"order"参数在tf.keras.utils.normalize()中意味着什么? [英] What does the `order` argument mean in `tf.keras.utils.normalize()`?

问题描述

考虑以下代码:

import numpy as np

A = np.array([[.8, .6], [.1, 0]])
B1 = tf.keras.utils.normalize(A, axis=0, order=1)
B2 = tf.keras.utils.normalize(A, axis=0, order=2)

print('A:')
print(A)
print('B1:')
print(B1)
print('B2:')
print(B2)

返回

A:
[[0.8 0.6]
 [0.1 0. ]]
B1:
[[0.88888889 1.        ]
 [0.11111111 0.        ]]
B2:
[[0.99227788 1.        ]
 [0.12403473 0.        ]]

我了解如何通过 order = 1 计算 B1 ，以便将 A 中的每个条目除以其中元素的总和柱子.例如， 0.8 变为 0.8/(0.8 + 0.1)= 0.888 .但是，我只是无法弄清楚 order = 2 是如何产生 B2 的，也找不到关于它的任何文档.

I understand how B1 is computed via order=1 such that each entry in A is divided by the sum of the elements in its column. For example, 0.8 becomes 0.8/(0.8+0.1) = 0.888. However, I just can't figure out how order=2 produces B2 nor can I find any documentation about it.

推荐答案

但是，我只是无法弄清order = 2如何产生B2，也找不到关于它的任何文档.

However, I just can't figure out how order=2 produces B2 nor can I find any documentation about it.

order = 1 表示L1规范，而 order = 2 表示L2规范.对于L2范数，您需要在对各个平方求和后取平方根.哪些元素要平方取决于轴.

order=1 means L1 norm while order=2 means L2 norm. For L2 norm, You need to take the square root after summing the individual squares. Which elements to square depends on the axis.

凯拉斯

A = np.array([[.8, .6], [.1, 0]])
B2 = tf.keras.utils.normalize(A, axis=0, order=2)
print(B2)

array([[0.99227788, 1.        ],
       [0.12403473, 0.        ]])

手册

B2_manual = np.zeros((2,2))
B2_manual[0][0] = 0.8/np.sqrt(0.8 ** 2 + 0.1 ** 2)
B2_manual[1][0] = 0.1/np.sqrt(0.8 ** 2 + 0.1 ** 2)
B2_manual[0][1] = 0.6/np.sqrt(0.6 ** 2 + 0 ** 2)
B2_manual[1][1] =  0 /np.sqrt(0.6 ** 2 + 0 ** 2)
print(B2_manual)

array([[0.99227788, 1.        ],
       [0.12403473, 0.        ]])

您可以在此处查找不同类型的Norm: https://en.wikipedia.org/wiki/Norm_(mathematics)工作示例: https://docs.scipy.org/doc/numpy/reference/generation/numpy.linalg.norm.html

You can look up the different types of Norm here: https://en.wikipedia.org/wiki/Norm_(mathematics) Worked examples: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.norm.html

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