行标准化？

这里，v是矩阵，|v|是行列式，也叫欧几里得准则。v-cap是归一化矩阵。

以下是实施上述内容的一些例子。

示例 1:

# import module
import numpy as np
  
# explicit function to normalize array
def normalize_2d(matrix):
    norm = np.linalg.norm(matrix)
    matrix = matrix/norm  # normalized matrix
    return matrix
  
# gives and array staring from -2
# and ending at 13
array = np.arange(16) - 2
  
# converts 1d array to a matrix
matrix = array.reshape(4, 4)
print("Simple Matrix \n", matrix)
normalized_matrix = normalize_2d(matrix)
print("\nSimple Matrix \n", normalized_matrix)

输出:

如何在Python的NumPy中对数组进行标准化？

示例 2:

我们也可以使用其他规范，如1-norm或2-norm

# import module
import numpy as np
  
def 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 staring from -2 and ending at 13
array = np.arange(16) - 2  
# converts 1d array to a matrix
matrix = array.reshape(4, 4)  
print("Simple Matrix \n", matrix)
normalized_matrix = normalize_2d(matrix)
print("\nSimple Matrix \n", normalized_matrix)